fin. Bldg.

NBS

Thermodynamic Properties of

HE

3

-HE

4

Solutions with

Applications to the HE

3

-HE

Dilution Refrigerator

ii

4

\

Q

*"*fAU O* '

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards
_

______

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UNITED STATES DEPARTMENT OF COMMERCE

Alexander B. Trowbridge, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

NBS TECHNICAL NOTE 362

ISSUED DECEMBER 29, 1967

THERMODYNAMIC PROPERTIES OF HE

3-HE

4 SOLUTIONS WITH APPLICATIONS TO THE

HE

3 - HE

4 DILUTION REFRIGERATOR

RAY RADEBAUGH

Cryogenics Division

Institute for Materials Research

National Bureau of Standards

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 20402

Price: 70 cents.

Table of Contents

Abstract

Page

viii

1. Introduction

Selection of a Theoretical Model

3. Computational Methods . „ „ 3 4

3. 1 Properties of He in Liquid He . . . ...... . 3 4

3. 2 Properties of the Total He - He Solution .....

3 4

3. 3 Applications to the He - He Dilution Refrigerator

4. Results and Discussion ........... ...... . 3 4

4. 1 Properties of He in Liquid He ..........

3 4

4. 2 Properties of the Total He - He Solution .....

3 4

4. 3 Applications to the He - He Dilution Refrigerator

5

5

21

25

37

37

44

47

5. Conclusions 75

6. References 77

7. Appendix A - Specific Heat of a Fermi-Dirac Gas

Appendix B - Physical Constants and Properties of Pure

3 4

He and He

9. Appendix C - The Correction of \i ° in the Concentrated Phase

from Regular Solution Theory.

10. Appendix D - Tables of Thermodynamic Properties of

3 4

He - He Solutions. . 89

List of Figures

3 4 Figure 1. Phase Diagram of He - He Solution ..........

3 4 3

Figure 2. Effective Mass Ratio of He in He as a Function of He

Concentration.

in
Table of Contents (continued) x ' t-, Page

Figure 3„ The Fermi Temperature and Deviation of the Chemical

Potential from the Ideal Fermi-Dirac Value ....... 12

Figure 4„ The Difference in Chemical Potential Between the Con

3

3

centrated Phase and Pure He 15

Figure 5„ The Phase Separation Temperature as a Function of He

Concentration . 18

3 4

Figure 6„ Schematic Diagram of the He - He Dilution

Refrigerator ........................ 26

3 4

Figure 7. The Entropy of He in Liquid He as a Function of

3

Temperature for Various He Concentrations 38

3 4

Figure 8. The Enthalpy of He in Liquid He as a Function of

3 Temperature for Various He Concentrations ...... 40

3 4 Figure 9. The Osmotic Pressure of He in Liquid He as a Function

3

of Temperature for Various He Concentrations 41

4 Figure 10 o Behavior of the Excess He Chemical Potential as Deduced

3 4 from the Osmotic Pressure of He in He 43

3 4 Figure 11. The Excess Enthalpy of He - He Solutions as a Function

3

of He Concentration for Various Temperatures .... .45

3 4 Figure 12. The Vapor Pressure of He - He Solutions Divided by the

3 3

Vapor Pressure of Pure He as a Function of He Concentration for Various Temperatures 46

Figure 13, The Deviation from the Ideal Differential Heat of Vapori3 4

zation of He - He Solutions . „ 48

Figure 14a. Plots of H (X , T), H (T), and Q(T, T)/n = H,(X.,T) - H °(T)

for Low Temperatures 49

Figure 14b. Plots ofH

3

(X ,T), H

3

( T )> and Q(T, T)/n for High

Temperatures . , 50

IV
Table of Contents (continued)

Page

Figure 15. The Ratio of Mixer Temperature to Inlet Temperature

2

for Zero Power Input and the Ratio Q/T as a Function

3

of He Concentration in the Circulated Gas • • • • • • 53

3 4 Figure 16. Enthalpy Inversion Curves for He - He Solutions ... 55

Figure 17. Concentration Profiles for Constant p. ........ . 57

3 Figure 18. The Specific Heat of He at Constant \l as a Function

of Temperature for Various Mixer Temperatures • • • 58

Figure 19. The Vapor Pressure of the Liquid in the Still as a Function of Still Temperature for Various Mixer

Temperatures 59

Figure 20. The Heat of Vaporization and the Vapor Composition

(Neglecting Film Flow) for the Liquid in the Still .... 60

Figure 21a. The Fraction of the Mixer Filled with Dilute Solution as a Function of Mixer Temperature for the Case

V /V = 0. 5 62

s mc

Figure 21b. The Fraction of the Mixer Filled with Dilute Solution

as a Function of Mixer Temperature for the Case

V /V =1 63

s mc

Figure 21c. The Fraction of the Mixer Filled with Dilute Solution

as a Function of Mixer Temperature for the Case

V /V = 2 . 64

s mc

Figure 22a. Comparison of Theory and Experiment for the Transient

Behavior of the Single -Cycle Dilution Refrigerator „ . 68

3

Figure 22b. The Fractional Amount of Pure He Remaining in the

Mixer as a Function of Mixer Temperature ...... 70

Figure 23. A Plot of the Term -(0. 01/T)(dS /<*X) and the Heat

3 Absorption Rate for the He Extraction Refrigerator . 72
Table of Contents (continued)

Page

Table 1.

Table 4.

Table 5.

Table 7

Table 8.

Table 9.

Table 10.

Table 11.

Table 12.

Table 13.

Table 14.

Table 15.

List of Tables

Some Temperature Independent Properties of He

in Super fluid He ...... ....... ........ . 9

Table 2. The Phase Separation Temperature or Solubility

3 4

Curve for Dilute Solutions of He - He . . . . . Table 3. Some Physical Constants and Basic Properties of

3

3 4

Pure He and He Used in this Work

Thermodynamic Properties oi Pure Liquid He

Below 1. 5°K

Thermodynamic Properties of Pure Liquid He

Below 1. 5°K .............

Table 6. The Solubility Curve for Concentrated Solutions of

3 4

He - He ........................

3 4

The Entropy of He in He and Its Rate of Change with

Respect to Concentration at Constant Temperature . . 3 4 3

The Chemical Potential of He in He When the He

Behaves as an Ideal Fermi Dirac Gas

3 4 The Enthalpy of He in He ................

3 4 The Osmotic Pressure ol He in He and the expression

19

84

85

86

88

90

97

101

-[H4

(X. T)-u °(T=0)] . 105

3 4 The Specific Heat of the Total He - He Solution .... 112

3 4 The Entropy of the Total He - He Solution. ....... 116

3

The Enthalpy and Excess Enthalpy of the Total He - 4

He Solution ........................ 120

3 4

The Vapor Pressure of He - He Solutions 127

3 3 4

The He Concentration in the Vapor Above He - He

S olutions 131

VI
Table o± Contents (continued)

Page

3

Table 16. The Enthalpy and Entropy of He Along the Solubility

Curve and the Heat Absorption Rate of the Dilution

Refrigerator 135

3

Table 17. The He Concentration, Specific Heat, and Entropy at

Constant |i 136

VII
ABSTRACT

3 4 The thermodynamic properties of liquid He - He solutions between and 1. 5°K are calculated by using the weakly interacting Fermi3 4 Dirac gas model for He in He . Certain experimental data below about

0.4°Kare used to evaluate some of the parameters in the model. The

3 4

properties of both He in He and the total solution are calculated for

3

concentrations of He up to 30 percent. All experimental data agree

very well with the calculated results, although little data exist below

0.4°Ko The calculated properties are used to analyze the behavior of

3 4

the He - He dilution refrigerator in both the continuous and single -

cycle processes. The maximum heat absorption below about 0. 04°K is

2 3

found to be 82 T joules per mole of He circulated. The effect of an

4 imperfect heat exchanger and He circulation on the refrigeration

capacity is discussed. An analysis of two new types of single-cycle

processes is also given.

Key Words: Cryogenics, dilution refrigerator, enthalpy, entropy,

Fermi-Dirac gas, helium-3, helium-4, liquid, mixtures,

osmotic pressure, quantum fluid, specific heat, thermodynamic properties.

vm
3 4 THERMODYNAMIC PROPERTIES OF HE - HE SOLUTIONS

WITH APPLICATIONS TO THE HE 3 - HE4

DILUTION REFRIGERATOR

Ray Radebaugh

1. Introduction

Early in 1966 Hall et al. [ l] and Neganovet al. [ 2] independently

succeeded in achieving continuous refrigeration below 0. 1°K using a

3 4

He - He dilution refrigerator. Such a refrigerator was first proposed

by London, Clarke, and Mendoza [ 3] . Previously such temperatures

could be reached only by adiabatic demagnetization of a paramagnetic

salt, although the process is not a continuous one. Since the dilution

refrigerator has certain advantages over adiabatic demagnetization,

researchers are rapidly turning their attention to this new technique.

Several new dilution refrigerators have been built since early 1966 with

many others in the construction or planning stage. Improvements are

constantly being made to these refrigerators and as a result the lowest

temperatures reached with them have steadily been reduced. Vilches

and Wheatley have just recently reached 0. 012°K in continuous operation

[4] and 0. 0045°K in transient operation [ 5], It should be possible to

reach even lower temperatures with this technique, but further design re3

finements are hampered by a lack of data on the properties of the He - 4

He solutions used in the refrigerator.

The purpose of this paper is to present a complete and consistent

3 4

set of data for the thermodynamic properties of liquid He - He solutions

for the temperature range - 1. 5°K. Such information is needed to

analyze the performance of dilution refrigerators and to help optimize
their design. These data, of course, are also necessary to predict the

3 4

behavior of any other process which involves He - He solutions at these

temperatures. Nothing will be said of the transport properties of the

solutions, which are also urgently needed for the optimum design of

dilution refrigerators.

Most of the properties to be discussed in this paper have been

measured experimentally, but unfortunately very few of the measurements have been done below 0. 5°K. An excellent list of the experimentally determined properties has already been given [ 6] . To this list

should be added the recent specific heat measurements of Edwards et al.

[ 7] down to about 0. 1°K and of Anderson et al. [ 8] down to about 0. 004°K.

The solubility curve has now been measured extensively down to about

0. 02°K [9] . The specific heat measurements, however, are not extensive

enough to permit a deduction of various thermodynamic properties as

functions of temperature and concentration down to 0°K without recourse

to some theoretical model. In this paper it will be shown that the thermodynamic properties of a weakly interacting Fermi-Dirac gas are in very

3 4

good agreement with all existing experimental data on He - He solutions

for temperatures below 1. 5°K, provided that values of certain parameters

of the model are determined from experiments. Application of these

thermodynamic properties will then be made to describe the behavior of

3 4

He - He dilution refrigerators. The Fermi-Dirac gas model has been

applied previously [ 4, 5, 10] to the analysis of the dilution refrigerator but

not to the extent of this paper. In addition the previous analyses did not

3 take into account interactions between the He atoms in solution,which is

important for many of the properties.

Z. Selection of a Theoretical Model

3 4 Experiments have shown that He is not miscible in He for all

3 4

concentrations and temperatures. The phase diagram of He - He
solutions, shown in figure 1, indicates that for temperatures less than

about 0. 86 °K certain intermediate concentrations are not permitted.

3

Instead the solution separates into a concentrated He phase floating on

3

top of the heavier dilute solution. At 0°K it is possible to dissolve He

4

in He up to a concentration of (6. 4 ± 0. 1) percent [ 9] . Thus at very low

temperatures the only concern is with dilute solutions and essentially

3

pure He . Only dilute solutions will be considered here since a satisfactory theoretical model has not been found for concentrated solutions,

i. e. , for concentrations greater than about 20 to 30 percent. The prop3

erties of pure He can of course be deduced directly from experimental

results, some of which extend down to the millidegree region.

Landau and Pomeranchuk[l4] were the first to propose a theoreti3 4

cal model for the behavior of dilute He - He solutions. According to

this theory the excitation spectrum of the liquid is modified by the addition

of noninteracting Fermi quasiparticles equal in number to the number of

3

He atoms. The analysis was limited, however, to the nonde generate

(high temperature) range where the quasiparticles can be treated as an

3

ideal gas and, thus, would contribute an amount 3/2 R per mole of He

to the specific heat of the solution. For temperatures somewhat less

4

than 1°K the specific heat of He becomes extremely small so the specif - 3

ic heat for T < 1°K is due solely to the He contribution. For temperatures of about 0. 5°K and for concentrations less than 15 percent the

prediction of a 3/2 R contribution to the specific heat has been borne out

by measurements of Edwards et al. [ 7] . Results of de Bruyn Ouboter

et al. [ 11] above 0.4°K, however, appear to be in good agreement only

3 4

in the limit of zero concentration. This ideal gas model of He - He

solutions has been used in the past to analyze the behavior of the dilution

refrigerator [ 1, 2, 6, 1 5] .
o

0) -H 5 s TM en n d

>* Oh s * O ,<:

*+-! <u

Hi £ M

id -g S c

fl o • r-t -r-l *" ft U

nj in

XS !-> a v .H ^ „, • I Si I § «

rS ^ ^ Wort 1 M

00

TM ^ O J3 TM (J fl

njMO,—. U H r\J <H Q- CO

en _i en

n) . <P M

*<> 'i
For temperatures approaching 0°K the 3/2 R term must disappear

according to the third law of the rmodynamics. Measurements [ 7, 8] show

that the specific heat begins to drop at about 0. 2 to 0. 5°K (depending on

concentration) and becomes proportional to T for much lower temperatures,

Since the dilution refrigerator usually operates below 0.1 °K, the ideal

gas model can not be relied upon to give a satisfactory explanation of the

behavior of a dilution refrigerator.

Edwards et al. [ 7] showed that their specific heat data were fit

3

very well at all temperatures by treating the He as a Fermi-Dirac gas

3 with an effective mass m* of 2. 5 times the mass of a He atom.

Anderson et al. [ 8] also found that the same model would fit their data

within experimental error, but with the values 2. 38 and 2. 46 for m*/m

in 1. 32 percent and 5. 02 percent solutions respectively. The data of

Anderson et al. extended well into the degenerate region of the FermiDirac gas where the specific heat is proportional to both m*/m and T.

Thus the Fermi-Dirac gas model shows excellent promise for predicting

3 3 4

the thermodynamic properties of He in liquid He - He solutions at all

temperatures.

The variation of m*/m with concentration can be accounted for by

3

considering weak interactions between the He atoms. Doing so, however,

does not change the specific heat from that of a noninteracting FermiDirac gas with the same m*/m [ 16] . It will be shown that the behavior

of the solubility curve also requires that interactions be introduced.

3 4

Thus, in this note the thermodynamic properties of He - He solutions

are derived from the weakly interacting Fermi-Dirac gas model.

3. Computational Methods

3 4

3. 1 Properties of He in Liquid He

The behavior of the interparticle interaction and its effects must

be evaluated before calculations of thermodynamic properties can be
made. Bardeen, Baym, and Pines [ 17] (BBP) assumed the interaction

3

between two He atoms separated by a distance r is spin, velocity, and

concentration independent, and weak. Their interaction is written in

terms of the Fourier transform V(k) by

V(r) = V(k) e

i k * r dk

(2lr)"

(1)

where k is the wave vector. For an isotropic system,V(k) = V(k). The

effective mass m* is then given as [ 17]

m 3 1 o

N(0)

2k

2k o

f

f V(k)k (l - —

2 k.

dk , (2)

where m is the value of m* at zero concentration,

o

N(0) = m*k/2-rr

^

(3)

is the density of energy states at the Fermi surface for one spin orientation, and k is the magnitude of the Fermi wav

of k on concentration is shown by the relation

tion, and k is the magnitude of the Fermi wave vector. The dependence

, ,,2 .1/3 ,_ 2 AT 1/3

f =

* n

3^ =

^ A^ (4)

where n is the number density of He atoms in solution, N is

Avogadro's number, and v is the volume of solution containing one mole

3

of He . The expression

v = V /X = 27. 58/X + 7. 60 + 1. 65 X

2

cm

3 /mole He

3

, m ' (5)

where V is the molar volume of the solution and X is the He concen- m

tration, will be used throughout these calculations. Equation (5) agrees
with experimental data [9, 18] to within 0. 3 percent for concentrations

less than X = 0. 3 and all temperatures less than 1. 5°K. The value

27. 58 cm /mole is the molar volume of pure He between and 1. 5°K.

To calculate m* from (2) knowledge of V(k) is necessary. The

simple two-parameter form used by BBP to fit spin-diffusion results

[ 8] is given by

V(k) = V cos (0k) (6)

2 -38 3 with M 3.16 A and V = -0. 0754 m„ s /n = -1. 303 x 10 ergs cm , o 4 4

& > 4 where m is the mass of the He atom, s is the velocity of first sound in

4 4 He at T = 0, and n is the number density of pure He at T = 0. Ebner

[ 19] recently extended these calculations for V(k) to higher concentrations

and used the form

V(k) = | V

q

| {or + a

2

exp[-C

z (k/2ko

) 2

] + ^ exp[-C

3

(k/2k

o

) 2

J } ,

where V is the same as that used by BBP and the other parameters are:

o

or. = 10, a, = -1.48, a, = -9/60, k =0.497 A

-1 12 , 3 o C

2

=4. 0752, C =0.0564. (8)

The form of V(k) given in (6) is limited to concentrations less than 5 percent, whereas the form in (7) is valid for concentrations even higher than

30 percent. Ebner states, however, that V(k) in (7) may contain some

10 -- 1 5 percent error. Both forms for V(k) were used in (2) to solve for

m*/m , assuming m /m = 2. 34 as suggested by BBP. Figure 2 shows

3 o 3

the calculated concentration dependence of m*/m compared with four

experimental points from specific heat data. Both curves give good agreement with experiment, but since Ebner's form of V(k) is valid for higher

concentrations, m*/m obtained by using his form of V(k) will be adopted

here. These values of m*/m are also listed in Table 1, along with k

and the Fermi temperature T given by
\ 1

1 1

i '

Uj^

pa

"N.

Anderson,

et

al

Edwards,

et

al

—

\

\

^\

S

N

v.

1

5

\

\

\>

l_

\ \

\ \

\ \

ro

EXPERIMENTAL^

_i

1 \ T \

\

1 \\ 1

1 1

H«

1 -^O—

V

i

1

>—

'

1 ^

CMd

o

CVJ d

d

o

d

od

CD

c\i ID

c\i £uj/ uu

c\i rO

c\j

o

u

u

aoU

0) a

o

1-1 M

o

ti

hi

X

o

CDOJ

ft)

O

<L> w
TABLE 1 SOME TEMPERATURE INDEPENDENT PROPERTIES OF HE3 IN SUPERFLUID HE4

X 10" 7 kf

(cm )

T

f m /m -(Ut3 +L3 °)/R

(°K) (°K)

.0000 0.00000 0.000000 2.34000 0.258728

• 0001 0.40136 0.005535 2.34046 0.258841

• 0002 0.50567 0.008784 2.34092 0.258956

• 0005 0*68628 0.016171 2.34225 0.259310

• 0010 0.86462 0.025643 2.34442 0.2599ZO

• 0020 1.08926 0.040627 2.34857 0.261201

.0030 1.24677 0.053137 2.35253 0.262544

.0040 1.37213 0.064255 2.35633 0.263940

.0050 1.47794 0.074432 2.36000 0.265382

.0060 1.57041 0.083910 2.36355 0.266865

.0080 1.72814 0.101322 2.37033 0.269938

• 0100 1.86124 0.117214 2.37674 0.273139

• 0150 2.12961 0.152510 2.39145 0.281601

•0200 2.34287 0.183572 2.40462 0.290600

• 0250 2.52263 0.211771 2.41656 0.300032

.0300 2.67947 0.237848 2.42748 0.309«25

.0350 2.81946 0.262265 2.43753 0.3l99 2 6

• 0400 2.94645 0.285332 2.44684 0.330293

• 045o 3.06304 0.307272 2.45550 0.340892

*05oo 3.17109 0.328251 2.46359 0.351698

.0550 3.27197 0.348395 2.47117 0.362685

•0600 3.36673 0.367807 2.47830 0*373837

.0640 3.43870 0*382864 2.48371 0*382864

• 0650 3.45620 0.386567 2.48502 0*385135

• 0700 3.54104 0.404742 2.49138 0.396565

.0750 3.62178 0.422388 2,49742 0.408115

• 0800 3.69887 0.439551 2.50315 0.419775

.0900 3.84352 0.472586 2.51381 0.443382

.1000 3.97732 0.504107 2.52357 0.467321

.1100 4.10202 0.534310 2.53255 0.491539

•1200 4,21894 0.563353 2.54088 0.515992

.1300 4.32914 0,591359 2.54864 0,540643

.1400 4.43344 0.618430 2.55592 0.565461

.1500 4.53252 0.644651 2.56278 0.590420

.1600 4.62694 0.670092 2.56927 0.615498

.1800 4.80362 0.718869 2.58133 0.665934

.2000 4.96644 0.765151 2.59239 0.716639

.2250 5.15379 0.819942 2.60512 0.780246

.2500 5.32610 0.871743 2.61690 0.843959

.2750 5.48575 0.920896 2.62796 0.907654

.3000 5.63456 0.967674 2.63844 0.971234

.3500 5.90503 1.054946 2.65810 1.097725

.4000 6.14589 1.134915 2.67648 1.222900

.4500 6.36280 1.208563 2.69392 1,346348

.5000 6.55978 1.276633 2.71062 1.467729

Page 9
T = fi Z k

f

2

/2 K m* = 54. 890/(v

Z' 3 mVm,) °K , (9)

where K is Boltzmann's constant.

Stoner [ 20l has evaluated the specific heat C of a Fermi-Dirac

v

gas for all temperatures as a function of the ratio T/T . Since he gives

only tabulated results for the intermediate temperature range, a power

series expression was fit to his data to facilitate calculations of thermodynamic properties. The details of this power series fit are given in

3 4 Appendix A. The specific heat and entropy of dilute He - He solutions

can now be calculated as functions of temperature and concentration.

However, to proceed with calculations of enthalpy, chemical

potential, osmotic pressure, and other related properties, the deviation

3

of the chemical potential of He in solution from that of an ideal FermiDirac gas must be found. There will be a considerable deviation because

3

of the presence of a binding energy and the interaction between He atoms,

3 The chemical potential of He in solution can be written as

H

3

(X, T) = Uf

(X, T) +\l f 3

(X, T) ,

where \l is the chemical potential of the ideal Fermi-Dirac gas with effec

tive mass m* and is given by

U = H - TSr = 5/3 U - TSr = RT, + 5/3 C

f f f f f f «J dTv

- T (C /T) dT . v (ID

In this equation H , S , and U r are the molar enthalpy, entropy, and

f f f internal energy of the ideal Fermi-Dirac gas and R is the gas constant.

Since C has been expressed as a power series in T, the integrations

can be easily carried out with the aid of a computer.

10
The term M- 1 can be evaluated from the experimental data for the

dilute solubility curve and then compared with theoretical results for |J.' The experimental values of |a' are found by making use of the fact that

3

in a phase separated solution the chemical potential of He must be the

same in both the dilute and concentrated phases. If at first it is con3 sidered that the concentrated phase is pure He , then

H (X , T) +M» (X T)= H • (T) , f -L 5 Kj 5 (12)

where X denotes the concentration of the dilute phase on the solubility

curve,

T T

U

3

° = - L

3

° + j C

3

° dT - T

J

(C

3

°/T) dT

o o (13 )

3

is the chemical potential of pure He , and L ° is the molar heat of vapor

3

ization of pure He at T = 0°K. The quantity \i ° + L ° is calculated

3 using values for the properties of pure He given in Appendix B. The

term |J (X , T) in (1Z) is evaluated using (11) at each data point [ 7, 9]

f Kj for the solubility curve. By combining (12) and (13), values for [l

1 (X , T)

3 \j + L ° can be determined. The results of such calculations are shown in

figure 3. Also in figure 3 are shown curves for T from (9) and a theoretical result for (J.

1 + L ° which will be discussed shortly. From (11), (12),

and (13) it is obvious that (-l-l

1 - L°)/R = T for T = 0°K, and the concentration at which this occurs is the limiting solubility of He

3.4

in He at

T = 0°K.

The theoretical behavior of [l ' using V(k) has been discussed by

BBP and Ebner. However, their definition of M1 is slightly different than

that used here. The difference is that they use the effective mass m

Q

instead of m* in evaluating (J in (10). The theoretical expression given by

BBP for their p.' at T = 0°K is

11
o ni COo l-H

0) rd

-Maohm

•—Ia

+jc

4! u

0, in 1—I b uamXU

0) ,£M

X

Oa

nj

•t-t > o <u Q o T3

floJ

<D , \ fH3

IT) . U 0)

(U CJ ft* oh yrd •s m

if) 8? OO 0) M

,£ <D H tq

CO

(L) u3

bo h

12
IV (X, T=0) = E^ + n. N A V(0) - N A V(k)

3

x '

' o 3 A

x ' A J- -» ^, x

' ,3 k+k f <k

f

(2ir)

2 _. A

N. 2k

o

x A ' ' v ' 2

f,2,, k

= E + (N. /v) V(0) - —= k (1 - —-) V(k) dk , (14) 2k.

4tt o f

where E is the binding energy and is independent of concentration. The

o second and third terms on the right side of (14) are the Hartree and exchange corrections to |i_. To be consistent with the theory of BBP and

Ebner, the |a_' defined by (10) and used here should contain an additional

term equal to the difference between |i evaluated at m and m* However,

f o when this additional term is neglected, the theoretical \i ' from (14) fits

experimental data very well even for temperatures up to 0. 6°K as will be

shown very shortly. Inclusion of the additional term requires |JL ' to be

temperature dependent to give agreement with experimental values at

finite temperatures. This temperature dependence has been worked out

by Ebner only for the high and low temperature limits. Since the primary

purpose of this paper is to find a model which can be used to fit experimental data over a wide range of temperature and concentration, the

additional term in (14) required by rigorous theory will not be considered

in this paper. Equation (14) was evaluated numerically using Ebner's

form of V(k). The quantity E + L ° is found from a best fit of the

theoretical (i ' + L ° to the data points in figure 3. Only the data for

X < 0. 075 were considered for the fit since it will be shown that the data

at higher concentrations and temperatures require some correction.

From this fit it is found that

and that

(-E - L °)/R = 0.259°K (15) o 3

X (T = 0) = 0.0640 (16)

13
3 4

is the limiting solubility of He in He at T = 0°K. Ifft et al. L 9] report

a slightly different value of 0. 0637 for X (T = 0) from a T extrapolation

of their data. The theoretical result for |i ' is given in Table 1 in addition

to being shown in figure 3. Including the additional term in (14) would

yield the result 0. 282°K for (15), which agrees with the value given by

Ifft et al. [ 9] . The uncertainty in V(k), however, is such that the difference in the two results for (-E - L °)/R is inconsequential [19, 21].

The discrepancy between experimental and theoretical values for

\l ' at higher concentrations can be completely explained by correcting |i ° 4

used in (12) to account for the presence of a small amount of He in the

concentrated phase. This correction then changes the experimental values

for \i '. The term |J which must be added to |i ° to give the chemical poj c 3

tential of the concentrated phase was actually found by forcing the experimental data for \i ' + L ° in figure 3 to agree with the theoretical result

shown in the same figure. This correction term \l is shown in figure 4 as

a function of temperature. For temperatures above 0. 4°K this curve was

deduced from a smoothly drawn phase separation line bridging the gap between the low and high temperature data shown in figure 1. Figure 4 compares this calculated behavior of U with two other results for \1 . One of

c c these other results is based on the experimental work of de Bruyn Ouboter

et al. [ 11] for the thermodynamic properties of concentrated solutions

down to about 0.4°K. The term li is calculated from their data by the

c relation

U = G

T +(1 -X ) (%-) , (17)

u v dx X=X

u

•• where X is the concentration of the concentrated phase and G is taken

u

to be

G

T = G -IX n

3

° +(1 - X) n

4

°]

= X (|i

3

- \± 3

°) + (1 - X) (|J4

- n

4

°) (18)

14
0.8

0.6

o

E

3 0.4

o

"3

o

0.2

— de Bruyn Ouboter et aI This Work

Regular Solution Theory

0.2 0.4 0.6

T, °KFigure 4. The Difference in Chemical Potential Between the Concentrated Phase and Pure He .

15
with G as the Gibbs free energy and LA - LA ° the difference in chemical

4 4 t potential between He in solution and pure He . The term (dGydX)X— X

is very difficult to evaluate from the experimental data but appears to

be fairly small. For a first approximation that term is chosen to be zero,

•r which then leaves la = G . A better approximation can be made. Since

the terms U and LA must be the same in both the dilute and concentrated

3 4

phases, the term <3G y SX must also be the same in both phases. The

theoretical behavior of LA„ - LA_ ° and LA. -la. (to be calculated later) in

3 3 4 4

the dilute phase can be used to find dG /dX. This then results in a

negative value for dGT/dX and makes la less than G . The difference,

c though, is only significant above about 0.4°K, but is still less than the

experimental uncertainty and so it is not shown in figure 4. The other

curve shown for comparison in this figure results from assuming that

the solutions behave as a regular solution. This assumption should give

reasonable results in the concentrated phase at least for the higher temperatures. The details of the calculation for la from the regular solution

c theory are given in Appendix C where the concentration X as a function of

temperature is listed in Table 6. It is evident from the curve shown in

figure 4, that the behavior of LA which results in an exact agreement of

experimental and theoretical la ' + L ° can be considered to be consistent

with all other estimates of its behavior, although possibly too high around

0. 2°K. In other words, the theoretical LA ' agrees with experimental data

along the solubility curve within experimental error and no temperature

dependence of LA * is necessary to give this agreement even for temperatures as high as 0. 6°K. Of course a small temperature dependence is

still possible in view of the fairly large uncertainty in la j but LA * is

assumed to be independent of T in all of the present calculations. In any

case a small temperature -dependent term would have very little effect on

most of the thermodynamic properties at all but the lowest temperatures

since LA ' contributes significantly to these properties only at low temperatur e s

,

16
By using the theoretical behavior of \l ' and u , (11) and (12) can

3 ' c be used to derive the theoretical phase separation temperature as a function of concentration. This calculation is just the reverse of the

case where the experimental \l * was deduced from the experimental

phase separation temperature. The results for the theoretical phase

separation temperature are shown in figure 5 along with experimental

values [ 7, 9] and are listed in Table 2. To summarize, the behavior of

the weakly interacting Fermi-Dirac gas model using Ebner's expression

for V(k), which was deduced from spin diffusion, predicts an m*(X)/m

in agreement with experiment. These values of m^XJ/m.- are used in

the specific heat of a Fermi-Dirac gas which then correctly predicts

3 4

specific heat of He in He at all temperatures. In addition this model

gives the correct concentration dependence of the phase separation

temperature.

The present definitions (10) and (13) for \1 and \1 ° result in large

negative values for these terms at T = 0°K due to the quantity L °. In

addition any uncertainty associated with L ° appears in U and (i °. The

absolute value of chemical potential in any system is arbitrary, and it makes numerical computations simpler if |J._ and \l ° are changed by a

3 3

constant value. The terms |JL and U ° are now redefined by adding L °

to the right sides of (10) and (13). The new definitions then become

U

3

(X, T) = |J

f

(X, T) + |i

3

« (X) + L

3

° (10»)

and

3

|i_° (T) = C ° dT - T (C„°/ T ) dT

3 o o

3

H

3

° (T) - TS

3

° (T) , (13«)

17
0.4

0.3

0.2

0.1

THIS WORK

EXPERIMENTAL

r o Ifft , et al

O Edwards , et aI

0.06 0.08 0.10

X

0.12 0.14

Figure 5. The Phase Separation Temperature as a Function of He

Concentration.

18
Table 2

The Phase Separation Temperature or Solubility Curve

for Dilute Solutions of He - He

X T

(°K)

X T

(°K)

0. 06400 0.0 0. 090 0. 1946

0. 06404 0. 00946 0. 095 0.2129

0. 0641 0.01486 0. 10 0.2301

0. 0642 0.0208 0. 11 0.2616

0. 0643 0. 0253 0. 12 0. 2902

0.0645 0.0323 0. 13 0. 3166

0. 0647 0. 0377 0. 14 0.3412

0.065 0. 0445 0. 15 0.3644

0.066 0.0606 0. 16 0.3863

0.067 0.0721 0. 17 0.4072

0.068 0. 0817 0. 18 0.4272

0. 070 0. 0970 0.20 0. 4647

0. 072 0. 1102 0.225 0. 5075

0.074 0. 1223 0.25 0. 5460

0. 078 0. 1436 0.275 0. 5809

0.082 0.1618 0. 30 0.6097

0.086 0.1789

19
where |i' is now shown as a function of X only. The term \±° now be3 4

comes zero at T = 0°K. The entropy and enthalpy of He in He "are

taken as T

V

S (X, T) = S (X, T) =

J [c (X, T)/TJ dT , (19)

H

3

(X, T) = u

3

(X, T) + TS

3

(X, T) = U«

3

(X) + 1^° + H

f

(X, T)

T

= u« (X) +L ° + RT, + (5/3) I C (X.T)dT . (20)

3 3 f «J v

o

3 4

The osmotic pressure II of He in liquid He can be determined

from the relation

nv

4

= -(m

4 -h4

°) , (2D

which follows from altering an equation given by London et al. [ 3] . In

(21) the term V. = V -X BV /SX = 27. 58 - 3. 30 X

3

cm

3 /mole is the

4 m . m' ' 4

partial molar volume of He in solution and is only slightly different than

4 V °. The right side of (21) is the difference in the He chemical potential

4 4 between He in solution and pure He and is easily evaluated from the

Gibbs-Duhem equation for constant temperature and pressure

d^3 d^4 (22)

In integral form (22) becomes

X

^ - V dli- , (23)1 - X ^3

o

20
which upon substitution into (20) yields

X

n v

4

= 1 rhc d^ • < 24> o

The integral is easily evaluated numerically since \i is known as a

function of X from (10*).

3 4

3. 2 Properties of the Total He - He Solution

Up to now consideration has been given only to the thermodynamic

3 4 properties of He in liquid He and not those of the total solution. How3 4

ever, in the case of the He - He dilution refrigerator operating in a

3

steady state, the He contribution is all that is needed. Ideally, in this

3 4 refrigerator He diffuses through a stationary column of He so that the

4

He contribution is not needed for thermodynamic calculations. For the

transient behavior of the dilution refrigerator, or any other process where

the bulk liquid is involved,the thermodynamic properties of the total

solution are needed. The total specific heat and entropy are taken as [ 14]

C = X C

v

+ (1 - X) C

4

°

, (25)

S = X S + (1 - X) S ° , (26)

4 where C and S ° are the specific heat and entropy of pure He . Equations (2 5) and (26) are good approximations only for temperatures not too

close to the X point since the X point changes with concentration (see

fig. 1). Below 1°K, however, C ° is very much smaller than C so the

approximation is certainly good up to X = 0. 3 for these temperatures. At

1. 5°K the results for C from (25) begin to deviate considerably from

experiment [ 11] for X much above 0. 1.

21
The enthalpy H (same as the internal energy U for the low temperatures and pressures of interest here) can be calculated in three

different ways. Unfortunately the results are not exactly the same in

each case. The first method makes use of the relation

H = G + TS = X \i + (1 - X) \l 4

+ TS

= X H

3 + (1 - X) (u4

- U

4

°) + (1 - X) H

4

' (27)

To be consistent with (10') and (13')

-T

H3° =

J C 3° dT ' o V = ".V + V +

,T

o C/dT 4

(28)

(29)

where L ° is the heat of vaporization of pure He at 0°K. The second

method uses

H = H + I C dT (30)

where H is the value of (27) at T = 0°K. The third method, which is o somewhat of a combination of the first two, replaces H in (30) for

o X > 0. 064 with the value of (27) on the phase separation curve instead of

at 0°K. The lower limit of the integral is also replaced by the phase

separation temperature. The results obtained by this third method should

be a good compromise except for the fact that curves of H versus X for

constant T will have an abrupt change in slope at X = 0. 064, which would

be unrealistic. The second method was chosen for these calculations

and will give the same results as the third method for X ^ 0. 064. Since

the theoretical behavior of C agrees so well with experiment,the resulting

22
values of H should be quite accurate, at least for X ^ 0. 064. The second

method eliminates the abrupt change in slope at X = 0. 064, but the result

for H above this concentration may not be quite so accurate. The first

method suffers from the disadvantage that it relies entirely on the theoretical behavior of [l and \l , both of which are more uncertain than the

calculated C The difference in H caused by using the various methods

is only a few parts per thousand. This difference is greatly magnified,

however, when the excess enthalpy

H

E

= H-XH

3

° - (1 -X)H

4

° (31)

is considered. The first method can give values for H which are 15 to

20 percent higher than the second method for large values of X. This

difference is due mainly to a temperature dependence of [1 that is not

quite consistent with properties such as specific heat. Possibly a small

temperature dependent term in \i ' might correct this inconsistency.

E

From (31) and (27) it is easy to see that at T = 0°K, H is just (1 - X)

3 4

The vapor pressure of He - He solutions is found from a trial

and error solution of the equation

H

3

- [± 3

° = RT £n(X

v

p/p

3

°)

+ (P-P3

)[B

33

+ (1-X

V

) 2( 2B

34

-B

33

-B

44)j ,

(32)

3 where X is the He molar concentration in the vapor, p ° is the vapor

v

3

3

pressure of pure He , and the B's are the second virial coefficients for

3 4

He and He from the work of Kilpatrick et al. [ 22] . Equation (32)

follows from a combination of expressions given by de Bruyn Ouboter

et al. [ 23] . A very good approximation for X , at least for temperatures

23
above about 0. 5°K, can be found from the theory of regular solutions. In

this case [ 23]

X (1 - X) p •* X

V

(1 _ x j = —jijt exp [(W/RT)(1 - 2X)] , (33)

where p.°* = p. ° exp (B.. p.°/RT) is the fugacity of the component i and W

is a constant taken to be W/R = 1, 37°K [ 24] . The results of (33) for X

are substituted into (32) to find p„

The heat of vaporization of a binary solution can be treated as

either integral or differential, depending on the conditions of vaporization

[ 2 5] . When a quantity of liquid solution is completely vaporized so the

initial liquid concentration and final gas concentration are equal, the

integral heat of vaporization is absorbed in the process. This integral

heat of vaporization is ^ if the process is done at constant pressure, and pX

^ if done at constant temperature. For the low pressures dealt with

1 .X. here the gas phase can be treated as ideal and thus the enthalpy in both

the liquid and gas phase are independent of pressure. The integral heats

of vaporization can then be written as

XpX + R(T " T,) = X TX

= XL3° (T) + (1 ' X) L4° (T) " ^

{X

' T)>

(34)

where T' is the final temperature in the constant pressure process and

3 4 L ° (T) and L °(T) are the heats of vaporization of pure He and He at

the temperature T. The term -Pi gives the deviation from the ideal

heat of vaporization and is just the negative of the excess enthalpy.

If a mole of gas is formed from an infinite reservoir of liquid,the

heat absorbed is X , the differential heat of vaporization. In this process the gas and liquid phase concentrations are different. From the

work of Ruhemann [ 25]

24
X , (X, T) = X L • (T) + (1 - X ) L • (T)

vL v 3 v 4

+ [-HE (X,T)-(X

v

-X) dH

J

X>T)

J

• 05)

The term in brackets gives the deviation from the ideal differential heat

of vaporization and will be denoted as X

v£

3 4

3„ 3 Applications to the He - He Dilution Refrigerator

3 4 A schematic diagram of the He - He dilution refrigerator is

3 shown in figure 6. Nearly pure He gas leaves the vacuum pump at a

4

pressure of about 30 torr and passes through a pumped He bath which

3

condenses the He . After passing through a flow limiting capillary the

3

liquid He is cooled by passing through the still and the heat exchanger.

3

The pure He liquid enters the mixing chamber, or mixer, where it 3 4

floats on top of, and is in equilibrium with, a dilute solution of He in He . 3

For very low temperatures the dilute solution contains 6. 4 percent He . This 6.4 percent solution communicates with the solution in the still via

the return line in the heat exchanger. For the solution in this return line to

be in mechanical equilibrium, the chemical potential \l must be the same

throughout the tube. Since the temperature of the still is higher than the

mixing chamber, the concentration of the solution decreases as it approaches the still. From results to be given later the concentration in

the still is about 1 percent for T = 0. 6°K, where T is the still temper

ature. As this liquid vaporizes in the still, nearly pure He is removed

from the solution provided, of course, super fluid film flow is greatly

3

restricted. To complete the cycle the He gas is compressed to about

30 torr at room temperature and returned to the condenser. As the con3 centration in the still is lowered, He will diffuse from the 6. 4 percent

solution in the mixing chamber through the heat exchanger to the still.

25
He

4

He4 - 1 % He3

He3 VACUUM PUMP

~ 300 °K

CONDENSER

0.8 - 1.2 °K

CAPILLARY

STILL

0.6- 0.7 °K

HEAT

EXCHANGER

He"

He4 - 6.4% He3

MIXING

CHAMBER

0.01 -05°K

Figure 3 „ 4 6. Schematic Diagram of the He - He Dilution Refrigerato gtor,

26
3

To preserve equilibrium in the mixing chamber He must pass from the

upper rich phase to the lower dilute phase to maintain a 6. 4 percent con3 , , centration in the latter. In so doing the He absorbs heat if the tempera3

ture is kept constant. As the He diffuses through the nearly stationary

4 3 column of He in the heat exchanger, it cools the incoming pure He

stream in the heat exchanger. A thermodynamic analysis of the dilution

3 4 refrigerator in a steady state uses only the properties of the He in He

4

since the He is stationary in the ideal case.

The heat absorption rate of the dilution refrigerator is of fundamental importance to those interested in the capabilities. First consider

3

the case where only pure He is circulated by the pump. By treating the

mixer as an open thermodynamic system, this heat absorption rate Q in

the steady state at a temperature T can immediately be written as an

enthalpy difference

Q(T,T.)/n, - H,(X,-T) -H,°(T.) , (36)

3 where n is the molar circulation rate of He , the first term on the right

3 4

is the enthalpy of He in He along the lower or dilute solubility curve,

c 3 and H (T.) is the enthalpy of He in the incoming concentrated stream

at temperature T.. When the mixer temperature is below about 0. 2°K,

1 3

the concentrated phase is nearly pure He and so the incoming stream

3 c must also be nearly pure He . Thus, H becomes equal to H °. However, at higher temperatures the concentrated phase in the mixer will

4 4

contain a certain amount of He . It is possible for this He to diffuse up

3

the incoming He stream to cause some dilution above the mixer. To

calculate the heat absorption in the mixer, the concentration of the stream

just as it leaves the last heat exchanger must be known. If the velocity of

3 4

the incoming He stream is high enough, He will be prevented from

27
diffusing up as high as the heat exchanger. Expressed analytically, the

3

stream leaving the heat exchanger will be pure He for n LV /DA » 1,

whereas for n, LV /DA « 1 the stream will have the same composition

j m

as the concentrated phase in the mixer. In this expression L, is the

length of tubing from the last heat exchanger to the mixer, V is the

molar volume of the incoming stream, D is the diffusion coefficient of

4 3

He in He , and A is the cross-sectional area of the tube. In practice,

something between the two extremes most likely will occur. The enthalpy

3 4

of He in a solution containing some He is rather uncertain and so little

4

can be said about the heat absorption in the extreme where the He easily

diffuses up to the heat exchanger. However, from the work of de Bruyn

Ouboter et al. [ 1 1

J it looks as though the enthalpy of He in the incoming

stream at about 0. 6°K will be on the order of 10 percent higher than H °. c The difference between H and H ° decreases to zero at about 0. 2°K.

Q Equation (36) should be very accurate when H can be taken as H ° since H is known very well along the solubility curve. Though in

principle H (X , T) can be found from (20),an alternative method for

-> Kj temperatures of 0. 1°K and below has been chosen. If the incoming pure

3

He stream is at the same temperature as the dilute solution, then the

process is reversible. The heat absorption is then given as

Q

r (T)/n3 = T[S

3

(Xr

T) -S

3

°(T)] (37)

from which it follows that

H

3

(X^, T) = Q

r

( T )/n

3

+H

3

°(T)= T[S

3

(X^, T) -S

3

°(T)] +H

3

°(T) .

(38)

Values of H and S along the solubility curve are obtained by second

order interpolation in tables of H and S as functions of X and T. However, interpolation in the S„ table is much more precise than that of the

28
H table for temperature of 0. 1°K and below. This is because p. ' + L_ ° 3 3 3

and RT- in H are very large numbers which cancel each other exactly

at 0°K on the solubility curve. Their resulting contribution to H slightly

above 0°K on the solubility curve is subject to considerable error unless

both terms are evaluated to a great number of places. Thus H (X , T)

is evaluated from (38) for temperatures of 0. 1°K and below. Above

0. 1°K,

(5/3)J

C dT is the dominating term in H and so H (X , T) is

accurately obtained by interpolation in the H„ table. Values for H„ ° (T.)

3 3 i are taken from Appendix B.

4

In the case where the gas circulated contains some He ,the calculation of heat absorption can become very complex, especially at temperatures above about 0. 2°K. Since operation of the refrigerator above

this temperature is of limited interest, analysis of the heat absorption at

these temperatures will not be made. Below about 0. 2°K the amount of

3

pure He available for refrigeration is reduced to

x -\

n_ = n

3 \1 - X • J ' (39)

where X is the concentration of the dilute phase at the temperature T., 1

3

x n is the number of moles of gas mixture circulated, and X is the He con- centration in the circulated gas. The dilute solution already separated

out at T. will contain

l

n-- = nX

31 I

- tr-rir) \1 - X J (40)

3 4

moles of He . Neglecting the very small He contribution, the heat absorption rate in the mixer per mole of gas mixture circulated can be written as

29
Q(T.T.) .X - X

-j-!- = X H

3

(X

t

, T) iiTTir) H3° < T

i> +X

t Vr^x7^ H

3 (Xr

T

i>.

(41)

where all the X inside the brackets must be evaluated at T..

For low flow impedences in the dilute stream between the mixer

and still,the solution will be in mechanical equilibrium throughout its length.

This equilibrium condition is expressed by \1 - constant, and from(21)this

implies that the osmotic pressure must be constant, at least for low

temperatures where d|i °/dT is extremely small and for low concentrations where V is nearly constant. At higher temperatures (T ~ 0. 5°K)

the change of M- ° with temperature must be taken into account. When

this is done, the condition \i = constant then is equivalent to n +pf r

constant for small X, where TI is the osmotic pressure and p is the

4

fountain pressure of pure He defined and calculated from (80) in Appendix B. For high concentrations the condition n + p, = constant does not

hold exactly since V in (21) changes slightly with concentration. However

the difference in V between X = and X = 0. 3 is only 0. 3 percent. Given

a temperature and concentration in the mixer, the concentration anywhere

in the heat exchanger or still may be found from curves of the osmotic plus

fountain pressure or, to be exact, curves of |i . In practice a small

3

gradient in the osmotic pressure must exist to drive the He through the

heat exchanger and may not always be negligible. The calculated concentration in the still then represents an upper limit and the deviation

from this value can be found if the flow impedance of the heat exchanger

is known. Fourth order interpolations can be carried out in a table of

\1 to find the concentration as a function of temperature. Once the con3 centration in the heat exchanger is known, the entropy of He anywhere

along it is easily found from fourth order interpolation in the S table.

3 The specific heat of the He at constant |JL. . designated as C , is then

4

&

\l

30
given as C = T i —i-

) (42)

4 u = const

The differentiation of S is carried out after fitting the data for S at

constant [± with a third order polynominal in T. It should be obvious

that C will be a function of the mixer temperature as well as the local

^4

temperature since the former determines the osmotic pressure in the

system.

The vapor pressure and vapor concentration in the still as a function of both still and mixer temperature can be easily found from

interpolation in the p and X tables using values of X in the still as determined from the condition \1 - constant in the dilute stream. The heat Q^

required to vaporize a mole of liquid in the still has contributions from

3 4

both the He and the He vaporized. Because of the large heat of vapori4

zation of He , this contribution which is given by (1 - X ) L. °(T) can

3

v 4

not be neglected. The He contribution is X L„(T), where L„(T) is just

v 3 3

the difference between the enthalpy of He in the saturated vapor and in

3

the dilute liquid. The He vapor enthalpy can be written as H °(T)

+ L. °(T). From this it immediately follows that

QQ/n=X L °(T) +(1 - X ) L°(T) +QcE

/n , (43) o v 3 v 4 S

where

Q

sE

/n = X [H °(T) - H (X, T)] (44)

is the deviation from the ideal heat of vaporization and n is the gas flow rate,

The interface between the dilute and concentrated solutions must

remain in the mixing chamber if the refrigerator is to operate properly.

Thus it is important to examine just where this interface will be for all

31
possible sets of conditions. The assumption is made at this point that

the liquid volumes in the heat exchanger and condenser are negligible

compared with the volume of both the still and mixing chamber. The

volume of the still containing liquid immediately after the initial filling

and before circulation begins is written as

V = r V , (45)

s mc

where V is the total volume of liquid in the mixing chamber. If the

mc

whole system is filled initially with n moles of solution at a concentration

of X , then the initial volume of liquid is o ^

n V ° = V +V=V (1+r), (46) m mc s mc

where V is the molar volume V of the solution from (5) for a con- m m

centration of X . During operation of the refrigerator, phase separation

occurs in the mixer, and h is the fraction of mixer volume occupied by m

the dilute solution. The total volume of solution during operation will be

different than the initial volume, which then results in a change in liquid

level in the still. Let the ratio of present to initial volume of liquid in

the still be h . Both h and h are found from a solution of the simultas m s neous equations

(1 - h ) V X /V U

+ h V X /V + h r V X /V * = nX , m mc u m m mc V m s mc s m o

(47)

(l-h)V /V U +h V /V^+hrV /V S = n

m rnc m m mc m s mc m

(48)

where the subscripts and superscripts u, t, and s on X and V refer to

m

the concentration and molar volume in the upper concentrated phase of

the mixer, in the lower dilute phase of the mixer, and in the still. The

32
3

first equation represents the total number of moles of He in the system

and the second gives the total moles of solution. Substituting (46) into

these two equations yields

X X N rX (1 + r) X X

, h + h= » (49) v^v um

v

ss V° v

u mm m mm

(li- - -L) h + .JL_ h

-_ ii±£l . J_ (50) mm m mm

after rearranging. The values used for X are given in Appendix C.

Problems associated with the heat exchanger can be eliminated by

operating the refrigerator in a single -cycle process. In this case the heat

3 exchanger is unnecessary since pure He is not returned to the mixer.

Vilches and Wheatley [ 5] have reached 0. 0045°K with this method and

3 maintained it for about an hour before depleting the He . The process is

reversible and thus for isothermal operation the heat absorption is simply

given by (37). However for T > 0„ 1°K the term S ° should be replaced by

3

the entropy per mole of He along the solubility curve for the concentrated

phase, although the difference is significant only for temperatures above

about 0. 2 or 0. 3°K. For T ~ 0. 1°K it is evident from (38) that (37) becomes identical to H (X , T) - H °(T) = Q(T, T)/ri , which is the maxi-

. 3 Kj 3 J

mum value of Q(T, T.)/n , and is a fairly good approximation for temperatures up to about 0. 2 or 0. 3°K. The greater refrigeration rate is

gained only at the expense of sacrificing the continuous nature of the

3

dilution refrigerator. The amount of He remaining in the mixer after

the lowest temperature is reached is important to know; thus, analysis

of the transient mode is needed. The natural assumption is made that

the heat capacity of the mixing chamber itself is negligible compared with

33
the solution. Unless a large amount of cerium magnesium nitrate is used

as the thermometer, the assumption is very good. Again by treating the

mixer as an open thermodynamic system the change in entropy of the

total system can be expressed as

dV^ + 6„

3

S

3

, (51,

where SQ is the increment of heat absorbed for the incremental change

3

6n of He in the system. Equation (51) can also be put in the form

dS

6/°3 = T V^T " s

s)

(52)

m

3 where Q is the heat input rate and n_ the molar rate of change of He

3

the mixer,- and S is the He entropy along the dilute solubility curve.

If n is the number of moles of dilute solution and if the concentrated

1

3 <

solution is assumed to be essentially pure He (T ~ 0. 15°K), then

S

t =n

t S+n3

S 3° ' (53)

where S is the molar entropy of the dilute solution from (26). The

derivative becomes

dS

t ss ht dn

; dV HT

~> J\. o i 3

,„, dn„ dT Jt c\T = n p C- + TS —- + n C ° f^ + TS ° . (54) I dn dn^ 3 3 dn 3

The mere process of cooling the liquid will automatically cause a small

3

transfer of He from the dilute to the concentrated phase. This is evident

from application of the leverage rule to the phase diagram. For temperatures less than about 0. 15°K this effect is quite small and so dn /dn„ is

34
taken to be zero. One calculation was made for a starting temperature

of 0. 3°K„ In this case dn /dn was still taken as zero but the value for C -1-1

was taken as [ 7] C = 6. 4T joules mole deg for a 12.4 percent solution

below 0. 3°K instead of using a 6. 4 percent solution. Combining (54) and

(52) yields the normalized equation

dT Q/n3+ T(S

3

- V) d(n /n ) (n /n ) C + (n,/n ) C ' _> O Aj O D O D (55)

3 where n is the original number of moles of pure He in the mixer. The

term T(S - S °) is the same as H (X T) - H °(T) for T < 0. 1°K.

3 3 j -L 5

Equation (55) was solved numerically for T as a function of n /n with

several different values for n./n and Q/n . In choosing values for

'L o j

Q/n a value for the ultimate temperature to be reached is picked and

-Q/n is set equal to T(S - S °) at that temperature.

3 When all the pure He is extracted from the mixer, continued

3 pumping will then begin to remove He from the remaining dilute solution.

The obvious question is, will this continue to produce a refrigeration effect?

3

As the concentration of He in the dilute phase is reduced,the osmotic

pressure is lowered; thus, work is being done by the system. Since the

process is reversible, (52) also describes the behavior in this case.

However, S now becomes

so that

dn 3 dn 3

The term n dS /dn can also be expressed as

S

t =n3

S

3

+n

4

S4°

• (56)

dS dS

: =n„ -t-^-+S„ . (57)

35
3 , 3\ dX , , 3\ dT

r SS3 S ht

= X(l - X) >—^) + —? — L\ BX/

T

T dXJ

(58)

where the relation X = n„/(n„ + n,,) has been used. When (58) is entered

3' 3 4

into (57), (52) may be written as

Q/n =X(1 -X)

L

T^; +C ^J

T

(59)

The term (dS /dX) is always negative and so heat is given off when He

is added to the system (n >0), but heat is absorbed during removal of

3 • He (n <0). Since S approaches infinity as X decreases to zero, the

limit -Q/n -* 00 as X -» must follow for T = constant. However, the

3

total isothermal heat absorption per mole of He originally in solution

when going from the concentration X. to X , given by

AQ/n

o - T v~x^ i i -x \ ax.

„

l .X.

.

-L 1

dX

(60)

has a finite value for X -*0. This is so because S increases only as -2/3 X ' for X - 0.

Cooling may also be accomplished by adding pure He to a dilute

4

solution through a superleak. If the incoming He is at the same temperature as the dilute solution, then the process also would be reversible.

In the reversible case the heat absorbed is also given by (52) but with S

replaced by S ° and n replaced by n^. From the system entropy in (56)

the derivative becomes

36
dS dS 3S X C

*T " n

3 dn~

+s

4

- _x \~W ; "~~f~~ dX +S

4 • 4 4 T

which then leads to a heat absorption rate of

(61)

oS

<^

4 =- x2

L

T br) +csi] • T (62)

Even though (62) is always less than (59), n. is not limited by a pumping

rate and therefore can be made much larger than ri_. Hence, Q could be

4 made larger in this second case where He is added to the solution com3 pared with the case where He is removed from the solution. However,

4

in practice the incoming He will always be at a temperature T. which is

higher than T. This reduces the refrigeration rate to

Q/^4 = - X' L

T 5f)T

+ C

3 I J

- L

H4° (T

i

} " V (T) ] '

(63)

4 where the last term in brackets represents the heat load in cooling the He

3 from T. to T„ The total heat absorbed per mole of He in solution when

l going from the concentration X.ifto X„ at T = constant is then

AQ/n

3 = T[S

3

(X

f

, T) - S^X., T)] - [ (X. - X

f

)/X. X

f

] [H

4

°(T ) - H °(T)] .

(64)

For T. - T this expression approaches infinity as X goes to zero. For

X «X. the last term in (64) becomes (l/X )[H °(T.) - H °(T)].

4„ Results and Discussion

3 4

4. 1 Properties of He in Liquid He

3 4 The entropy of He in He calculated from (19) is shown in

figure 7 as a function of temperature for various values of X. The

37
50

40 —

'« 30

O

E

O

Q_O

LlI

20 -

1 / 1 i

1 1 1 L/l 1 1 | 1 1 1 | 1

/>. - /&

- /§

- I?

p ¥

:/

V

-

j /

J

/

/

oT /^ ^^ -

- / > / &/ ^^ ^-^ - / C$X

^^ ^^

/ // / o$y ^^ j£^

y/yy ^y^

^^\^^<** / / '

^

y

y y

'

^

^

y / s

/y s

^

^^_

/ /

/ y

' y'

y

3

-

\\ //''''' pure ri^_

ll7///S

\\ ///y

v/ft/

^-l"" W^^ 1i i i 1 i i i 1 i i i 1 i 0.1 0.2

T,

0.3 0.4

K

3 4 Figure 7. The Entropy of He in LiquicLHe as a Function of Temperature for Various He Concentrations.

38
3

entropy of pure He is also shown for comparison. All the properties of

3 4 3

He in He are listed as per mole of He . Of special interest is the entropy

for X = 0. 064 in the low temperature limit, which is given as S = 107. 2 T

-1 -1

joules deg mole . This expression is good to within 1 percent for temperatures up to about 0. 04°K. For those interested in more precise

values, S is listed in Table 7 of Appendix D along with values of (dS /dX)

3

_ 4

3 T

for temperatures below 1. 5°K and X between 10 and 0. 3. The horizontal

line drawn in the columns for X > 0. 064 indicates the location of the solubility curve. The only uncertainty in S comes from the specific heat. The

weakly interacting Fermi-Dirac gas model fits the measured specific heat

to within experimental error; thus, the experimental uncertainty of about

1 --2 percent is all that carries over to the calculated specific heat and

entropy. The ideal Fermi-Dirac gas chemical potential \l is listed in

Table 8 since it may be useful for certain calculations.

The enthalpy H from (20) is shown in figure 8 and also compared

with H °. Again more precise values are listed in Table 9 of Appendix D.

It is evident from figure 8 that (dH /dX) changes sign at about 0. 2°K and

that H for X < 0. 064 becomes less than H ° for temperatures below 0. 1°K.

The effect of these two occurrences on the dilution refrigerator will be discussed in section 4.3. The enthalpy values contain an additional uncertainty

not found in the specific heat and entropy, namely, the uncertainty in

|i '. It can be speculated that the resulting uncertainty in H for high

temperatures will never be larger than the order of 5 percent. The

greatest uncertainty will be for large concentrations. For concentrations

much less than 6. 4 percent the error in H should be less than about

0. 2 joules/mole at all temperatures. On and very near the solubility

curve, H will be nearly as accurate as the specific heat and entropy.

The osmotic pressure has been evaluated from (24). The results

are shown in figure 9 and listed in Table 10 of Appendix D. Table 10

39
8

v 6

o

E

CO —

=3

O

. 4

Q.

UJ

-2

1

1

1 i

i

1

1

—

%./0

— ^ —

__£-

—

J^/s

—

1 i J_ 1

2 —

0.2

T,°K

0.3 0.4

Figure 8. 3 4 The Enthalpy of He in Liquid He as a Function of

Temperature for Various He Concentrations

40
uo

u

H

O

ao

• Ho

c

<t>

2

• r-f

cu

CD

inw

CD

"CO 2 E

CD H O 6

H >

cu

JJO| c ji

41
also lists values for the expression -[|J (X, T) -|~l °(T=0)] . The fountain

pressure p is shown in figure 9 for comparison with the osmotic pressure.

The dashed line in the figure represents the osmotic pressure of a 6. 4

3

percent solution if the He is treated as an ideal or non-interacting FermiDirac gas. In that case II is given as TIv = 2/3 U , where U is the internal

energy of the ideal Fermi-Dirac gas. It is evident that even weak interactions can change the osmotic pressure considerably. The limiting

values of II at low temperatures are strongly dependent on the shape of

the (-^o

! - L °)/R curve below X = 0. 064 and, consequently, contain fairly

large uncertainties, perhaps the order of 10 percent. Measurements of

the osmotic pressure for temperatures somewhat less than T would then

be extremely useful in determining the exact behavior of |i ' and the interactions. The classical expression [3] for the osmotic pressure

E

TI V = - RT £n(l - X) - p> 4

(65)

E 4 where (J. is the excess chemical potential of He in the liquid solution,

r i E

has been used in the past [ 3 J for high temperatures. The term \l . contributes only a very small part to II at these temperatures and, thus, II

is nearly proportional to T. For temperatures less than the order of

T quantum effects come into play and prevent II from going to zero at

T = 0°K. It is instructive to compare the calculated values of II with experimental results at temperatures of 0.8°K and above. The comparison

E

is most effective if \1 is observed instead of n,because any differences

E E . in P. would be greatly magnified in p. . Figure 10 shows values of p. /R

calculated by (65) from the theoretical results for II V . The dashed lines

give two typical experimental values [ 3, 24] for a temperature of 0. 8°K.

The lack of agreement indicates more experimental results are needed

before any conclusion can be made about the reliability of the calculated

42
0.05

0.04

0.03

o

QC

0.02

0.01

Data of London et a/. (T= 0-8 °K)

T= O °K

-0.01

0.01 0.02 0.03

Figure 10. Behavior of the Excess He Chemical Potential as Deduced

from the Osmotic Pressure of He in He .

43
II, although the uncertainty in II is approximately an order of magnitude

E , less than that of \i /R.

3 4

4. 2 Properties of the Total He - He Solution

Tables 11 through 13 of Appendix D list the specific heat, entropy,

3 4

enthalpy, and excess enthalpy for the total He - He solution. These

3

results are listed as per mole of solution instead of per mole of He as

in the previous section. Figure 11 compares the values of H calculated

from (31) with experimental results [ 11, 26] . In general the agreement

is very good except for high temperatures and concentrations, which is

to be expected from the model used here. It is interesting to note that

EH becomes negative for temperatures less than about 0. 15°K. This

inversion temperature is shown as a function of X in figure 16 (p. 55)

denoted as curve II. Below this temperature, heating, rather than cool3 4

ing, occurs when pure He and He are mixed together to form a solution.

This result, of course, has no bearing on the dilution refrigerator, since

in that case it is not the pure components which are mixed together. The

reverse process, separating a mixture into its two pure components,

does produce some refrigeration and will be discussed in detail in section

4.3.

3 4 The vapor pressure of the He - He solutions, as derived from

(32), are shown in figure 12 and listed in Table 14. The results in

figure 12 show the ratio p/p_° so that curves for several temperatures

can be included on one graph. Again there is good agreement with experimental results [ 27] . The experimental curve shown for 0. 4°K was

taken as the vapor pressure of the concentrated phase, given approximately by p = X p °, The vapor composition used in the calculation of

p is listed in Table 15. Fortunately, X is not very sensitive to W/R for

X larger than about 0. 5. v

44
O

E

3

O

UJX

3 4 Figure 11. The Excess Enthalpy of He - He Solutions as a Function

of He-' Concentration for Various Temperatures.

45
This Work

—• Experimental

OtO

a.

0.3

3 4 Figure 12. The Vapor Pressure of He - He Solutions Divided by the

Vapor Pressure of Pure He^ as a Function of He-*

Concentration for Various Temperatures.

46
The differential heat of vaporization X is derived from (3 5) and

E

Vl

the term X , which represents the deviation from the ideal differential

V-L heat of vaporization, is plotted as a function of X in figure 13. The dashed part of the curves are in the region of X > 0. 3 and so represent interpolations. The assumption was made previously that the solutions could be

treated by regular solution theory to find X from a given value of X at the

temperature T. The relationship between X and X is therefore subjected

to some uncertainty, especially for X less than about 0. 5. The term

X . from (3 5) uses both X and X which would appear to cause an unVl E

V E

certainty in X . However, the term H in (3 5) is very nearly linear in

v£ E X which results in X being practically independent of X. Thus for a

E

given value of X the uncertainty in X is nearly removed. The direct

r n E

experimental results of Sommers [ 28J and results deduced from H

data [ 11] are also shown in figure 13 for comparison.

3 4

4. 3 Applications to the He - He Dilution Refrigerator

The enthalpy H (X , T) and entropy S (X , T) along the lower

solubility curve are listed in Table 16. The maximum heat absorption

rate Q(T, T)/n calculated from (36) is also listed and applies to the case

3 where only pure He is circulated. Plots of H (X , T), H °(T), and

Q(T, T)/n are given in figures 14a and 14b. For temperatures less

than about 0. 04° K the expressions

Q(T, T.)/n

3

= H

3

(XrT) - H^T.) = 9 4 T

2

- 12 T.

2

joules/mole He

3

, (66)

Q(T, T)/n

3

, 82 T

2

joules/mole He

3

< 66 >'

fit the results within 1 percent. These numbers are somewhat smaller

than those given previously by this author [ 29] , since the binding energy

E was changed to fit the latest results [ 9] on the solubility curve. The

experimental behavior of Q(T, T)/n is (83 ± 4) T

2 joules/mole He 3

.

47
X

(D

i—l

o

u

co

H>Q

<u H

<uu

9|0OI/S8|n0p

48
o

E

O

£io3

<

x

H

Z

LJ 5

10

/ V-*/. 7\; /<? Tf 7-;,//

•

// <T)

T, °K

10

Figure 14a. Plots of H

3

(X^, T), H

3 (T), and Q(T, T)/n

3 = H3

(X

t

* T)

- H ° (T) for Low Temperatures.

49
IU

5

2

0> 10°

o A' /r. r;. E J

'^7' ' \

3

T • "7" T"

.

? >

' G1(T,T)/ n

O-3

•* X / >- '/'r/

<

/

1*

5

2

.n

2

10' Id'

T, °K

icr

Figure 14b. Plots of H (X , T), H (T), and Q(T, T)/n for High

Temperatures.

50
2 3 Peshkov [ 1 0] gave the value 100 T joules/mole He from his calculations

using X = 0. 05 as the limiting solubility. The same result would be

reached in the present work by considering a 5 percent solution. Vilches

r i 2

and Wheatley [ 5] also derived the value 82 T , but 5.9 percent was used

as the limiting solubility. The uncertainty of the present results between 0. 004°K and 0. 2°K for H (X , T) and Q(T, T)/n, are estimated to

be about 2 percent, judging from the experimental uncertainties in C , C °, and the solubility curve. Above 0. 2°K the accuracy may not be

quite as good.

For temperatures less than about 0. 010°K considerable uncertainty exists in C °. According to Balian and Fredkin [30] the limiting

temperature dependence of C ° should have the form C °/T = 1/2 A[£n(B/T)] /

. The experimental results [ 31] below 0. 010 °K neither

confirm nor deny this temperature dependence. If this form is correct,

then at sufficiently low temperatures Q(T, T)/n would become zero, though

temperatures less than 10 °K would probably be required. A more

recent theory [32] shows that C °/T approaches a constant value at

3

T = 0°K. A transition of He to a superfluid phase in either the pure or

dilute liquid would also alter the present analysis below the transition

temperature. However, neither of these effects should change the present calculations at 0. 004° K and above.

It is obvious from the curves in figures 14a and 14b that the

3 incoming pure He can be at a much higher temperature than the outgoing

3

dilute He and still provide refrigeration. It can be deduced from (66)

that for temperatures less than about 0. 04°K the refrigeration power

goes to zero when (T /T ) ^ '= 0. 36, where T is the temperature of

& m i Q=0 m

the mixer. More exact values of this ratio are given in Table 16 and

are slightly dependent on T . For small residual heat leaks the limiting

temperature of the mixer is thus determined solely by the inlet

51
3

temperature of the pure He . For example, if the residual heat leak is

_ 5

about 1 erg/min or less for a circulation rate of about 2x10 moles/

sec, then the mixer will reach 0. 005°K for an inlet temperature of

0. 014°K. Unfortunately heat transfer at these low temperatures becomes very poor, and it looks as though considerable research on heat

exchanger properties and design are required to reduce the temperature

3

of the incoming He to this low value.

4 3

Any He in the incoming He stream will reduce the refrigeration

effect as given by (41) for temperatures below about 0. 2°K. For tem4

peratures of 0. 040 °K and below, the influence of He is easily evaluated

since H (X , T) and H °(T.) can be represented as in (66). Figure 15

shows how the concentration of He in the circulated gas stream can

affect the refrigeration capacity in the mixer. The figure shows plots of

2 2

(Q/T )__ obtained from (41) normalized by the quantity (Q/T )„ , mX J m X=l

for various values of the ratio T /T . Values of T /T. near 1. can mi mi

only be achieved with nearly perfect heat exchangers, something quite

difficult at very low temperatures. If it is assumed that the presence

4

of He has no effect on the heat exchange properties, then T. and T

l m

will remain the same for all X and the curves will then show the ratio

(Q) /(Q) . The dashed line in this figure represents the reduction in

refrigeration capacity which would be due only to a reduced amount of

3

He . Obviously this curve is quite different than the more exact curves,

especially for low values of T /T.. Most of this difference is due to m i the fact that some dilute phase with its very high heat capacity must be

4

cooled from T. to T whenever He is present in the incoming stream.

i m

From the curves shown in figure 1 5 it is easy to see the importance of

4

eliminating He from the gas stream, particularly at low temperatures

where Tmi/T. will be low and near its ultimate value. The other curve

in figure 15 shows how the ratio (T /T )^ _ varies with the He m i Q=0

52
en 5 <u

4)Oou

<u NHO

MHu3£ o

J!

w

nj

MINI 4 a o B

.2 piv

XIc

a)u

GO

53
4 concentration in the gas stream. The effect of He on this ratio is

4

fairly small for less than about 50 percent He .

It will now be shown that the fractional change in T itself is m

only slightly larger than the fractional change in the ratio (T /T.)n_ n This fact can only be found from an analysis of the heat exchanger. A

system of several individual heat exchangers of the type used by Vilches

and Wheatley [4] will be assumed, but only the lowest temperature heat

exchanger will need to be analyzed. In the ideal case both the dilute and

concentrated streams will leave the lower heat exchanger at the same

temperature T.. The dilute and concentrated streams enter the heat

exchanger at the temperature T and T, respectively. At low tempera- m b

tures the specific heat of the two streams are C = 107 T joules mole

-1 -1 -1 fi4

deg and C = 25 T joules mole deg . A heat balance is then made

on the heat exchanger, which leads to the condition

(67)

For T /T = 0.36 this becomes dT /T = 0. 11 dT /T . Therefore, mi li mm

T. changes very little for a change in T and the fractional change in

i m

T will be only about 11 percent larger than the fractional change in the m

ratio (T /T.)_ „ at least for (T /T } . near 0.36. The ratio

m i Q=0^ m l Q=0

(T /T.) decreases by about 7. 5 percent when going from X = 0. 7 5 to

X = 1. 0, so T will decrease by about 8. 3 percent for this change in X.

m

In the case where the two streams do not reach the same temperature in

the heat exchanger, the change in T will be slightly less than in the

ideal case.

In figure 16 is shown the locus of points where H = H °, which

3

is designated the inversion curve III. Diluting the He to any point below

54

dT.

i T dT

- n °i i m ) m

T.

i

- u. oil / V T / T

l m
0.02 0.04 0.06 0.08

3 4

Figure 16. Enthalpy Inversion Curves for He - He Solutions. The

inset shows the high temperature end of the curve I.

55
this curve without doing work results in a heating effect, whereas above

this curve a cooling effect takes place. This inversion curve I given by

(BH /dX) = is also shown in the same figure. Below this curve the maxi3 mum cooling effect is achieved by diluting the He no farther than the solu3

bility curve. Above it maximum cooling occurs when the He is diluted as much as possible but still remains above the curve I. To prevent a loss

of refrigeration at temperatures below inversion curve I requires the

3 mixer to have a very small impedance for the flow of He so that dilution

below the solubility curve can not take place. The technique of bringing

about extra dilution above curve I is discussed later. The curve II in

figure 16 was mentioned in section 4. 2, but for completeness is restated

3 4

here. Mixing pure He and pure He such that the resultant solution is at a point below curve II results in heating, whereas cooling results for a

point above curve II.

The concentration in the dilute stream between mixer and still is

shown in figure 17 for various mixer temperatures. These concentra3

tions are for constant u, .. The specific heat Cn . of the He in the dilute

4 ^4

stream is shown in figure 18, also given for various mixer temperatures.

For a mixer temperature of 0°K the specific heat becomes Cp, . = 107. 2 T

-1 -1

joules mole deg in the low temperature limit, which is the same as C for X = 0. 064. The classical value of 5/2 R would hold at high temperatures if the process was at constant II instead of constant p. . Values of

Cp are useful in the design of heat exchangers and so are listed in Table

17 along with X and S for constant [i> for several mixer temperatures.

The vapor pressure of the solution in the still is plotted in figure

19 as a function of still temperature with the mixer temperature as a parameter. The heat of vaporization of the liquid in the still and the

vapor composition (neglecting film flow) are both shown in figure 20.

56
—

1 11

J *> /

/ 1 1

1 /

'

'

1 \ 1

1

I

1

i —

05 /

" / 1>.5 — V

*c / 1

1

-/ /

* /

\ 1

£ - —

* / —

/ — *> /

— Q/

- ^ /

«Vl /

-

o>/

f—

^y

>

n

—

fC" —

——

1 1 1 I

1 1 1 1 1 i I

—

(VI d

o

O

-*

00 <A o CO o ou

u

<0^

hi o c O rth

a

CDu

ti U

*- f- o

"H o

bJO

• i-H h

CVJ O

d

COdCOd

Ho '1 d

CMd

57
o

u3

u

a,£H

oM

u

^

i

03

0)M

-M

nj

0)ftH

0)

iS * x 2

o .2

4)

00

,_6ap |_9|ouu s9|nop * ^q

58
u

O

0.05 -

0.02 —

0.01

Figure 19. The Vapor Pressure of the Liquid in the Still as a Function of Still Temperature for Various Mixer

Temperatures.

co
.00

0.95

0.90

0.85

0.80

075

T

S

,°K

Figure 20. The Heat of Vaporization and the Vapor Composition

(Neglecting Film Flow) for the Liquid in the Still.

60
The heat of vaporization is in joules per mole of solution vaporized.

This figure shows that the optimum still temperature is about 0. 6 to

0. 7°K for mixer temperatures below about 0. 1°K„ Higher still temper4

atures would cause excess amounts of He to be vaporized, whereas

lower temperatures would lower the pumping speed because of lower

vapor pressures.

The change in level of the interface between the dilute and concentrated solutions with a change in mixer temperature is shown in

figures Zla, 21b, and 21c. These results are from the solution of the

equations (49) and (50) for h and are for the case where the heat exchanger and condenser volumes are negligible. The three different

figures correspond to the values 0. 5, 1. 0, and 2. for the ratio r of

still to mixer volume in (45). Curves for still temperatures of 0. 5,

0. 6, and 0. 7°K are shown in each figure. These figures show that the

initial fillinges concentration X for the refrigerator must be within cero tain limits to keep the interface inside the mixer. For h < the mixer

_ m

is flooded with He and the interface will be moved to the still, or possibly the heat exchanger if we assume it has a finite volume. In such

cases the refrigerator would fail to operate. The other case, h > 1, m

may not be quite as serious. What actually happens when h becomes

greater than 1 is that the dilute solution which completely fills the mixer

is further diluted from its equilibrium value. The mixer is then said to

3

be starved for He . If this occurs at temperatures greater than 0. 15°K -

above the inversion curve I in figure 16 -then an increased cooling effect

3

results as the pure He enters the mixer in a process analogous to flash

evaporation. However, special precautions would have to be taken (perhaps an orifice at the mixer inlet) to insure that the dilution takes place

3

in the mixer and not in the He side of the heat exchanger. Dilution in

3

the He side of the heat exchanger will still cause the mixer to cool

61
TS =0.7°K

0.2 Tm,°K

0.4 0.6

Figure Zla. The Fraction of the Mixer Filled^with Dilute, Slolution as a

stion of Mixer Temperature for the Case V s / mc Funct

62
Figure 21b. The Fraction of the Mixer Filled with Dilute Solution as a Function of Mixer Temperature for the Case V /V = 1.

63
Figure 21c. The Fraction of the Mixer Filled with Dilute Solution as a Function of Mixer Temperature for the Case V /V = 2. c s mc

64
although the "effective" heat exchanger is shortened and leads to a lower

efficiency. It is probably best to try to keep h < 1 for all temperatures m

below about 0. 6°K since there usually is no need to achieve extra refrigeration above 0. 15°K.

The level of the interface in the mixer will also influence the

time constant of the mixer regarding temperature changes. Since pure

3 3

He has a much higher specific heat than the diluted He on a volume

basis, a small value of h gives a higher time constant. This is more m ° expensive as it requires more He in the system but may be desirable for

maintaining very uniform temperatures in the mixer.

Nothing has been said yet about the variation of h with change in

mixer temperature. This was also evaluated from equations (49) and (50)

but the variation is very small. The value of h increases with decreasing

s mixer temperature though the value is always within 5 percent of 1. When the volumes of the heat exchangers and the condenser are not

negligible compared with the still and mixer volumes, then the curves in

figuresZla, 21b, and 21c are no longer valid. Exact solutions in this case

can not be made unless the temperature distribution is known throughout

the dilute side of the heat exchanger. It is possible, however, to make an

approximate analysis and still use the curves in figures 21a, 21b, and

21c. The assumption that must be made is that the concentration in the

dilute stream decreases linearly between the mixer and still. The linear

decrease must be with respect to volume and not distance. This assumption is reasonable when one examines the curves in figure 17 along with

temperature distributions in typical dilution refrigerators [1,4]. With

this linear decrease in concentration it is possible, for computational

purposes, to assign one half of the dilute side heat exchanger volume to

be included with the mixer and the other half with the still. All liquid

volumes in the condenser and the concentrated side of the heat exchanger

65
are added to the mixer volume. A new value of the ratio V /V is

s mc

calculated from the revised still and mixer volumes and then the appropriate graph, figure 21a, 21b, or 21c, is used. The bottom and top of the

mixer now no longer correspond to the values and 1 for h . The value m

of h corresponding to the bottom of the mixer is equal to one half the

dilute side heat exchanger volume divided by the total revised mixer

volume. By adding to this the ratio of actual to revised mixer volumes,

the value of h corresponding to the top of the mixer can be obtained, m

To be sure the method of correcting for heat exchanger volumes

is clear, consider an example where the volume of liquid in the still and

3

the mixer volume are each equal to 4 cm , the heat exchanger volume

3

filled with dilute liquid is 3 cm , and the volume of concentrated liquid in

3

the condenser and heat exchangers is 2 cm . The revised still volume

3

now becomes 4 4- l/2 • 3 = 5. 5 cm and the revised mixer volume becomes

4 + 1/2 • 3+2=7.5 cm

3

. The revised ratio V /V =5. 5/7. 5 = 0. 73 is

s mc

obtained. Interpolation between figures 21a and 21b is simple since hm

varies linearly with the ratio V /V . The bottom of the mixer now

s mc

corresponds to the value of h = l/2 • 3/7. 5 = 0. 2. The top of the mixer

m

is represented by h = 0. 2 + 4/7. 5=0. 73. For T = 0. 6°K the mixer m ' • s will now be flooded with pure He at T = 0°K when X > 0. 40 and be

- m o starved for He at T = 0. 6°K when X < 0. 38. Fortunately, it turns out m o

that almost identical results would be obtained no matter how the dilute

side heat exchanger volume is divided between the still and mixer to

arrive at the revised volumes. In the example it would probably be best

to make X somewhat less than 0. 4, possibly 0. 3 to 0. 35, as insurance

against the interface passing out through the bottom of the mixer due to

slight uncertainties in the volumes used in the calculations. At the higher

3 temperatures the mixer will become starved for He , but experiment [ 1]

shows that the refrigerator should still work at these temperatures. The

66
interface could be kept in the mixer at all tempeatures by starting with a

3

fairly high X and then removing some He from the overall system as T decreases, m

An alternative but equivalent way of treating the volume of the

concentrated side of the heat exchanger is to neglect it completely at

first in the calculation of revised V /V . The system is then filled

s mc

with a solution that has a concentration determined as follows: First,

the desired concentration is read from the appropriate graph of h versus

T . The amount of this solution added to the system is just that required

to fill all but the volume of the concentrated side of the heat exchanger.

3

This heat exchanger volume is then filled with pure He and makes the

resulting solution the same concentration as calculated by the first method.

However, this second method shows that the volume of concentrated solution above the mixer has no effect on the behavior of h with T , which m m

should be fairly obvious. It is only the dilute side heat exchanger volume

which when large can cause a rapid variation of the interface level with

T . m

The transient behavior of the single -cycle dilution refrigerator is

shown in figure 22a for values of the constants in (55) matching those of

experiments by Vilches and Wheatley [ 5] . They used an original concentration of X = 0.85 so the term

o

n 1 - X

--T—5T , (68) n 1 - X„

o I

which is valid below about 0. 20 °K, is about 0. 160 below 0. 1°K. The

limiting temperature used for the calculation of Q/n was taken as

0. 0048 °K. Our calculated behavior of T shows very good agreement with

experiment for a starting temperatue of 0. 032°K. For a starting temperature of 0. 11°K the agreement is not so good, possibly because the

67
u o• r-i M U o ^ m tf 2 o

.§ 3

ft

Q

X

M

w «

njU

<u

O bo o •£> O <D U CQ

0)

&0 h

68
approximations made for n and C is this temperature range. The heat

capacity of the cerium magnesium nitrate may be important when n

becomes small but has been neglected in these calculations. Any nonequilibrium conditions of the experiments could also produce the discrepancy noted above.

Vilches and Wheatley [ 5] made the approximation that 6=0 and

n = to arrive at the equation

T n a AT/T = ^An

3

/n

3 or — = [-± j , (69)

i o

where they calculated oi = 3. 3. With the same approximation the present

calculations lead to a = 3. 2 at T = 0°K and about 3. 8 at 0. 1°K. Finite

values of Q and n reduce ot, and the reduction can be significant for low

starting temperatures. Figure 22b shows the complete solution of (55)

for various arbitrary parameters. It is evident from this figure that

millidegree temperatures can be reached by this single-cycle process

even when starting at temperatures as high as 0. 3°K.

The curves for S in figure 7 indicate that the refrigeration

capacity of the dilution refrigerator can be greatly increased if reversible

dilution can be done at concentrations considerably below the solubility

curve. There are two techniques by which this extra dilution can be

3 carried out. The first is by the removal of He from a dilute solution,

such as in the case of continued pumping in a single -cycle dilution refrig3

erator after all of the pure He phase has been removed. This could be

3

called a He extraction refrigerator. The second case is accomplished

4

by adding pure He to a dilute solution in such a way to make the process

reversible. This technique has been carried out experimentally [ 33] and

temperatures of about 0. 15°K were reached.

69
o• Hoa

60a£

Pi o

0)DM

ftos<

i-H

aiO

•t-i U

nJ

ft

0) ,3H

0)

60

a)H

El +J

nJ

ftsH

a) .3

70
In the first case the refrigeration rate is given by (59). For

T = constant and for concentrations along the solubility curve, this heat

absorption is less than the expression H (X , T) - H °(T). For

<

5 15 2

T ~ 0. 1 T the isothermal heat absorption rate can be expressed as aT , where a = -Q/(n, T ) increases for decreasing X as shown in figure 23.

For X < 0. 04 the extraction process has a higher refrigeration rate than <

the single -cycle dilution refrigerator. When X « 1 and T ~ 0. 1 T., the

entropy is given by

2/3 T : _,_ „, -1 ,_

"I

S = 16, X T joules mole deg

(70)

At X = 0. 064 this expression is about 7 percent smaller than the correct

value, and at X = 0. 01 it is about 1 percent too low. Therefore it follows

from (59) and (7 0) that in this range of X and T, the following approximation

can be made:

-2/3 2 3 Q/n

3 = - 10. 7 X ' ( 1 - X) T joules/mole He , , ?1)

for T = constant. Hence, Q approaches infinity as X goes to zero. Of

3

course it is impossible to remove all of the He in this process. When3

ever the He concentration in the still becomes less than about 0. 05 per3

cent, the He vapor concentration at 0. 6°K drops off very rapidly and

3 makes it impossible to remove any more He from the system. With this

still concentration and temperature the solution in the mixer (or extractor)

3

will contain about 1 percent He . At this concentration the refrigeration

rate is about 2. 7 times that of the single-cycle dilution refrigerator. Two

disadvantages of this new technique are that the extractor must be very

3

large to contain an equivalent amount of He and that the refrigeration

rate does not remain constant.

The total amount of heat absorbed in going from the concentration

X. to X at T = constant is given by (60). For X. = 0. 064 and X = ,

71
300

0.02 0.03 0.04 0.05 0.06

X

0.07

Figure 23. A Plot of the Term -(0. 0l/T)(3S /dX) and the Heat

Absorption Rate in the He Extraction Refrigerator

for T ~ 0. 1 T .

72
2

a finite amount of heat is removed which is approximately AQ/n = 190 T

3 ° 2 joules/mole He . For X. = 0. 064 and X = 0. 01, then AQ/n = 86 T joules/

3

if o mole He . If the process is carried out adiabatically instead of is other

< mally, the path S = constant is followed. For X « 1 and T ~ 0. 1 T the

temperature may be expressed from (70) as

T/T. = (X/X.) 2/3

f (?2)

4

since the entropy of the He can always be neglected at least for X > 0. 01.

For X. = 0. 064 and X = 0. 01 then T/T. = 0. 290 from (72), whereas the

i i exact value from constant S is 0. 306. Comparing (72) with (69), it is

seen that the extraction refrigerator cools less for the same number of

3 moles of He removed than does the single -cycle dilution refrigerator.

This is a result of the high specific heat of the dilute solution.

The second method of producing reversible dilution below the

4

solubility curve is carried out by adding pure He through a superleak to

3 4

a dilute solution of He - He . The osmotic pressure is then balanced by

4

the fountain pressure of the pure He at a higher temperature so that the

4

pure He and the dilute solution will be in equilibrium. Taconis et al.

[33] then apply a pressure to the pure He by collapsing a bellows around

4 4

the liquid He . This additional pressure then causes the He to flow through

3

the superleak and into the dilute solution. A He cryostat is attached to

4

the long superleak to precool the He before it enters the dilute solution.

In principle there is no reason that an external force has to be applied to

4 4

the pure He . Simply by lowering the temperature of the pure He the

4

fountain pressure is reduced, thereby causing the He to flow through the

superleak to the dilute solution. However, much higher flow rates can be

achieved when applying an external pressure. The refrigeration rate for

this type of dilution refrigerator is given by (63) and depends on the rate

4 <

at which He is added. The derivative - (0. 0l/T)(SS

3

/BX) T

for T ~ 0. 1 T

f

73
is shown in figure 23 and can be put in (63) to find Q/ n . For small X

and T = constant this becomes approximately

Q/n

4

= 10.7 X

1/3 T

2

- [H

4

°(T.) - H °(T)] joules/mole He

4

. (73)

The general behavior of this refrigerator in the adiabatic case can

be worked out by solving (63) and for the case Q = 0. The general solution,

however, is quite difficult to obtain and is not given here. Of greater

interest is the low temperature limit of this refrigerator, which is a special case of the general adiabatic behavior where the condition dT/dX =

2

holds. This limit appears as the solution to - X T(3S /dX) = H °(T.) - H °(T), which follows from (63). Usually H °(T) can be replaced with H °(0), since T is considerably smaller than T. and H ° goes

4

l 4 as T . There will be a locus of points in the S versus T diagram for

2

- X T (SS /BX) with the same value. A second equation gives another

curve in the S versus T diagram and the intersection of the two curves

is the solution sought. This second equation gives the approximate final

entropy; the exact entropy is found only from the general solution just

discussed. The approximate final entropy is found from AS %H °(T.)/

X T ), where X is the final concentration and T is the average

i ave f ave

temperature defined by T AS = T dS A reasonable guess is needed

ave 3

3' for T since the general behavior is unknown. The final calculated

ave

entropy is only approximate, but the solution for the ultimate temperature

is quite insensitive to the final entropy. Results will be given for the

case where the starting temperature and the temperature of the incoming

4

He is 0.4°K and for the case where these two temperatures are 0. 05°K.

3 These temperatures would correspond to a first stage composed of a He

3 4 refrigerator in the first case and a continuous He - He dilution refrigerator in the second case. In each case the starting concentration lies on

74
the solubility curve. For the 0. 4°K case the value T =0. 1°K is used

ave

and the ultimate temperature is found to be T = 0. 032 °K, which is

u

reached at X„ = 0. 0022. In the 0. 05°K case it is assumed that T =

f ave

0. 002°K which then leads to T =0. 0006°K and X„ = 5 x 10~ . These

u f ultimate temperatures contain a small uncertainty due to T , but using

T = T. would decrease T by only about 10 percent and using T = T

ave l u ave u

would increase T by about 20 percent. The addition of any more He^

after T is reached causes heating rather than cooling.

5. Conclusions

It can be concluded that the weakly interacting Fermi -Dirac gas

3 4 model gives an excellent description of He in liquid He for concentrations

less than about 15 percent with a good approximation to about 30 percent

and for all temperatures below the lambda point. The major uncertainty

3 results from a limited knowledge of the interaction between He atoms.

Further experiments at temperatures below about 0. 5°K are necessary to

better evaluate this interaction. The thermodynamic properties of both

3 4

He in He and the total solution have been derived from this model, but

for the latter the properties are good only for temperatures below about

1. 2 to 1. 5°K. In nearly every case the calculated properties agree very

well with all existing experimental data, especially for concentrations

less than about 15 percent. In general,the calculated thermodynamic

properties should be accurate to about 5 percent and in some cases to

within 1-- 2 percent. These properties have been used to accurately de3 4

scribe the behavior of the He - He dilution refrigerator for temperatures

below 0. 6°K. The calculated values of the heat absorption rate below

about 0. 1°K agrees with the measured value in this range. The calculated

transient behavior of the single-cycle dilution refrigerator is in reasonable

agreement with experimental results. Millidegree temperatures could be

maintained for reasonable time periods by this single-cycle dilution

75
refrigerator starting at temperatures as high as 0. 3°K. Two new types

of dilution refrigerators have been analyzed and could be useful in certain

situations.

Acknowledgments

The author wishes to thank Mr. T. R. Strobridge, Dr. J. D.

Siegwarth, and Professor David Edwards for many valuable discussions

concerning this work. I am grateful to Professor David Edwards and to

Dr. David Rorer for communicating their latest results of measurements

3 4

on the solubility of He in He prior to publication.

This work was carried out while the author was a National Academy

of Sciences - National Research Council Postdoctoral Resident Research

Associate at the National Bureau of Standards.

76
6. References

1. Hall, H. E. , P. J. Ford, and K. Thompson, Cryogenics 6, 80

(1966).

2. Neganov, B. , N. Borisov, and M. Liburg, Zh. Eksperim. i. Tear. Fiz. _50, 1445 (1966) L English transl. : Soviet Phys. - JETP 23, 959 (1966)]; Borisov, N. S. , N. I. Kvitkova,

Mo Yu Liburg, B. S„ Neganov, and F. A. Tagirova, Tenth

International Conference on Low-Temperature Physics,

Moscow, (1966).

3. London, H. , G. R. Clarke, and Eric Mendoza, Phys. Rev. 128 , 1992 (1962); London, H. Proceedings of the International

Conference on Low- Temperature Physics , Oxford (Claredon

Laboratory, 1951), p. 157.

4. Vilches, O. E„, and J. C. Wheatley, to be published and private

communication.

5. Vilches, O. E., and J. C. Wheatley, Phys. Letters 24A, 440(1967).

6. Taconis, K. W. , and R. de Bruyn Ouboter, in Progress in LowTemperature Physics, edited by J. C. Gorter (North-Holland

Publishing Company, Amsterdam, 1964), Vol. IV, p. 38.

7. Edwards, D. O. , D. F. Brewer, P. Seligman, M. Skertic, and

Yaqub, Phys. Rev. Letters 15, 773 (1965).

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and J. C. Wheatley, Phys. Rev. Letters 17, 367 (1966);

Anderson, A„ C. , W. R. Roach, R. E. Sarwinski, and J. C.

Wheatley, Phys. Rev. Letters 16, 263 (1966).

77
9. Ifft, E. M. , D. O. Edwards, R. E. Sarwinski, and M. M. Skertic,

Phys. Rev. Letters 1_9, 831 (1967). Rorer, D. C. (private

communication) from Brookhaven National Laboratory has also

reported a tentative value of 6. 4% as the limiting solubility at

0°K from neutron transmission measurements.

10. Peshkov, V. P. , Tenth International Conference on Low- Temperature

Physics, Moscow, 1966; Zh. Eksperim. i. Teor. Fiz. 51, 1821

(1966) [ English transl. : Soviet Phys. - JETP 24, 1227 (1967)] .

11. Bruyn Ouboter, R. de, K. W. Taconis, C. Le Pair, and J. J. M.

Beenakker, Physic a 26, 853(1960).

12. Brewer, D. F. , and J. R. G. Keyston, Phys. Letters 1_, 5(1962).

13. Graf, E. H. , D. M. Lee, and J. D. Repply, Phys. Rev. Letters

1_9, 417 (1967).

14. Landau, L. D. and I.Pomeranchuk, Dokl. Akad. Nauk SSSR 59,

669 (1948); I. Pomeranchuk, Zh. Eksperim. i. Teor. Fiz. _19,

42 (1949).

15. Das, P., R. de Bruyn Ouboter, and K. W. Taconis, in Proceedings of the Ninth International Conference on Low- Temperature

Physics, Columbus, Ohio, 1964, edited by J. G. Daunt, D. O.

Edwards, F. J. Milford, and M. Yaqub (Plenum Press, Inc. , New York, 1965). Vol. B, p. 1253.

16. Landau, L. D. , Zh. Eksperim. i. Teor. Fiz _30, 1058(1956)

[English transl. : Soviet Phys.- JETP 3, 920 (1957)]. Ebner,

C. (Ph. D. thesis, Department of Physics, University of

Illinois, Urbana, Illinois, 1967) in a more exact treatment

finds a very small difference (^ 1%) between the specific heat of

an ideal and a weakly interacting Fermi-Dirac gas.

78
17. Bardeen, J., G. Baym, and D. Pines, Phys. Rev. 156 , 207 (1967).

18. Kerr, E, C. , Low -Temperature Physics and Chemistry, edited by

J. R. Dillinger (University of Wisconsin Press, Madison,

Wisconsin, 1958), p. 158; Kerr, E. C, and R. D. Taylor,

Ann Phys. 2_6, 292 (1964).

19. Ebner, C. , Phys. Rev. 156, 222 (1967).

20. Stoner, Edmund C. , Phil. Mag. 25, 899 (1938).

21. Abel, W. R. , R. T. Johnson, J. C. Wheatley, and W. Zimmerman,

Jr., Phys. Rev. Letters 18, 737 (1967).

22. Kilpatrick, JohnE., William E, Keller, and Edward F. Hammel,

Phys. Rev. 97, 9 (1955); Kilpatric, JohnE., William E. Keller,

Edward F. Hammel, and Nicholas Metropolis, Phys. Rev. 94, 1103 (1954).

23. Bruyn Ouboter, R. de, J. J. M. Beenakker, and K. W, Taconis,

Physica25, 1162(1959).

24. See discussion by E. Mendoza, in Helium Three , edited by J. G.

Daunt (Ohio University Press, Columbus, I960), p. 150

25. Ruhemann, M. , The Separation of Gases (Oxford University Press,

London, 1949) 2nd edition, p. 96.

26. Sommers, H. S., W. E. Keller, and J. G. Dash, Phys. Rev. 91_,

489 (1953) and 92, 1345(1953).

27. Sydoriak, S. G. and T. R. Roberts, Phys. Rev. 118 , 901 (I960).

28. Sommers, H. S. , Phys. Rev. 88, 113 (1952).

29. Radebaugh, Ray, Bull. Am. Phys. Soc. L2, 919 (1967).

30. Balian, R. and D. R. Fredkin, Phys. Rev. Letters 15, 480(1965).

79
31. Abel, W. R. , A. C. Anderson, W. C. Black, and J. C. Wheatley,

Phys. Rev. 147 , 111 (1966).

32. Amit, D. J , J. W. Kane, and H. Wagner, Phys. Rev. Letters

19, 425 (1967).

33. Taconis, K. W. , P. Das and R. de Bruyn Ouboter, Xllth International Congress of Refrigeration, Madrid, Spain, 1967.

34. Committee on Fundamental Constants of the National Academy of

Sciences - National Research Council, Natl. Bur. Std. (U.S.)

Tech. News Bull. 47, 175 (1963).

35. Anderson, A. C. , W. Reese, and, J. C. Wheatley, Phys. Rev.

130, 495 (1963).

36. Strongin, M. , G. O. Zimmerman, and H. A. Fairbank, Phys.

Rev. Letters 6, 404 (1961); Phys. Rev. 128 , 1983 (1962).

37. Sydoriak, S. G. , T. R. Roberts, and R. H. Sherman, J. Res.

Natl. Bur. Std. (U.S. ) 68A, 559(1964). The third term in

2

their equation (3b) should be changed from 0. 54064 T to

0. 54206 T

2

.

38. Roberts, T. R. , R. H. Sherman, and S. G. Sydoriak, J. Res.

Natl. Bur. Std. (U.S.) 68A, 567(1964).

39. Wiebes, J., C. G. Niels -Hukkenberg, and H. A. Kramer,

Physica 23, 625 (1957).

40. Kramers, H. A. , J. D. Wasscher, and C. J. Gorter, Physica 1_8,

329 (1952).

41. van Dijk, H. and M. Durieux, in Progress in Low -Temperature

Physics , edited by J. C. Gorter (North- Holland Publishing

Company, Amsterdam, 1957), Vol. II, p. 431.

42. Edwards, D. O. and J. G. Daunt, Phys. Rev. 124, 640 (1961).

80
7 . Appendix A

Specific Heat of a Fermi-Dirac Gas

It was found necessary to divide the specific heat data of Stone

[ 20J for a Fermi-Dirac gas into three temperature regions before a satisfactory power series fit could be obtained. The three regions used

are: (a) T/T * 0. 1 5, (b) 0. 15 < T/T * 0. 7, and (c) T/T > 0. 7. The

asymptotic series given by Stoner for T/T ~ 1 is used for region (c) and

fits the data to within 0. 01 percent. The other two regions were fitted by

least squares with a resulting maximum error of 0. 01 percent in region

(a) and 0. 02 percent in region (b). The specific heat in each region is

given by the following equations with t = T/T :

t £ 0. 15, C /R = 4.934802 t - 14.400636 t 3

- 167.8453 t 5

- 4313.735 t 7 + 203138.64 t 9

; (74)

0. 15 <t ^ 0. 7, C /R = - 0. 133181 + 7.494399 t - 15.901203 t 2

v

+ 12. 856768 t 3 + 8. 691396 t 4

- 22. 741195 t 5

+ 11.466865 t 6

j (75)

t > 0. 7, C /R = 3/2 - 0. 09973557 t~

3' 2 + 0. 00560236 t"

- 0. 00024872 t~

9' 2

. (76)

81
8. Appendix B

3 4

Physical Constants and Properties of Pure He and He

Values of various physical constants used in these calculations

were taken from the latest recommended [ 34] results wherever possible.

Some of the more important constants along with some basic properties

3 4

of pure He and pure He are given in table 3.

The calculation of the various thermodynamic properties of pure

3 4

He and pure He requires a knowledge of the specific heat of each.

3 Considerable data exist for pure He and a somewhat arbitrary decision

was made as to which data are most reliable and representative of the

3

specific heat of pure He . For 0. 006 < T < 0. 50°K the data of Abel

et al. [31] were used. A combination of data [3 5, 36] were used for the

region 0.1 <T < 0. 3 °K and a smooth curve was drawn between the two

regions to bridge the gap in which data [3 5] might be unreliable [ 31] . Above 0. 5°K the analytical curve suggested by Sydoriak et al. [ 37] was

used and again a smooth curve was drawn between the gap of 0. 3°K to

0. 5°K. A power series fit was made to the smooth curve between and

2°K to facilitate computer calculations of thermodynamic properties.

The smooth curve was divided into three regions and the resultant power

series fit is shown below:

2 „ 3 < T ^O. 2°K, C ° = 25. 333T - 87.475 T + 284. 618 T

4 5 -1-1

1097.33 T + 1903. 57 T joules mole deg

(77)

2

0. 2 < T ^0. 5°K, C ° = - 1. 2846 + 48. 3061 T - 228. 9698 T

+ 556. 0303 T

3

- 666.821 T

4

5 -1-1 + 315. 642 T joules mole deg ; (78)

82
2

0. 5 < T £ 2°K, C ° = 2. 0914 + 3. 948 T - 4. 5068 T

3 4 + 3. 37857 T - 0. 68783 T joules

mole deg . (79)

The expression in (79) was taken from the work of Sydoriak et al. [ 37]

The accuracy of the data upon which the results of (77) through (79) are

based is probably not much better than about 2-- 5 percent. Table 4 lists

the specific heat, entropy, enthalpy, chemical potential,and the heat of

3 vaporization of pure He . The heat of vaporization was found from interpolation of the data given by Roberts et al. [ 38] , whereas all of the other

properties are calculated from the specific heat in equations (77) through

3

(79). The enthalpy of pure He has arbitrarly been set to zero at T = 0°K

and then used as a reference point in all other calculations in this paper.

4 The specific heat of pure He is taken from the work of Wiebes

et al. [ 39] for T < 0. 055°K and from the work of Kramers et al. [ 40]

for 0. 85 ^ T ^ 1. 5°K. A smooth curve was drawn between the two regions.

3 Below 0. 55°K the specific heat is given by [ 39] (0. 0817±0. 0016) T joules

-1 -1 4 mole deg . All of the thermodynamic properties of He except the

heat of vaporization are deduced directly from the specific heat. The

4

fountain pressure of pure He is given by

P

f = d/V

4

) j S

4

° dT= -(1/V

4

°)[M °(T)-u

4

°(0)] . (80) o

4 The heat of vaporization of He as a function of temperature was calculated

from the work of van Dijk and Durieux [ 41] using their equation (18). The

4 various thermodynamic properties of pure He are listed in Table 5.

83
Table 3

Some Physical Constants and Basic Properties of Pure

He and He used in this Work

Constant Symbol Value

Avogadro constant

Planck constant

N

A

23 -1

6. 02252 x 10 mole

-34

1. 05450 x 10 joules sec

Gas constant R 8. 3143 joules mole 'K

-1

Boltzmann constant K -23

1.38054x10 joules "K1

3

mass of He atom m

3

5. 00792xl0" 24

g (a)

Molar Volume of Liquid

He 3at 0°K 3 -1 V 36. 83 cm mole (b)

Heat of Vaporization of

He 3 at 0°K L ° 20. 56 joules mole

3

(b)

mass of He atom m

4

6. 64605xl0"

24

g (a)

Molar Volume of Liquid

He 4 at 0°K V4°

3 -1

27. 58 cm mole (c)

Heat of Vaporization of

He 59. 62 joules mole 4 at 0°K V (d)

Velocity of Sound in Liquid

He 4 at 0°K s 4 -1 2.3827x10 cm sec (e)

4 Enthalpy of Liquid He at

0°K (with respect to He ) " (L

4 •- v> -39. 06 joules mole

(a) Handbook of Chemistry and Physics, 45th ed. , 1964-1965, The

Chemical Rubber Co. , Cleveland, Ohio, p. B-6.

(b) T. R. Roberts, R. H. Sherman, and S. G. Sydoriak, J. Res.

Natl. Bur. Std. (U.S. ) 68A, 567(1964).

(c) E. C. Kerr and R. D. Taylor, Ann. Phys. 2_6, 292 (1964).

(d) F. G. Brickwedde, H. van Dijk, M. Durieux, J. R„ Clement, and

J. K. Logan, J. Res. Natl. Bur. Std. (U.S. ) 64A, 1 (I960).

(e) W. M. Whitney, and C. E. Chase, Phys. Rev. Letters 9, 243 (1962).

84
TABLE 4 THERMODYNAMIC PROPERTIES OE PURE HE3 RELOW 1.5°K

T V V V - U3° L

3 °(T)

<°K> (J/MOLE-K) (J/MOLF) (J/MOLE-K) (J/MOLE) (J/MOLE)

0.000 0.00000 0.0000*000 0.00000 0.0000*000 20.56

O.0O1 0.02525 1.2637-005 0.02529 1.2652-005 20.58

0.002 0.05032 5.C434-005 0.05049 5.0550-005 20.60

0.003 0.07522 1.1322-004 0.07561 1.1361-004 20.62

0.004 0.09995 2.0082-004 0.10064 2.0174-004 20.64

0.006 0.14R91 4.4979-004 0.15044 4.5288-004 20.68

0.00H 0.19721 7.9601-004 0.19991 8.0329-004 20.72

0.010 0.24486 1.2382-003 0.24905 1.2523-003 20.76

0.012 0.29187 1 .7750-003 0.29786 1.7993-003 20.80

0.01* 0.33826 2.4052-003 0.34634 2.4435-003 20.84

0.016 0.38403 3.1276-003 0.39450 3.1R44-003 20.88

0.01B 0.42920 3.9410-003 0.44235 4.0213-003 20.91

0.020 0.47378 4.8440-003 0.4P988 4.9536-003 20.95

0.Q25 0.58269 7.4867-003 0.60737 7.6975-003 21.05

0.030 0.68810 1.0665-002 0.72297 1.1024-002 21.15

0.035 0.79nl5 1.4362-002 0.83675 1,4924-002 21.25

0.0*0 0.88*96 1.8561-002 0.94875 1.9389-00*: 21.35

O.Q*5 0.98464 2.3247-002 1.05901 2.4409-002 21.44

0.050 1.07728 2.8403-002 1.16757 2.9976-002 21.54

0.060 1.25381 4.0068-002 1.37976 4.2718-002 21.74

o.o^o 1 . 41916 5.3441-002 1.58559 5.7550-002 21.93

0.080 1.57382 6.8415-002 1.7853] 7.4409-002 22.12

0»090 1.71815 8.4883-002 1.97911 9.3236-002 22.31

0.100 1 .85P47 1 .0274-001 2.16717 1.1397-001 22.51

0.120 2.09196 1.4225-001 2.52667 1.6095-001 22.89

0.1*0 2.29393 1.8617-001 2.86478 2.1490-001 23.27

0.160 2.46017 2.3377-001 3.1P233 2.7540-001 23.64

0.180 2.59T40 2.8436-001 3.48010 3.4206-001 24.02

0.200 2.69796 3.3732-001 3.7589R 4.1448-001 24.39

0.250 2.87276 4.7707-001 4.38195 6.1842-001 25.30

0.300 2.97853 6.2350-001 4.9156? 8. 5U9-001 26.20

0.350 3.06486 7.7461-001 5.38133 1.1089*000 27.09

0.400 3.15017 9.2998-001 5.79613 1.3885+000 27.97

0.450 3.23568 1.0896*000 6.17213 1.6878+000 28.85

0.500 3.31729 1 .2535+000 6.51731 2.0052*000 29.72

0.550 3.39*66 1.4214*000 6.83734 2.3391*000 30.58

0.600 3.47838 1.5933+000 7.13648 2.6886*000 31.42

0.650 3.55853 1.7692+000 7.41806 3.0525*000 32.24

0.700 3.64037 1.9492+000 7.68476 3.4301*000 33.05

0.750 3.72503 2.1333+000 7.93878 3.8208*000 33.84

0.800 3.81354 2.3218+000 8.18199 4.2238*000 34.61

0.650 3.90685 2.5148+000 8.41596 4.6388*000 35.36

0.900 4.00578 2.7126*000 8.64204 5.0653*000 36.10

0.950 4.11107 2.9155+000 8.86142 5.5029*000 36.81

1.000 4.22334 3.1238+000 9.07511 5.9513*000 37.51

1.100 4.47080 3.5582+000 9.48899 6.8797*000 38.84

1.20C 4.75109 4.0190+000 9.88977 7.8487*000 40.08

1.300 5.06552 4.5096+000 10.28225 8.8573*000 41.23

1.400 5.41370 5.0333+000 10.67018 9.9050*000 42.29

1.500 5.79363 5.5934+000 11.05647 1.0991*001 48.86

Page 8 5
TABLE 5 THERMODYNAMIC PROPERTIES OF PURE HE4 BELOW 1.5°K

T <Y

(<K) (J/MOLE-K)

.000 0.000*000

.001 8.170-011

.002 6.536-010

.001 2.206-009

.004 5.229-009

.006 1.765-008

.008 4.183-008

,010 8.170-008

.012 1.412-007

.014 2.242-007

.016 3.346-007

,018 4.765-007

.020 6.536-007

,025 1.277-006

.030 2. 206-006

,03? 3.503-006

.040 5.229-006

.045 V. 445-006

.050 1.021-005

.060 1.765-005

.070 2.802-005

.080 4.183-005

.090 5.956-005

.100 8.170-005

.120 1.412-004

.140 2.242-004

.160 3.346-004

.180 4.765-004

.200 6.536-004

.250 1.277-003

.300 2.206-003

.350 3.503-003

.400 5.229-003

.450 7.445-003

.500 1.021-002

.550 1.359-002

.600 1.773-002

.650 2.439-002

.TOO 3.570-002

.750 5.488-002

.800 8.594-002

.850 1.334-001

.900 2.019-001

.950 2.958-001

1 .000 4.191-001

1 .100 7.695-001

1 .200 1.290*000

1 .300 2.045*000

1 .400 3.114*000

1 .500 4.531*000

H

4

°(T) - H

4

°(0) (J/MOLE)

000*000

043-014

268-013

654-012

229-012

647-011

366-011

042-010

235-010

846-010

339-009

144-009

268-009

979-009

654-008

065-008

229-008

376-008

277-007

647-007

904-007

366-007

340-006

042-006

235-006

846-006

339-005

144-005

268-005

979-005

654-004

065-004

229-004

376-004

277-003

869-003

647-003

686-003

163-003

386-003

085-002

625-002

454-002

687-002

461-002

128-001

142-001

786-001

337-001

013*000

(J/MOLE-K)

0.000*000

2.723-011

2.179-010

7.353-010

1.743-009

5.882-009

1.394-008

2.723-008

4,706-008

7.473-008

1.115-

1.588-

2.179-

4.255-

7.353-

1.168-

1.743-

2.482-

3.404-

5.882-

9.341-

1.394-

1.985-

2.723-

4.706-

7.473-

1.115-

1.588-

2.179-

4.255-

7.353-

1.168-

1.743-

2.482-

3.404-

4.531-

5.881-

7.541-

9.725-

1.279-

1.724-

2.378-

3.324.

4.654-

6.472-

1.199-

2.078-

3.390-

5.275-

7.888-

007

007

007

007

007

006

006

006

006

006

006

005

005

005

005

005

004

004

004

004

004

003

003

003

003

003

003

003

003

002

002

002

002

002

002

001

001

001

001

001

-M4 °(T)+H

4

°(0) U/MOLE)

0.000*000

6.808-015

1.089-013

5.514-013

1.743-012

8.823-012

2.789-011

6.808-011

1.412-010

2.615-010

4.462-010

7.147-010

1.089-009

2.659-009

5.514-009

1,022-008

1.743-008

2.792-008

4.255-008

8.823-008

1.635-

2.789-

4.467-

6.808-

1.412-

2.615-

4.462-

7.147-

1.089-

2.659-

5.514-

1.022-

1.743-

2.792-

4.255-

6.230-

8.823-

1.216-

1.645-

2.203-

2.947-

3.962-

5.374-

7.350-

1.011-

1.911-

3.518-

6.211'

1.049-

1.701-

007

007

007

007

006

006

006

006

005

005

005

004

004

004

004

004

004

003

003

003

003

003

003

003

002

002

002

002

001

001

L

4

°(T)

(J/MOLE)

59.62

59.64

59.66

59.68

59.70

59.74

59.79

59.83

59.87

59.91

59.95

59.99

60*04

60* 14 60.24

60.35

60.45

60.56

60*66

60.87

61.08

61.28

61.49

61.70

62.11

62.53

62.95

63.36

63.78

64.82

65*86

66.89

67.93

68.97

70.01

71.05

72.09

73.13

74.17

75.20

76.24

77.27

78.30

79.32

60.34

82.35

84.32

86.21

87.99

89.62

<TOPR)

.000*000

.851-012

.962-011

.500-010

.740-010

400-009

584-009

851-008

i839-008

113-008

213-007

.944-007

.962-007

232-007

.500-006

778-006

740-006

.592-006

157-005

.400-005

.445-005

584-005

.215-004

851-004

839-004

113-004

.213-003

.944-003

962-003

.232-003

500-002

.778-002

.740-002

=192-002 157-001

694-001

399-001

308-001

474-001

992-001

.014-001

.078*000

.461*000

.999*000

.749*000

196*000

567*000

.689*001

.853*001

.625*001

Page 86
9. Appendix C

to |i ° in the Cc

Regular Solution Theory

The Correction to |i ° in the Concentrated Phase from

t The term G defined by (18) can also be expressed as

t E

G = G - TS (81) m

where S = -R[X£n X + (1 - X)£n(l - X)] is the ideal entropy of mixing. m E

For a regular solution,G is given by

G

E

= WX (1 - X) , (82)

where W is a constant independent of temperature and concentration.

This constant was evaluated by setting the phase separation temperature

predicted by the regular solution theory,

T ^ = W(l - 2X)/Rtn[ (1 - X)/X] , (83)

ps

equal to the experimental values on the concentrated side of the phase

f diagram. Equation (83) follows from (81) by setting dG /dX equal to

zero, which gives the condition for phase separation in a regular solution.

The fact that W/R only varies from 1. 14°K at T =0. 2°K to 1. 48°K at

ps

T =0. 6°K indicates that the regular solution theory is a fairly good

approximation to the actual behavior of the concentrated solutions. The

appropriate value of W/R was used for each temperature in the calculation

t of p. . In the case of a regular solution the term dG /dX is zero on the

C

t solubility curve which according to (17) leaves \i - G . The results for

|i are shown in figure 4 (p. 15) and the values used for X are given in

c u Table 6. These values for X are from a smooth fit of the data shown in

u

figure 1, and fit quite well to the theoretical result of Edwards and

Daunt L 42] .

87
Table 6

3 4

The Solubility Curve for Concentrated He - He Solutions

T

(°K)

X

u

0. 10 1.0

0. 15 0.99934

0.20 0.9965

0. 25 0.9905

0. 30 0.982

0.35 0.968

0.40 0.949

0.45 0.928

0. 50 0.904

0. 55 0.876

0.60 0. 847

88
10. Appendix D

3 4 Tables of Thermodynamic Properties of He - He Solutions

Tables 7 through 17 are given here and have been discussed in the

main text. With the exception of Table 16 these are all computer generated tables. Powers of ten are expressed as follows: 2. 53-004 represents

-4

2. 53 x 10 . Where certain quantities are expressed as J/mole or J/mole -°K, this is meant to be per mole of the substance of interest.

In tables 11, 12, and 13 this is a mole of total solution, whereas in

3

tables 7, 8, 9, 16, and 17 tnis is a mole oi He in solution. In Table 10

4

the He chemical potential is naturally in units ol joules per mole oi

4

He in solution. The location of the phase separation temperature is

shown in these tables by a horizontal line between two numbers at the

appropriate place.

89
TABLE 7 THE ENTROPY OF HE3 IN HF4 AND ITS RATE OF CHANGF WITH RESPECT TO CONCENTRATION AT CONSTANT TEMPERATURE

X u 0.0001 X = n.oooZ X » 0.0005 X ' 0.0010 X .0020

T S3 -DS3/PX S3 -0S3/0X S3 -OS3/DX S3 -0S3/DX S3 -DS3/DX

(K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) U/MOLE-K) (J/MOLE-K) (j/mole-k) (J/MOLE-K) (j/MOLE-K) (J/MOLE-K) (J/MOLE-K

n 0000 0.0000 -0.00*000 0.0000 -o. 00*000 0.0000 -0.00- 000 0.0000 -0.00*000 0.0000 -0.00*000

0005 3.6751 2.40*00* 2.3278 7, 70*003 1.267* 1.68. 003 0.7997 5.28*002 0,50*9 1.67*002

0010 7.127f, *. 33*00* 4.6059 1. *9*00* 2.5275 3.31- 003 1.5976 1.05.003 1.0093 3.34*002

0020 12.7131 6.31*00* 8.7572 2, 52*004 *.9S99 6.35- 003 3.1802 2.08*003 2.0150 6.64*002

n 00*0 19.9623 7.4b*no* 14.9907 3. 0*00* 9.*011 1.05- 004 6.2215 3.85.003 3.9987 1.30*003

n 0060 2*. 636-) 7,84*00* 19.3312 3, 71*00* 12.9654 1.26- 004 8.9658 5.09*003 5.9097 1.85*003

n 0080 28.0591 8.00*00* 22.6021 3. 86*00* 15.8460 1.37- 00* 11.3616 5.87.003 7.7053 2.29*003

0100 30.^5*2 8.()8*00* 25.2136 3. 9**004 18.2333 1.45- 004 13,*45l 6.*2*003 9.3619 2.63*003

n 0120 32.97*6 8.14*00* 27.3828 3. 99*00* 20.2606 1.49- 004 15.2702 6.80*003 10.8795 2.89*003

n 01*0 34.8619 8.17*00* ?9.2360 4. 02*00* 22.0177 1.52- 00* 16.8858 7.06*003 12.2681 3.08*003

n 0160 36.5026 8.20*00* 30.8527 *, 0**004 23.5660 1.54. 00* 18.3311 7.22*003 13.5*12 3.23*003

n oiso 37.9535 8.21*00* 32.2860 *, 06*004 2*. 9485 1.57- 004 19.6358 7,38.003 14.7124 3.35*003

0200 39.2538 8.23*00* 33.5729 *, 07*00* 26.1967 1.56. 004 20.8237 7,50*003 15.79*6 3.45.003

n 0250 42.01*0 8.25*00* 36.3107 *, 10*00* 28.8691 1.60- 004 23.3934 7.70*003 18.1793 3.62.003

o 0300 **.27*1 8.26*00* 38.5573 4, 1 1*00* 31.0759 1.60-•004 25.5366 7.83.003 20.20*9 3. 7*. 003 0350 46.1876 8.27*00* 40.*616 *, 12*00* 32.9541 1.60- 004 27.3723 7.90*003 21.9609 3,81.003

o*on *7.8466 8.28*00* *2.11*6 4, 13*004 34.5884 1.63->004 28.9767 7.92*003 23.508* 3.87*003

0*50 *9.3lln 8.28*00* 43.5744 4, 13*004 36.0346 1.61- 00* 30.*009 7.95*003 24.8903 3.91*003

0500 50.6215 8.29. no* 44,8814 4, 13*004 37.3314 1.63- 00* 31.6609 8.06.003 26.1380 3.94*003

0600 52.890* 8.29*00* 47.1455 4, 1**004 39.5811 1.64- 00* 33.9 70 8.08*003 28.3183 3,98*003

.0700 54,8097 8.29*00* 49.0616 4, 1**004 41.4877 1.62 00* 35.7980 8.05*003 30.1789 4,01*003

0800 56.*72B 8.30*00* 50.7225 4, 1**00* 43.1420 1.64, 00* 37,4413 8.08*003 31.8009 4, 04.003

.0900 57.9401 8.30*00* 52.1882 4 15*00* 44.6028 1.62. 00* 38,8942 8.06*003 33.2380 4,05.003

.1000 59.2525 8.30*00* 53,*997 4 l5»00* 45.9107 1.63 >oo* 40.1960 8.11*003 3*. 5279 4.06.003

n .1200 61.5250 8.30*00* 55.7701 4 15*004 48,1759 1.62 >004 42.4527 8.05.003 36,7679 4.08.003

n .1*00 63.4463 8.30*00* 57.6903 4 15*00* 50.0928 1.63 .004 44.3640 8.08*003 38,6681 4,09.003

.1600 65.1109 8.30*00* 59.35*1 4 15*00* 51.7542 1.63 004 46.0215 8.06*003 40.3179 4.10*003

.1800 66.5793 8.30*00* 60.8218 4, 15*004 53.2202 1.61 • 00* 47.48*7 8.17.003 41.7754 4.10*003

.2000 67.8928 8.30*00* 62.1350 4 15*004 54.5320 1.64 >00* 8.7943 8.1**003 43.0808 4.11*003

.2500 70.6750 8.30*00* 64.916* 4, 15*004 57.3114 1.63->00* 51.5701 8.12*003 *5.8*94 4.12*003

.3000 72.9484 8.31*00* 67.1894 4 15*004 59.5830 1.63..00* 53.8395 8.09*003 46.1146 4.12.003

.3500 74.8706 8.31*00* 69.1113 4 15*004 61.5040 1.64.-00* 55,7592 8.14.003 50.0314 4,12.003

.*000 76.5357 8.31*00* 70.7762 * 15*004 63,1684 1.63 .004 57.4226 8.18*003 51.6927 4.12.003

.*500 78.00*5 8.31*00* 72.2**9 * 15*004 64.6366 1.65 -004 58.8900 8.23*003 53.1588 4.13*003

.5000 79.3184 8.31*00* 73.5586 * 15*004 65.9500 1.61 004 60.2629 8.17*003 54.4706 4,13*003

.5500 80.5069 8.31*00* 7*. 7471 * 15*004 67.1383 1.60->00* 61.3907 8.11*003 55.6575 4.13*003

.6000 8l.592o 8.31*00* 75.8322 4, 15*004 68,2231 1.63-004 6Z.*752 8.20*003 56.7413 4.13*003

.6500 82.5902 8.31*00* 76.8303 4 15*004 69.2210 1.63 '004 63.*729 8.15.003 57.7385 4.13*003

.7000 83.5144 8.31*00* 77.75** 4 15*004 70.1*51 1.63 004 64.3966 8.0**003 58.6618 4.13*003

.7500 84.374H 8.31*00* 78.6148 4 15*004 71.0053 1.59-00* 65.2567 8.00*003 59.5215 4.13*003

.8000 85.1797 8.31*00* 79.4196 4 16*004 71.8100 1.62 004 66.0613 8.15.003 60.3257 4.13*003

.8500 85.9357 8.31*00* 90.1756 4 15*004 72.5660 1.60- 004 66.8171 8.29*003 61.0813 4.13*003

.9000 86.6485 8.31*00* 80.8884 4 15*004 73.2787 1.61- 004 67.5297 8.07*003 61.7936 4.13*003

.9500 87.3228 8.31*00* 81.5627 4 15*004 73.9529 1.65<•004 68.2038 8.08.003 62.4675 4.13*003

1 .0000 87.9625 8.31*00* 82.202* 4 15*004 74.5925 1.64. 004 68.8433 8.1*. 003 63.1069 4,13.003

1 .1000 89.1511 8.31*00* 83.3910 4 16*004 75.7810 1.62 00* 70-0316 8.15*003 64.2949 4.13*003

1 .2000 90.2363 8.31*00* 8*.*761 4 15*00* 76.8660 1.6Z-00* 71.1166 7.91*003 65.3796 4.13*003

1

• 3000 91.23*5 8.31*00* 85.*7*3 4 15*00* 77.8642 1,59 004 72.11*6 8.02*003 66.3775 4.13*003

1 • *000 92.1587 8.31*00* 86.3985 4 15*00* 78,7883 1,62 004 73.0387 8.08*003 67.3014 4.13*003

1 .5000 93.0191 8.31*00* 87.2589 4 15*00* 79,6487 1.66 004 73.8990 8.18*003 68.1615 4.13*003

Page 90
TABLE 7 (CONTINUED)

X • 0.0030 X » 0*0040 0.0050 X = 0.0060 0.0080

T(K) 0000 0905

0010

0020 00*0

0060

0080 oioo

0120

61*0

0160

6180

0200 0250

0300

0350

0400

0*56 0500

0600 0700

0800

0900

1000 1200

1*00 1600

1809 2000

2500 3000

3500 *000 500

5000

5500

6000

6500

7000

7500 8000

8500

9000

?5P0

0000

1000 2000

3909

*000 5000

53 -DS3/DX S3 -DS3/DX S3 -DS3/0X S3 -DS3/DX S3 -0S3/DX

(J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOlE-K) (J/MOLE-K) (j/MOLE-K) (J/MOLE-K) (j/MO|E-K) IJ/MOLE-K) (J/MOLE-K) 0.0000 6.3866 6.7719

1.5*21 3.0708 4.5696

6.0178

7.3970 8.6956

9.9116

11.0478 12.1094

13.1025

15.3255

17.2453

18.9279

20.4221 21.7641 22.9810 25.1174

26.9486

28.5498

29.9715

31.2497

33.4733

35.3626

37.0048

38.4567

39.7579

42.519* 44.7803

46.6943

48.3537 49.8183

51.1291 52.3152 53.3983

54.3949

55.3178

56.1771 56.9810 57.7363

58.4484

59.1221 59.7612

60.9490 62.0334

63.0311 63.9549

64.8149

-0.00*000

8.51*661 1.70*662 3.39*992

6.69*002

9.77*002

1.25*003

1.48*993

1.66*003

1.81*003 1.94*003 2.64*603

2.12*003

2.27*693 2.37*003

2.44*003

2.49*663

2.53*993 2.56*003

2.61*003 2.63*003

2.66*663 2.67*n03

2.68*993

2.70*003

2.71*003

2.72*663

2.72*003

2.73*003

2.73*003

2.74*003

2.74*663

2.74*663

2.75*993

2.75*003

2.75*003 2.75*003

2.75*663

2.75*003

2.75*003

2.75*003 2.75*663

2.75*663

2.75*093

2.75*003

2.75*003

2.75*003

2.75*993

2.75*003 2.75*003

0.0000 0.3192

0.6384

1.2759 2.5442 3.7965 5.0219

6.2082

7.3458

8.4282 9.4540

10.4241 11.3412

13.4229

15.2467

16.861* 18.3060

19.6102 20.7977

22.8919

2*. 69*7 26.2756

27.682*

28.9*91 31.1565

33.0352

3*. 6698 36.1162

37.*132 0.1677

*2.4244

44.3356

45.9931 47.4563 *8.7659 9.9512

51.0336

52.0297

52.9521

53.8111

5*. 61*7 55.3697

56.0816

56.7550 57.39*0 58.5815

59.6657 60.6632

61.5868

62.**67

•0.00*000 5.26.001 1.05*002 2.10*002

*. 16*002 6.1**002

7.97*002 9.59*002

1.10*003

1.22*003 1.32*003

1 .40*003 1.47*003 1.60*003

1.69*003

1.76*003 1.81*003

1.8**003

1.87*003 1.91*003

1.9**003

1.96*003

1.98*003

1.99*003 2.00*003

2.01*003 2.02*003

2.03*003

2.03*003 2.64*003

2.04*003 2.65*003

2.05*003

2.95*003 2.05*003

2,05*003

2.65*003

2.65*003 2.05*003

2.65*003

2.05*003

2.05*003

2.65*003

2.65*003

2.05*003

2,05*003

2.65*003

2.66*003

2.06*003

2.66*003

0.0000 0.2756

0.5511

1.1017 2.1986

3.2855

4.3558

5.4020

6.4164

7.3934

8.3291 9.2225

10.0742

12.0309

13.7680

15.3200 16.7177

17.9864 19,1459 21.1995

22.9747 24.5359

25.9281 27.1836

29,3751 31.2432

32.8703

34.3113

35.6041 38.3517 40.6042

42.5i27 44.1682

45.6300 46.9386

48.1230

49.2048 50.2003

51.1223

51.9809 52.7842

53.5389 54,2506

54,9239

55.5627

56.7498 57.8338

58.8311 59.7545

60.6143

0.00*000

3.62*001

7.24*001 1.45*002 2.87*002

4.26*002

5.57*002 6.78*002

7.86*002

8.81*002

9.62*002

.03*003

.09*003

.21*003

.29*003

.35*003

.40*003 .43*003

.46*003

.50*003

.53*003 .55*003

.56*003

.57*903

.59*003 .60*003

.61*003

.61*003

.62*003 .62*003

.63*003

.63*003

.63*003

.63*003

.63*003 .64*003 .64*003

.64*003

.64*003

.64*003

.64*003 .64*003

.64*003

.64*003 ,64*003

.64*003

.64*003 .64*003

.64*003

.64*003

0.0000 0.2445

0.4889 0.9774

1.9515 2.9187

3.8747 4.81*6

5.7326

6.6242

7.4854

8.3139 9.1692

10.9550 12.6130

14.1071 15.4609 16.6956

17.8286 19.8432 21.5916

23.1336 24.5114

25.7560 27.9319

29.7895

31.4094

32.8*50

34.1337

36.8744

39.1227 41.0285

42.6821 44.1*25

*5.*500 6.6336

*7.7l*7

*8.7 97 *9.6313 50.*89*

51.2924 52.0469

52.7583

53.*314

54,0700 55.2569

56.3406 57.3377

58.2610

59.1206

-0.00*000 2.67.001 5.34*001

1.07*002 2.12*002

3.15*002 4.15*002

5.08*002

5.94*002 6.71.002

7.39*002

.99*002

.51*002

.56*002 .03*003

.09*003 .13*003

.16*003 .19*003

.23*003

.25*003

.27*003

.29*003

.30*003

.31*003

.32*003 .33*003

.34*093

.34.003 .35*003

.35.003

.35*003

.36*003

.36*003

.36*003

.36*003 .36.003

.36*003

.36*003

.36*003

.36*003 .36*003

.36*003

.36*003

.36*003

.36*003

.36*003 .36*003

.36*003

.36*003

0.0000

0.2025

0.4049

0.8096

1.6173

2.4211 3.2189

4.0081 4.7857

5.5483

6.2934

7.0186

7.7220

9,3811 10.9006

12.2906

13.5648

14.7369 15.8198

17.7608 19.4582 20.9633

22.3134 23.5366

25.6820

27.5193

29.1248

30.5497

31.8303 34.5575

36.7976

38.6979

40.3478

41.8054 43.1108

44.2927

45,3726 46.3665

47.2872

48.1446

48.9470 49,7009

50.4119

51.0846 51.7228

52.9091 53.9924

54.9891

55.9121 56.7715

0.00*000

1.65.001 3.30*001 6.59*001

1.31*002

1.96*002 2.59*002

3.19*002

3.77*002 4.30*002

4,80*002 5.25*002

5.65*002

6.48*002 7.11*002

7,60*002

7.97*002

8.27*002 8.51*002

8.86*002

9.11*002

9.29*002

9.43*002

9.53*002

9.68*002

9.78*002

9.85*002

9.90*002

9.9**002

1.00*003 1.01*003

1.01*003

1.01*003 1.01*003

1.01*003

1.01*003 1.01*003

1.01*003

1.01*003

1.02*003 1.02*003

1.02*003

1.02*003

1.02*003 1.02*003 1.02*003

1.02*003

1.02*003

1.02*003

1.02*003

Page 91
TABLE 7 (CONTINUED)

0.0100 X o 0.0150 X o 0.0200 X * 0.0250 X a 0.0300

T S3 -DS3-'DX S3 -DS3/DX S3 -0S3/DX S3 -DS3/DX S3 -DS3/OX

(K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (j/MOLE-K) (J/MOLE-K) (J/MOLE-K) 0000 0.0000 -0.00 >000 0.0000 -0.00*000 0.0000 -0.00*000 0.0000 -0,00*000 0.0000 -0.00*000

6 0005 6.1750 1.1* 66i 0.13*5 5.79.000 0.1118 3.5e*000 0.0969 2,47*000 0.0863 1.82*000

6 0010 9.3500 2.28 001 0.2690 1.16*001 0.2235 7.15*000 0.1937 4.94,000 0.1725 3,6**000

0020 0.6999 *.55 001 0.5380 2.32*001 0.4470 1.43*001 0.3875 9.87*000 0.3450 7.28*000

6 66*0 1.398ft 9.08 66i 1.075* 4.62*001 0.8936 2.86*001 0.7747 T. 97*001 0.6898 1.46*001

n 0060 2.09*B 1.36 002 1.6117 6.92*001 1.3396 4.28*001 1.1616 2.95*001 1.03*4 2.18*001

6 0080 2.7872 1.80 002 2.1*6* 9.19*001 1.7847 5.69*001 1.5478 3.93*0Ql 1.3785 2.90*001

6 oioo 3.*7*2 2.23 002 2.6787 l.i'4*002 2.2285 7.09*001 1.9332 4.90*001 1.7220 3.62*001

6 0120 *.15*1 2.6* •002 3.2080 1.36*002 2.6706 8.47*001 2.3175 5.87*001 2.0648 4.34*001

6 01*0 *.82*9 3.03 002 3.7335 1.58*002 3.1106 9.84*001 2.7605 6.82*001 2.4067 5.05*001

0160 5.484* 3.40 002 4.25*4 1.79*002 3.5481 1.12*002 3.0820 7.76.001 2.7475 5,75*001

n 0186 6.1309 3.75 002 *,7697 1.98*002 3.9827 1.25*002 3.4615 8.68*001 3.0870 6,44*001

0200 6. 763Q *.06 002 5.2785 2.18*002 4,4137 1.37*002 3.8389 9.59*001 3.4250 7,12*001

6 0256 8.272P *,7* 002 6.5165 2.61*002 5.4723 1.67*002 4,7708 ). 18*002 4.2622 8.77*001

6 0300 9.67*9 5.28 002 7.6981 2.97*002 6.4980 1.94*002 5.6814 1.37*002 5.0850 1.03*002

0350 10.97** 5.70-002 8.8176 3.28*002 7.*8*7 2.17*002 6.5663 1.55*002 5.8896 1.17*002

6 0*00 12.1777 6.03 'OQZ 9.87** 3.53*002 8.*288 2.36*002 7.*216 1.71*002 6.6731 1.30*002

n 0*50 13.293* 6.30 002 10.8705 3.75*002 9.3295 2.54*002 8.2450 1.85*002 7.4327 1.42*002

6 0500 14.3307 6.52 '002 11.809* 3.93*002 10.187* 2.68*002 9.0357 1.97*002 8.1670 1.52*002

0600 16.2032 6.85 •002 13.5311 4.20*002 11.7815 2.92*002 10.5206 2.18*002 9.5581 1.70*002

0700 17.8527 7.08"002 15.0718 4.40*002 13.2280 3,09*002 11.8842 2.33*002 10.8481 1.8**002

0800 19.3226 7.25 662 16.4611 4.56*002 1*.5456 3.23*002 13.1377 2.45*002 12.0439 1.95*002

0900 20.6*61 7.38.002 17,7233 4.67*002 15.7519 3.33*002 14.2936 2.55*002 13.1S37 2.03*002

1000 2i.8*89 7,*9 002 18.8778 4.76*002 16.8623 3.42*002 15.3633 2.63*002 14,1861 2.11*002

n 1200 23.96*9 7.63 662 20.92*0 4,90*002 18.8*40 3.54*002 17.2847 2.74*002 16.0512 2.21*002

1*00 25.7823 7.73 002 22.69*1 4.99*002 20.5695 3.63*002 18.9685 2.83*002 17.6954 2.29*002

n 1600 27.3737 7.80 002 2*. 2516 5.06*002 22.0951 3.69*002 20.4636 2.88*op2 19.1616 2.35*002

6 1800 28.7882 7.85 •002 25.6*11 5.10*002 23.4606 3.74*002 21.8662 2.93*002 20.4823 2.39*002

2000 30.0609 7.89 662 26.89*5 5.14*002 24.6956 3.78*002 23.0236 2.96*002 21.6826 2.42*002

n 2500 32.774A 7.95'•002 29.5760 5.21*002 27,3459 3.84*002 25.6438 3,02*002 24.2737 2.48*002

3000 35.0068 7.99-•002 31.7883 5.24*002 29.5390 3.87*002 27.8183 3.06*002 26,4302 2.52*002

6 3500 36.9017 8.02-•002 33.6701 5.27*002 31.4082 3.90*002 29.6751 3.08*002 28.2749 2.54*002

*6oo 38.5*78 8.6* •002 35,3070 5.29*002 33.0361 3.92*002 31.2943 3.10*002 29.8856 2.56*002

*500 *0.0027 8.05 •002 36.7551 5.30*002 34,*777 3.93*002 32.7294 3.11*002 31.314* 2.57*002

n 5000 *1.3060 8.66 002 38.0533 5.31*002 35.7709 3.94*002 34.0178 3.12*002 32.5960 2.58*002

5500 42.486-* 8.07 •002 39.2297 5.32*002 36.9*33 3.95*002 35.1864 3.13*002 33.7629 2.59*002

6 6000 *3.56*9 8.68 •002 40.3050 5.33*002 38.0156 3.95*002 36.2556 3.14*002 34.8291 2.59*002

n 6500 44.5577 6.68 •002 *1.2953 5.33*002 39.0034 3.96*002 37.2409 3.14*002 35.8119 2.60*002

n 7000 45.4775 8.09 •002 42.2130 5.34*002 39.9189 3.96*002 38.1544 3.15*002 36.7235 2.60*002

7500 46.334? 8.09-•002 43.0679 5.34*002 40.7721 3.97*002 39.0059 3.15*002 37.5732 2.61*002

8000 *7.136o 8.10 • 002 43.8682 5.34*002 41.5709 3.97*002 39.8032 3.15.002 38.3691 2.61*002

6 8500 *7.889* 8.10 •002 44.6203 5.34*002 42,3217 3.97*002 40.5528 3.16*002 39.1175 2.61*002

9000 *8.5999 8.10 • 002 45.3297 5.35*002 43.0300 3.97*002 41.2600 3.16*002 39,8236 2.61*002

n 9500 *9.2722 8.10 •002 46.0010 5.35*002 43.7004 3.98*002 41.9294 3.16*002 40.4921 2.61*002

T 0000 49.9101 8,10 002 46.6381 5.35*002 44,3366 3.98*002 42.5648 3.16*002 41.1267 2.62*002

l 1000 51.0959 8.11-•002 47.8224 5.35*002 45,5195 3.98*002 43.7*63 3.16*002 42.3069 2.62*002

1 2000 52.1787 8.11 •002 48.9040 5.36*002 46,6001 3.98*002 44.8258 3.17*002 43.3853 2.62*002

l 3000 53.1750 8.11 •002 49,8994 5.36*002 47.5946 3.98*002 45.8194 3.17*002 44.3781 2.62*002

I *6o6 5*. 0977 8.11-•002 50.8213 5.36*002 48.5157 3.99*002 46.7399 3.17.0Q2 45.2978 2.62*002

l 5000 5*. 9568 8.11 002 51.6798 5.36*002 49.3736 3.99*002 47.5971 3.17*002 46.1544 2.63*002

Page 92
TABLE 7 (CONTINUED)

X 0.0350 X « 0.0400 X 0.0450 X * .0500 X = 0.0550

T •53 -DS3/DX S3 -0S3/DX S3 -0S3/0X S3 -OS3/DX S3 -DS3/0X

<K> (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) Ij/MOLE-K) (J/MOLE-K) ( ,/MOLE-K) (J/MOLE-K) (J/MOLE-K)

0000 0.0000 -0.00*000 0.0000 -0.00*000 0.0000 -0.00*000 0.0000 -0.00*000 0.0000 -0.00*000

6 0005 6.0782 i.*i*66o 0.0719 l.l3*000 0.0668 9.29-001 0.0625 7.81.001 0.0589 6.67-001

6 oolo 6.1564 2.82*000 0.1*38 2.26*000 0.1335 1.86*000 0.1250 1.56*000 0.1178 1.33*000

6 6620 6.3129 5.63*000 0.2876 .51*000 0.2670 3.72*000 0.2500 3.12*000 0.2355 2.67*000

00*0 0.6256 1.13*001 0.5751 9.02*000 0.5340 7.43*000 0.*999 6.2**000 0.4710 5.34*000

0060 0.9382 1.69*001 0.862* 1.35*001 0.8009 1.11*001 0.7497 9.36*000 0.7064 8.00*000

6. 0080 1.250* 2.25*001 1.1*95 1.80*001 1.0675 1.48*001 0.9994 T. 25*001 0.9417 1.07*001

6 0100 1.5622 2.81*001 l.*362 2.25*001 1.3339 1.85*001 1.2488 1.56*001 1.1767 1.33*001

0120 1.873* 3.36*001 1.7225 2.69*001 1.5999 2.22*001 l.*980 1.87.001 1.4116 1.60*001

5 01*0 2.18*6 3.91*001 2.0083 3.i**ooi 1.8656 2.59*001 1.7468 2.17*001 1.6461 1.86*001

0160 2,*93B *.*6*001 2.2935 3.58*001 2.1307 2.95*001 1.9952 2.*8*001 1.8803 2,12*001

6 0180 2.8026 5.00*001 2.5780 .01*001 2.3953 3.31*001 2.2432 2.79.001 2.11*2 2.38*001

6 0200 3.110* 5.53*001 2.8617 .5*001 2.6592 3.67*001 2,*906 3.09*001 2. 3*76 2.64*001

6 0256 3.87*1 6.8**901 3.5665 5.51*001 3.3156 4.55*001 3.1665 3.83*001 2.9289 3.28*001

0300 4.627* 8.08*001 .2635 6.52*001 3.9659 5.40*001 3.717* .56.001 3.5061 3.91*001

0350 5.3675 9.2**001 .9505 7.*9*001 .6085 6.22*001 .3221 5.26*001 .0782 .52*001

6*00 6.0916 1.03*002 5.6252 8.39*001 5.2414 6.99*001 *.9l9l 5.93*001 4.6440 5.10*001

6 6*56 6.7979 1.13*002 6.2859 9.g**ooi 5.8630 7.72*001 5.5069 6.56*001 5.2023 5.65*001

0500 7.*8*2 1.22*002 6.9309 1.00*002 6.4720 8.39*001 6.0843 7.15.001 5.7518 6.18*001

6 0600 8.7937 1.37*002 8.1692 1.13*002 7.6474 9.57*001 7.2637 8.21*001 6.8211 7.13*001

0700 10.0186 1 .49*002 9.3357 1.2**002 8,7616 1.06*002 8.2709 9.10*001 7.8455 7.94*001

0800 11.1619 1.59*902 10.*315 1.3**002 9. 81*1 1.14*002 9.2836 9.86*001 8.8219 8,64*001

6 0900 12.2294 1.68*002 ll.*600 1. 1*092 10.8066 1.21*002 10.2428 1.05*002 9,7503 9.23*001

iooo 13.2273 1.74*992 12.*258 1. 7*002 11.7*2* 1.27*002 11.1506 1.10*002 10.6319 9.74*001

1200 15.0398 1.8**002 14.1891 1.57*002 13.*593 1.36*002 12.8239 1.19*002 12.2638 1,05*002

0< 1*00 16.6*65 1.92*002 15.7601 1,6**002 1*.9967 1.42*002 14.3292 1.25*002 13.7385 1.11*002

6 1600 18.0851 1.97*662 17.1722 1.69*002 16.3833 l.*7*002 15.6916 1.30*002 15.0776 1.16*002

1800 19.38*9 2. 01*002 I8.*518 1.73*002 17.6435 1.51*002 16.9329 1.34*002 16.3008 1.20*002

2000 20.5687 2.0**002 19.6199 1.76*002 18,7964 1.5**002 18.0711 1.37*002 17.4247 1.22*002

2500 23.1316 2.10*002 22.155* 1.81*002 21.305* 1.59*002 20.55*2 1.42.002 19.8828 1,27*002

3000 25.2705 2.13*002 2*. 2772 1.85*002 23.*10* 1.63*002 22.6430 l.*5*002 21.9555 1.30*002

6 3500 27.103* 2.16*662 26.0986 1.87*002 2S.2205 1.65*002 24.4420 l.*7.002 23.7437 1.33*002

6 000 28.7058 2.17*002 27.6928 1.89*002 26.8067 1.66*002 26.0203 l.*9*002 25.3143 1. 34*002

6 506 30. I?8 * 2.19*902 29.109* 1.90*002 28.2174 1.68*002 27.*251 1.50*002 26.7134 1.35*002

5000 31.*073 2.20*002 30.3836 1.91*002 29.4871 1.68*002 28.690* 1.51*002 27.9742 1.36*002

5500 32.5685 2.20*002 31.5*13 1.91*002 30.6411 1.69*002 29,8409 1.51*002 29.1213 1.37*002

6000 33.6318 2.21*662 32.6016 1.92*002 31.6986 1.70*002 30.8956 1.52.002 30.1732 1,37*002

6500 34.6122 2.21-902 33.5797 1.92*092 32.6744 1.70*002 31.8691 1,52*002 31.1445 1.38*002

7000 35.5218 2.22*902 3*.*873 1.93*002 33.5801 1.71*002 32.7729 1.53*002 32.0463 1.38*002

7500 36.3699 2.22*002 35.3338 1.93*002 3*.*2*9 1.71*002 33.6]62 1.53*002 32.8881 1.39*002

8000 37.16*4 2.22*002 36.1269 1.93*002 35.2166 1.71*002 3*.*065 1.53*002 33.6771 1.39*002

6 8500 37.9115 2.23*662 36.8728 1.9**092 35.961* 1.71*002 35.1501 1.5**092 3*.*195 1.39*002

6 9000 38.6166 2.23*002 37.5769 1.9**002 36.66*5 1.72*002 35.8522 1.54.002 35.1206 1.39*002

Q 9500 39.28*2 2.23*902 38.2436 1.9**002 37.3303 1.72*002 36.5171 1.54.002 35.7847 1.39*002

l 0000 39.9180 2.23*002 38.8766 1.9**002 37.9626 1.72*002 37.1486 1.54.002 36.4154 1.40*002

l 1000 *1.0969 2.23*002 *0.05*1 1.9**002 39.1388 1.72*002 38.3236 1. 5**002 37.5891 1.40*002

T 2000 *2.17*2 2.2**002 1.130* 1.95*002 0.21*6 1.72*002 39.3978 1.55.002 38,6623 1,*0*002

1 3000 *3.166i 2.2**902 42.1215 1.95*092 ' *1.?0*2 1.73*002 40.3871 1.55*002 39.6508 1.40*002

l >*000 **.085l 2.2**002 43.0398 1.95*002 42.1218 1.73*002 41.3641 1.55.002 40.5671 1.40*002

T .5666 .9*11 2.24*662 43.8952 1.95*002 42.9767 1.73*002 42.1584 1.55*002 41.4208 1.40*002

Page 93
TABLE 7 (CONTINUED)

X • 0.0600 X o 0.0640 X » 0.0650 X * 0.0700 X a 0.0750

T S3 -0S3/0X S3 -DS3/0X S3 -0S3/OX S3 -DS3/DX S3 -DS3/OX

(K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOlE-K) (J/MOLE-K) (J/MOLE-K)

0. 0000 0.0000 -0.00*000 0.0000 -0.00*000 0.0000 -0.00*000 0.0000 -0.00*000 0.0000 -0.00*000

6, 0005 6.0558 5.78-001 0,0536 5.21-001 0.0531 5.05-001 0.0507 4.*9.001 0.0*86 4,00-001

?< 0010 6.111ft 1 . 16*000 0.1072 1 .0**000 0.1061 1.01*000 0.1014 8.98-001 0.0971 8.00-001

ft. 0020 6.2231 2. 31*000 0.21*3 2.08*000 0,2123 2.02*000 0.2627 1.80*000 0.19*3 1,60*000

6 66*6 6.**62 *. 62*000 0.*286 .16*000 0,*2*5 *.0**000 0.*65* 3.59*000 0.3885 3.20*000

0060 0.6691 6.93*000 0.6*28 6.2**000 0.6367 6.06*000 0.6081 5.38*000 0.5827 4.80*000

n 0080 6.8926 9.2**660 0.8570 8.32*066 0,8*87 8.07*000 0.8107 7.17*000 0.7768 6.39*000

6 0100 1.11*7 1.15*001 1.0709 1.0**001 1.0607 1.01*001 1.0131 8.96*000 0.9708 7.98*000

6. 912Q 1.3372 1.38*001 1.28*7 1.25*001 1.2725 1.21*001 1.215* T«07*001 1.16*7 9,57*000

01*0 1.5595 1.61*001 l.*983 l.*5*001 l.*8*0 1.41*001 1.*175 1.25*001 1.3585 1.12*001

A. 0160 1.7815 1.8**001 1.7117 1.66*001 1.6953 1.61*001 1.6195 1 .43*001 1.5520 1,27*001

6 6i«o 2.0032 2.07*001 1.9247 1.86*001 1.906* 1.81*001 1.8211 1.61*001 1.7*53 1.43*001

6. 0200 2.22*5 2.29*661 2.1375 2,07*001 2.1171 2.00*001 2.0225 1.78*001 1.9384 1.59*001

6. 0250 2.7758 2.85*001 2.6677 2.57*001 2.6423 2,*9*001 2.5246 2.22*001 2.4199 1.98*001

6 0300 3.3238 3.40*001 3.1948 3.06*001 3.1646 2.97*001 3.02*2 2.65*001 2,8993 2.36*001

0350 3.8675 3.93*001 3.7183 3.5**001 3.6833 3.*5*001 3.5207 3.07*001 3.3759 2.74*001

0*00 *.*06g *.***66l .2372 *. 01*001 *.1976 3.90*001 4.0134 3.47*001 3.8*92 3.11*001

n 0*50 *.938i *. 93*001 *.7506 *,*6*001 .7065 *. 34*001 4*5616 3.87*001 *.3l86 3.46*001

6 0500 5,*629 5.40*001 5.2575 *. 89*001 5.2092 4.75*001 4,9843 4.25*001 *,7833 3.81*001

0600 6.*87i 6.26*001 6.2*87 5.68*001 6.1926 5.53*001 5.9307 4.95*001 5,6961 4.45*001

0700 7.*725 7.00*001 7.205* 6.38*001 7,142* 6.21*001 6.8478 5.58*001 6,5829 5,03*001

0800 8.M55 7.6**00l 8.1235 6.98*061 8.05*6 6.80*001 7.7313 6,13*001 7,*399 5.54*001

6 0900 9.3152 8.19*001 9.0017 7,50*00"i 8,9276 7.30*001 8.5795 6.62*001 8.26*8 5,99*001

6 1000 10.1723 8.67*001 9.8402 7,95*001 9,7616 7.76*001 9.3919 7.04*001 9,0568 6.39*001

6 1200 11 .7651 9.*3*66l ll.*032 8.68*001 11.3173 8.47*001 10.9124 7.72*001 10.5*39 7.04*001

1*00 13.2106 1.00*002 12.8263 9.2**001 12.73*9 9.02*001 12.3032 8.25*001 11.9091 7.54*001

6 1600 1*.5274 1 . 6**002 l*.12S9 9.66*001 1*.0303 9.4**001 13.5780 8.65*001 13.16*0 7.93*001

6 1800 15.7332 1.08*002 15.3181 9,99*001 15.2192 9.77*001 14.7506 8,97.001 1*.3208 8,2**001

2000 16.8*36 1 . i 1*002 i'6.*171 1.03*002 16.3155 1.00*002 15.8 3 38 9.23*001 15.3914 8,*9*001

6 2500 19.2768 1.15*002 18.8318 1.07*002 18.7255 1.05*002 18.2205 9.69*001 17,7554 8,94*001

3000 21.3339 1.18*002 20.8766 1.10*002 20.7673 1.08*002 20.2*7* 9.98*001 19.7676 9,23*001

6 3500 23.1115 1.21*002 22.6*59 1.12*002 22.53** 1.10*002 22.00*3 i. 02*002 21.51** 9,43*001

6 4000 2*. 67*4 1.22*002 24. 2028 l.i**002 2*. 0899 1.11*002 23.5524 1.03*002 23.0553 9.57*001

*500 26.0678 1.23*002 25.5918 1.15*002 25,*778 1.13*002 2*. 93*8 1.0**002 24. 4322 9.68*001

6 5000 27.32*3 1 .2**002 26.8*48 1.16*002 26.7300 1.13*002 26,1828 1.05*002 25.6761 9, 76*001 5500 28.*68o 1.25*002 27.9858 1.17*002 27.8703 1.1**002 27.3198 1.06*002 26.8098 9,83*001

6 6000 29.5172 1.25*002 29.0329 1.17*002 28,9168 1.15*002 28.3636 1.06*002 27.8510 9.88*001

6 6500 30.*862 1.26*662 30.0001 1.18*002 29.8836 1.15*002 29.3282 1.07*002 28.8135 9.92*001

.7000 3i,3862 1.26*002 30.8987 1.18*002 30.7818 1.16*002 30.22*6 1.07*002 29.7081 9.96*001

.7500 32.2264 1.26*002 31.7376 1.18*002 31.620* 1.16*002 31.0617 1.08*002 30.5436 9.99*001

8000 33.01*1 1.27*002 32.52*2 1.19*002 32.4068 1.16*002 31.8468 1.08*002 31.3275 1,00*002

8500 33.7554 1.27*002 33.26*7 1.19*002 33.1*70 1.16*002 32.5859 1.08*002 32.0655 1,00*002

.9000 3*.*556 1.27*902 33,96*0 1.1«*002 33,8*62 1.17*002 33.28*1 1.08*002 32.7627 1.01*002

.9500 35.1188 1.27*002 3*. 6265 1.19*002 3*. 5085 1.17*002 33.9456 1.08*002 33.4234 1.01*002

T 0000 35.7*87 1.27*002 35.2559 1.19*002 35.1377 1.16*002 3*. 57*1 1.09*002 34.0511 1.01*002

i 1000 36.9211 1.28*002 36,*273 1.19*002 36.3089 1.17*002 35.7440 1.09*002 35.2199 1.01*002

I .2000 37.993* 1.28*662 37,*987 1.20*002 37.3801 1.17*002 36.8143 1.09*002 36.2891 1.01*002

T .3000 38.9811 1.28*002 38.4858 1.20*002 38.3671 1.18*002 37.860* 1.09*002 37.2745 1.01*002

I .4900 39.8966 1.28*002 39.4008 1.20*002 39,2819 1.18*002 38.7146 1.09*002 38,1880 1.02*002

i .5000 6.7*98 1.28*002 40.2536 1.20*002 40.1346 1.18*002 39.5667 1.09*002 39,0396 1.02*002

Page 94
TABLE 7 (CONTINUED)

0*0800 X * 0.0900 0.1000 X = 0.1100 X = 0.1200

T

<K> 0000 0005

0010

9020

00*6

0060

0080 6J00

0120

0140

0160

0180 0200

P250

0300

0350 0400

6*50 0500

0600 0700

0800 0900

1000

1200

1*00

1600 1800 2000

2500

3000

3500 *000

*500 SOOO

3500 6000

6500

7000

7500

8000

8500

9000

9500

0000

1000 2000

3000

4000 5000

S3 -0S3/DX S3 -DS3/DX S3 -0S3/DX S3 -DS3/DX S3 -0S3/DX

(J/MOLE-K) (J/MOLF-K) (J/MOUE-K) (J/MOlE-K) (J/MOLE-K) (j/MOLE-K) (J/MOLE-K> (j/MO|E-K) (J/MOLE-K) <J/MOl_E-K> 0.0000 6.0467

6.0933

6.1867

0.3733

0.5600 6.7*65

6.9336

1.1193 1.3055

1.491ft 1.677*

1.8631 2.3261 2.7872

3.2459

3.7018

4.1541 4.6025

5.*8*5

6.3433 7.1756

7.9786

8.7514 10.2068

12.7831 13.9247 1*.9829

17.32*7

19.3227

2i. 059ft 22.5932

23.96*9

25.20*6

2ft. 3351 27.3737

28.33*0 29.226B

30.0609

30.8*35

31.580* 32.2767

32.9366

33.5636

3*. 7311 35.7994

36.78*6 37.6969

38.5478

-0.00*000

3.59-001 7.19-001

1 .44*jpo 2.87*000

4.31*000

5. 74*000

7.18*000 8.61*000

1 .00*001 1.15*001 1.29*001

1 .43*001

1 .78*001

2."l3*o6l 2.47*001

2.80*001

3.12*661

3.44*001 4.02*001

4.56*001 5.04*001

5. 46*661 5.84*001 6.45*001

11.5474 6.94*001

7.31*001

7.61*001

7.86*001 8.30*001

8.58*001

8.77*001 8.92*001 9.02*001

9.10*001

9.17*001

9.22*001 9.26*661 9.30*001

9.33*661

9.35*001

9.37*001 9.39*601

9.41*661

9.42*001 9.45*001

9.47*66l

9.48*001

9.50*001

9.51*661

0.0000

0.0434 0.0868

0.1736

0.3473

0.5208 0.6944

0.8678

1.0412

1.2144 1.3875

1.5605

1.7333 2.1644

2.5941 3.0218 3.4472

3.8700 4.2895

5.1171

5.9261 6.7137

7.4769 8,2144

9.6108

10.9052

12.1044

13.2169

14.2515 16.5505

18.5206 20.2382

21.7579

23.1190

24.3S07

25.4748 26.5083

27.4644

28.3538 29.18*9

29,9650

30.6997 31.39*2

32.0524

32.6780

33.8432 34.9095 35.8925

36.80*2

37.65*1

-0.00*000 2.96-001 5.91-001

1.18*000 2.36*000

3.55*000

4. 73*000 5,91*000

7.68*000

8.26*000

9.43*000

1.06*001 1.18*001 1.47*001

1.75*001 2.03*001

2.31*001 2.58*001

2.85*001

3.35*001

3,81*001 4.23*001

4.60*001 4.94*001

5.50*001

5.94*001 6.29*001

6.58*ooi

6.81*001

7.22*001

7.50*001

7.69*001

7. 83*001 7.93*001

8.01*001 8.07*001

8.12*001 8.16*001

8.20*001

8.23*001

8.25*001 8.27*001

8.29*001

8.31*001

8.32*001

8,35*001

8.36*001 8.38*001

8.39*001

8,*0*001

0.0000 0.0*07

0.0814

0.1628 0.3255

0.4883

0.6510

0.8136

0.9761 1.1386

1.3010 1.4632

1.6253 2.0298

2.4331 2.8348

3.2347

3.6324

4.0276

4.8086

5.5746

6.3226

7.0505

7.7564 9.0992

10.3509

11.5159

12.6010

13.6132

15.8714

17.8147

19.5136 21.0197 22.3707

23.5945

24.7124 25.7408

26.6928

27.5787

28.4070

29.1846 29.9172

30.6099

31.2665

31.8907

33.0535

3*. 1180 35,0995

36.0098

36.8587

0.00*000

2,*8-001

*. 97-001 9.94-001

1.99*000 2.98*000

3.97*000 4.96*000

5.95*000

6.94*000 7.93*000

8.91*000

9.89*000

1.23*001

1.47*001

1.71*001

1.95*001 2.18*001 2.40*001

2.84*001 3.24*001

3.61*001 3.9**001

*. 2**001 4.75*001 5.16*001

5.49*001

5.76*001

5.98*001 6.38*001

6.64*001

6.83*001

6.96*001

7.06*001 7.14*001

7.20*001

7.25*001

7.29*001

7.32*001

7.35*001

7.38*001

7.40*001 7.*2*001

7,*3*001

7,*5*001

7.47*001

7.49*001

7.50*001 7.51*001

7.53*001

0.0000 0.0384

0.0768

0.1536

0.3071 0.4607 0.6142

0.7676

0.9210

1.0743

1.2276 1.3807

1.5337

1.9156 2.2965

2.6761

3.0541 3.4304 3.8045

4.5453 5.2735

5.9867 6.6828

7.3601

8.6541 9.8663

10.9994 12.0585

13.0495

15.2688

17.1860 18.8669 20.3598

21.7008

22.9169

24.0287

25.0522

26.0002

26.8827

27.7682

28.*834

29.2140

29.96*8

30.5598

31.1827

32.3431 33.*058

34.3858

35.29*9

36.1*27

-0.00*000 2.12-001

4.25.001 8.50-001

1.70*000 2.55*000

3.40*000 4.24*000

5.09.000

5.94.000

6,78*000

7.62*000

8.46*000

j .06*001 1.26*001

l.*7*001

1.67*001

1.87*001 2.06*001

2.***001 2.79*001

3.12*001

3.42*001 3.69*001

*. 16*001 .54*001

*.85*0?1

5.10*001

5.31*001

5.69*001 5.95*001

6.12*001 6.25*001

6.35*001 6.43*001

6.49.001

6.54.001

6.58.001 6.61.001

6,64.001

6,66*001

6.68*001

6.70*001

6.72*001 6.73*001

6.75*001

6.77*001

6.79*001 6.80*001

6.81*001

0.0000

0.0364

0.0728

0.1457

0.2913 0.4369 0.3825

0.7281 0.8736

1.0190

1.16**

1.3096

1.4548 1.8172 2.1788

2.5392

2.8984

3.2561 3.6119 *.3173

5.0123 5.69*5

6.3621 7.013*

8.2626

9.*38l 10.5*13

J1.5759

12.5*67

I*. 7288 16.6209

18.28*2

)9.76*3 21.0956

22.30*2 23.*100

2*.*287

25.3727 26.2519

27.07*6

27.8*7*

28.5760

29.2650 29.9185

30.5*00

31.6982

32.7590 33.7375

3*. 6*5* 35.4922

-0.00*000

1,84-001 3.68-001 7.36-001

1.47*000 2.21*000

2,94*000

3.68*000 4.41*000

5.15*000 5.88*000

6.61*000 7.34*000

9.15*000

1.10*001

1.27*001

1.45*001

1.62*001 1.79*001 2.13*001

2,44*001 2.73.001

3.00*001

3.25*001

3.68*001 4,03*001

4.32*001 4.56*001 4.76*001

5.12*001

5.37*001

5,5**001 5.67*001

5.76*001

5.84*001

5.90*001 5.95*001

5.98*001

6.02*001

6.04*001 6.07*001

6.09*001

6.11*001

6.12*001

6,13*001

6.16*001

6.18*001

6.19*001

6.20*001

6.21*001

Page 9 5
TABLF 7 (CONTINUED)

X 0.1300 X . O.1400 X « 0.1500 0.1600 X o 0.1800

T

(K) 0.3000

0.3S00

6 .4000 0.4500

6.5000 0.5500

6.6000 6.6500

6.7000

0.7500

0.8000 0.8500

6.9000

0.9500

1.0000

1.1000 1.2000

1.3000 1.4000

1.5000

S3 -DS3/DX S3 -DS3/DX S3 -0S3/DX S3 -0S3/0X S3 -DS3/OX

(J/MOLE-K> (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) <J/MOLE-K) (J/MOLe-K) Ij/MOlE-K) (J/MOLE-K) (J/MOLE-K) 16.1088

17.7551 19.2227 26.5*45

21.7*57

22.8*57

23.8597

2*. 799a 25.6758

26,*957

27.2662 27.9927

28.6800 29.3320

29.9521

31.1081 32.167i

33.1**1

3*. 0508

3*. 8966

*. 88*001 5.05*001

5.17*001

5. 27*001 5.3**66l

S.*0*O01 5.*5*001

5.48*66l

5.52*001

5.5**001

5.57*001 5.59*001

5.60*Q01

5.62*001

5.63*001

5.65*001

5.67*001

5.69*001

5.70*001

5.71*001

15.6*17 17.271*

18.7268 20.039*

21.233* 22.3276

23.3370

2*. 2732 25.1*60

25.9633

26.7315

27.*S60 28.1*16

28,7921 29.4109

30.56*7

31.6219

32.5975

33.5030

3*. 3*77

*. 47*001

*. 63*001 4.75*001

4.84*001

4.91.001

4.97*001 5.02*001

5.05*001 5.09*00i

5.11*001 5.14*001

5.16*001 5.17*001

5.19*001

5.20*001 5.22*001

5.24*001

5.25*001

5.27*001

5.28*001

15.2132

16.8267 J8.2703

19.5738 20.7607

21.8493

22.8541 23.7866

24.6563 25,4709

26.2368 26.9594

27.6433 28.2924

28.9098

30.0614

31.1169

32.0910 32.9953

33.8391

4.11*001

4.27*001

4.39*001

4.48*001

4.55*001 4.60*001

4.65*001

4.68*001 4.71*001

4.74*001

4.76*001

4.78*001

4.80*001

4.81*001

4.83*001 4.85*001

4.87*001 4.88*001

4.89*001

4.90*001

14.8181 16.4158

17.8*79

19.1*26 20.3226

21.4057

22.4659 23.3348

24.2014

25.0133

25.7770 26.4977

27.1800 27.8275

28.4*37

29.5931 30.6*69

31.6196

32.5228

33.3655

3.80.001 3.95.001 .07.0Q1

.15.001

.22*001

.28.001

.32.001

.36.001

•39.001

.1.001

.001

.6*001

.7.001

.9.001

.50.001

.52.001

4.54.001 .55.001

.56.001

.57*001

14.1121 15.6797

17.0892

18,3669

19,5335 20.6058

21.5974

22.5l9 23.3796

24.1864 24.9458

25.6627

26.3417

26.986*

27.6001 28.7*52

29.7956

30.7656

31.666*

32.5072

3.28*001

3,*3*001

3.54*001 3.62*001

3.69*001 3.74*001

3. ?8*001 3.82*001

3.85*001

3.87*001

3.89*001

3.91*001 3.93*001

3,9**001

3.95*001

3.97*001

3.99*001 .01*001

.02*001

.03*001

TABLE 7 (CONTINUED)

X 0.2000 X = 6.2250 X = 0.2500 X * 0.2750 X = 0.3000

T S3 -DS3/DX S3 -DS3/OX S3 -DS3/DX S3 -DS3/DX S3 -DS3/OX

(K) (J/MOLE-K) IJ/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (j/MOj E-K) (J/MOLE-K) (J/MOLE-K) 0.3000 13.*978 2.87*001 12.8318 2. +7*001 12.2557 2.15*001 11.7514 1.89.001 11.3057 1.68*001 0.3500 15.0376 3.01*001 14.3375 2.60*001 13.7300 2.27*001 13.1961 2.01.001 12.7226 1.79*001

0.4000 16.*25l 3.11*001 15.7002 2.70*001 15.0688 2.36*001 14.512+ 2.09.001 1+.017+ 1.87*001 0.*500 17.686* 3.20*001 16.9*18 2.77*001 16.2917 2.44*001 15.7176 2.16*091 15.2058 1.94*001

0.5000 18.8*01 3.26*001 18,0802 2.83*001 17,*153 2.49*001 16.8271 2.22.001 16.3018 1.99*001 0.5500 19.9021 3.31*001 19.1298 2.88*001 18,*532 2.54*001 17.8535 2.26.001 17.317* 2.03*001

0.6000 20.8852 3.35*001 20.1028 2.92*001 19. +16* 2.58*001 18.8 75 2.30*001 18.262* 2.07*001

0.65OO 21.7998 3.38*001 21.0090 2.95*001 20.31+5 2.61*001 19.6978 2.33*001 19.1+53 2.10*001

0.7000 22.654* 3. 1*001 21.8567 2.98*001 21.155+ 2.64*001 20.5322 2.36*001 19.9733 2.12*001

0.7500 23.*565 3. 001 22.6526 3.00*001 21.9*56 2.66*001 21.3168 2.38*001 20.7525 2.14*001

0.8000 24.2116 3. +6*001 23.4026 3.03*001 22.6906 2.68*001 22.0570 2. + 0*001 21. +882 2.16*001

0.8500 24.9249 3.48*001 24.1115 3.6**001 23,3952 2.70*001 22.7575 2. + 1*091 22.18+6 2.18*001

0.9000 25.6007 3.*9*001 24.7834 3.66*001 2*. 0634 2.71*001 23. +221 2. +3. 001 22.8+57 2.19*001

0.950Q 26.2426 3.51*001 25. +219 3.67*001 24.6987 2.72*001 2*. 05+2 2.++.001 23. +7+8 2.20*001

1 .0000 26.8538 3.52*001 26.0302 3.08*001 25.3046 2.73*001 2*. 6567 2. +5. 001 2*. 0746 2.21*001

1.1000 27.99+9 3.5**001 27,1662 3.10*001 26.4352 2.75*001 25.7832 2.47.001 25.1965 2.23*001

1.2000 29.0+20 3.55*001 28,2093 3.12*001 27. 4744 2.77*001 26.8186 2. +8. 001 26.2282 2.25*001

1.3000 3?.0092 3.57*001 29,1733 3.13*001 28.4351 2.78*001 27.7763 2.50.001 27.1829 2.26*001

l.*000 30.9078 3.58*001 30.0691 3.14*001 29.3283 2.79*001 28.6669 2.51.001 28.0710 2.27*001

1.5000 31.7468 3.59*601 30.9058 3.15*001 30.1628 2.80*001 29. +991 2.51.001 28.9011 2.28*001

Page 96
TABLE 8 THE ChEmICAL POTENTIAL OF HE3 In HF4 WHEN THE HE3 BEHAVES AS AN IDEAL FERMI. DIRAC GAS

M (J/MOLE)

0.0001 0.0002 0.0005 0.0010 0.0020 0.0030 0. 110*0 0.0050 0.0060 0.0080

T \

(K) 0.000 0,,0460 0.0730 0.1344 0.213? 0.3378 0.4418 0.&342 0.6189 0.6977 0.8424

0.001 o t ,0447 0.0722 0.1340 0.2129 0.3376 0.4417 0.5341 0.6188 0.6976 0.8424

0.002 ,0401 0.0ft96 0.1327 0.2121 0.3371 0.4413 0.5338 0.6185 0.6973 0.8422

0.003 0,,032n 0.0648 0.1304 0.2108 0.3363 0.4406 0.5333 0.6180 0.6969 0.8418

0.00* 0,,020Q 0.0576 0.1269 0.2087 0.3350 0.4397 0.5325 0.6174 0.6963 0.8413

0.006 -o ( ,008* 0.0374 0.1162 0.20?ft 0.3315 0.4371 0.5304 0.ftl55 0.6947 0.8400 0.008 -o,,045ft 0.0105 0.1007 0.1934 0.3262 0.4332 0.5272 0.6129 0.6924 0.8381

0.010 -0,,0884 -0.0218 0.0808 0.1810 0.3190 0.4281 0.5231 0.6094 0.6893 0.8356

0.012 -0,,1359 -0.0586 0.0571 0.165ft 0.3099 0.4215 0.5179 0.6050 0.6855 0.8325

0.014 -o,,187<s -0.0992 0.0300 0.1474 0.2987 0.4134 0.5115 0.5996 0.6808 0.8287

0.016 -o,,242=; -0.1432 •0.0002 0.1266 0.2856 0.4038 0.503B 0.5932 0.6753 0.8243

0.018 -o,,3006 -0.1901 -0.0331 0.1034 0.2706 0.3926 0.4949 0.5858 0.6689 0.8192

0.020 -0,,3613 -0.2397 -0.0684 0.0779 0.2538 0.3800 0.4848 0.5 7 73 0.6616 0.8134

0.025 -0,,523* -0.3738 -0.1664 0.00*6 0.2044 0.3420 0.4539 0.5512 0.6390 0.7954

0.030 -o,,698l -0.5200 -0.2761 -0.0777 0.1453 0.2956 0.4155 0.5184 0.6103 0.7725

0.035 -0,,8B3p -0.6765 -0.3956 -0.1704 0.0778 0.2415 0.3701 0.4792 0.5758 0.7446

0.040 -1,,0767 -0.8418 -0.5238 -0.2713 0.0027 0.1803 0.3182 0.4340 0.5356 0.7117

0.045 -1

,

,278? -1.0148 -0.6595 -0.3795 -0.0793 0.1128 0.2602 0.3831 0.4901 0.6741 0.050 -1

,

,4867 -1 .1946 -0.8019 -0.4943 -0.1674 0.0394 0.1968 0.3269 0.4396 0.6319

0.060 -1,,921ft -1 .5723 -1.1046 -0.7411 -0.3603 -0.1233 0.0546 0.2000 0.3247 0.5348

0.070 -2,,3774 -1.9707 -1.4277 -1.0081 -0.5725 -0.3046 -0.1055 0.0557 0.1930 0.4220

0.080 -2,,8509 -2.3869 -1.7684 -1.2924 -0.8016 -0.5023 -0.2816 -0.1040 0.0462 0.2949

0.090 -3,,3401 -2.8186 -2.1246 -1.5920 -1.0456 -0.7146 -0.4719 -0.?777 -0.1141 0.1548

0.100 -3,,8431 -3.2642 -2.4945 -1.9052 -1.3029 -0.9399 -0.6750 -0.4639 -0.2868 0.0029

0.120 -4,,8854 -4.1916 -3.2704 -2.5673 -1.8527 -1.4252 • 1.115.3 -0.8698 -0.6652 -0.3330

0.140 -5,,9694 -5.1606 -4.0878 -3.2707 -2.4432 -1.9506 -1.5951 -1.3U9 -1.0821 -0.7065

0.160 -7,,089? -6.1652 -4.9407 -4.0094 -3.0687 -2.5106 -2.1093 -1.7938 -1.5327 -1.1130

0.180 -8,,2401 -7.2011 -5.8248 -4.7791 -3.7249 -3.1012 -2.6537 -2.3028 -2.0130 -1.5487

0.200 -9,,4189 -8.2648 -6.7366 -5.5764 -4.4085 -3.7189 -3.2251 -2.R386 -2.5199 -2.0106

0.250 -12,,4700 -11.0281 -9.1200 -7.6734 -6.2207 -5.3658 -4.7556 -4, ? 795 -3.8882 -3.2653

0.300 -15,,6467 -13.9169 -11.6288 -9.8954 -8.1574 -7.1366 -6.4095 -5.R433 -5.3787 -4.6413

0.350 -18,,9278 -16.9101 -14,2418 -12.2215 -10.1977 -9.0108 -8.1665 -7.5097 -6.9716 -6.1189

0.400 -22,,2982 -19.9926 -16.9441 -14.6368 -12.3270 -10.9737 -10.0118 -9.2644 -8.6525 -f.6841

0.450 -25,,7467 -23.1532 -19.7244 -17.1300 -14.5341 -13.0142 -11.9347 -11.0963 -10.4105 -9.3262

0.500 -29,,2647 -26.3832 -22.5741 -19.6925 -16.8104 -15.1238 -13.9265 -12.9971 -12.2372 -11.0366

0.550 -32,,8451 -29.6757 -25.4862 -22.3174 -19.1490 -17.2956 -15.9803 -14.9599 -14.1258 -12.8088

0.600 -36,,4823 -33.0249 -28,4551 -24.9990 -21.5441 -19.5239 -18.0907 -16.9790 -16.0707 -14.6371

0.650 -40,,1715 -36.4261 -31.4759 -27.7326 -23.9912 -21.8040 -20.2528 -19.0499 -18.0673 -16.5170

0.700 -43,,9087 -39.8754 -34.5447 -30.5141 -26.4862 -24.1320 -22.4627 -21.1686 -20.1116 -1«.4445

0.750 -47,,6905 -43.3692 -37.6581 -33.3401 -29.0257 -26.5044 -24.7170 -23.3316 -22.2002 -20.4163

0.800 -51,,5139 -4ft. 9046 -40.8131 -36.2077 -31.6067 -28.9184 -27.0128 -25.5360 -24.3303 •22.4294

0.850 -55,.3762 -50.4789 -44.0070 -39.1143 -34,2267 -31.3712 -29.3475 -27.7793 -26.4991 -24.4813

0.900 -59,,2753 -54.0900 -47.2377 -42.0576 -36.8833 -33.8607 -31.7188 -30.0592 -28.7045 -26.5696

0.950 -63,.2090 -57.7358 -50.5030 -45.0355 -39.5745 -36.3848 -34.1247 -32.3736 -30.9445 -28.6925

1.000 -67 .1756 -6] .4)43 -53.6011 -48.0462 -42.2985 -38.9417 -36.5633 -34.7208 -33.2171 -30.8480

1.100 -75 .2008 -68.8636 -60.4894 -54.1597 -47.8385 -44.1473 -41.5324 -39.5070 -37.8542 -35.2508

1.200 -83,,339ft -76.4263 -67.2912 -60.3866 -53.4920 -49.4663 -46.6149 -44.4064 -42.6045 -39.7666

1.300 -91,.5824 -84.0931 -74,1970 -66.7176 -59.2494 -54.8893 -51.8012 -49.4097 -47.4587 -44.3862

1.400 -99 .9212 -91.8559 -81.1988 -73.1445 -65.1027 -60.4082 -57.0834 -54.5089 -52.4086 -49.1015

1.500 -108 ,349\ -99.7079 -88.2898 -79.6606 -71.0452 -66.0161 -62.4546 -59.6970 -57.4475 -53.9058

Page 97
TABLE 8 (CONTINUEO)

( K

)

0.0100 0.0150 0.0200 0.0250 0.0300 0.0350 0.0*00 0.0*50 0.0500 0.0550

0.000 0.9746 1.2680 1.5263 1.7607 1.9775 2.1805 2.3723 2.55*8 2.7292 2.8967

0.001 0.9745 1.2680 1.5262 1.7607 1.9775 2.1805 2.3723 2.55*7 2.7292 2.8966

0.002 0.9743 1.2678 1.5261 1.7606 1.977* 2.180* 2.3722 2.55*7 2.7291 2.8966

0.003 0,9740 1.2676 1.5259 1 .760* 1.9773 2.1803 2.3721 2.55*6 2.7290 2.8965

0.004 0.9736 1.2673 1.5257 1.7602 1.9771 2.1801 2.3720 2.5544 2.7288 2. 8963

0.006 0.9724 1.266* 1.5249 1.7596 1.9765 2.1796 2.3715 2.55*0 2.7284 2.8V60

0.008 0.9708 1.2651 1.5239 1.7587 1.9757 2.1789 2.3708 2.5533 2.7278 2.8954

0.010 0.9686 1.2635 1.5225 1.7575 1.97*7 2.1779 2.3699 2.5525 2.7271 2.89*7

0.012 0,966(1 1.2615 1.5209 1.7561 1,973* 2.1768 2.3689 2.5515 2.7262 2.8938

0.014 0.9628 1.2591 1.5189 1.75** 1.9719 2.1754 2.3676 2.550* 2.7251 2.8928

0.016 0.9591 1.2563 1.5166 1.752* 1.9701 2.1738 2.3662 2,5*90 2.7238 2.8916

0.018 0.954a 1.2531 1.51*0 1.7501 1.9681 2.1720 2.36*5 2.5475 2.722* 2.8903

0.020 0.9499 1.2495 1.5111 1.7476 1.9659 2.1700 2.3627 2.5458 2.7208 2.8666

0.025 0.9349 1.2386 1.5022 1.7401 1.9592 2.16*0 2.3572 2,5407 2.7160 2.88*3

0,030 0.9157 1.2247 1.4911 1.7306 1.9509 2.1566 2.350* 2.5344 2.7102 2.8788

0.035 0.892? 1.2076 l.*775 1.7191 1.9*09 2.1*76 2.3*22 2.5269 2.7032 2.8722

0.0*0 0.8643 1.1R72 l.*613 1.7055 1.9291 2.1370 2.3326 2.5181 2.6950 2.86*6

0.0*5 0.8322 1.1636 l.**24 1.6897 1.9153 2.12*8 2.3216 2.5079 2.6856 2.8558

0.050 0.7959 1.1365 1.4207 1.6715 1.8996 2.1108 2.3089 2.*96* 2.67*9 2.8*58

0.060 0.7115 1.0727 1.3691 1.6280 1.8618 2.0773 2.2787 2.*688 2.6*94 2.8220

0.070 0.6125 0.9962 1.3065 1.57*9 1.8155 2.0362 2.2*17 2.4349 2.6182 2.7930

o.oeo 0.4999 0.9078 1.2334 1.5123 1.7607 1.987* 2.1975 2.3946 2.5810 2.7585

0.090 0.3748 0.8083 1.1501 1.4405 1.6975 1.9308 2.1*63 2.3*76 2.5376 2.7181

0.100 0.236* 0.6982 1.0572 1.3599 1.6261 1.8666 2.0879 2.2941 2.4861 2.6720

0.120 -0.0655 0.4*94 0.8447 1.1736 1.4598 1.7163 1.9505 2.1674 2.3706 2.5622

0.140 -0.4062 0.1660 0.5995 0.9564 1.2643 1.5381 1.7867 2.0157 2.2290 2.*296

0.160 -0.7792 -0.1483 0.3249 0.7111 1.0419 1.3343 1.5981 1.8402 2.0647 2.2750

0.180 -1.1809 -0.4901 0.0237 0.4402 0.7948 1.1065 1.3866 1.6424 1.8788 2.0996

0.200 -1.6086 -0.8571 -0.3018 0.145B 0.5249 0.8566 1.1536 1.4237 1.6727 1.90**

0.250 -2.776* -1.8705 -1.2091 -0.6816 -0.2389 0.1451 0.*861 0.7942 1.0763 1.3373 0.300 -4.0645 -3.0017 -2.2317 -1.6220 -1.1137 -0.6753 -0.2881 0.0599 0.3770 0.6691

0.350 -5.4536 -4.2324 -3.3524 -2.6590 -2.0835 -1.5894 -1.15*7 -0.7654 -0.4120 -0.0877

0.400 -6.9299 -5.5491 -4.5579 -3. 7798 -3.1363 -2.5854 -2.1023 -1.6710 -1,2804 -0.9228

0.450 -8.4826 -6.9*15 -5.8385 -4.9749 -4.2625 -3.6543 -3.1221 -2.6479 -2.2196 -1.8281

0.500 -10.103" -8.*016 -7.1861 -6.2366 -5.4548 -4.7886 -*.2068 -3.669* -3.2227 -2.7969

0.550 -11.7860 -9.9227 -8.594* -7.558* -6,7069 -5.9823 -5.3505 -*.789* -4.2840 -3.8236

0.600 -13.52*5 -ll.*995 -10.0579 -8.9352 -8.0136 -7.2303 -6.5*82 -5.9*31 -5.3987 -4.9033

0.650 -15.31*4 -13.127* -11.572* -10.3626 -9.3706 -8.5265 -7.7957 -7,]*6* -6.5627 -6.0321

0.700 -17.1518 -1*.8026 -13.1339 -11.8369 -10.77*3 -9.8730 -9,089* -8.3957 -7.7725 -/.2064

0.750 -19.033* -16.5218 -14.7392 -13.3547 -12.221* -11.2607 -10.4262 -9.6878 -9.0251 -8.4234

0.800 -20.9561 -18.2821 -16.3854 -14.9134 -13.7091 -12.6890 -11.8033 -11.0202 -10.3176 -9.6802

0.850 -22.9179 -20.0810 -18.0701 -16.5103 -15.2350 -14.1552 -13.218* -12.3903 -11 .6478 -10.9745

0.900 -2*.916n -21.9162 -19.7910 -18.1*3* -16.7968 -15.6574 -1*,6692 -13.7961 -13.0136 -12.30*3

0.950 -26.9*8* -23.7857 -21.5461 -19.8105 -18,3927 -17.1935 -16,1538 -15.2356 -14.4131 -13.6677

1.000 -29,0136 -25.6878 -23.3337 -21.5101 -20.0209 -18.7618 -17.6706 -16.7072 -15.8**5 -15.0630

1.100 -33.235* -29.583* -27.0000 -25.0001 -23.3680 -21.9889 -20.79*4 -19.7*04 -18.7971 -1 f.9*31 1.200 -37.5703 -33.5918 -30.7789 -28.6025 -26.8272 -25.3278 -2*. 0297 -22.8650 -21.8609 -20.93*2

1.300 -42.008B -37.7035 -3*. 6610 -32.3078 -30.3891 -28.7693 -27.3676 -26.]3l« -25.0268 -2*. 0271 1.400 -*6,5*3o -41.9108 -38.638* -36.1083 -3*. 0*61 -32.3057 -30. "001 -29.4732 -28.2870 -2'. 21*4

1.500 -51.1661 -46.2068 -42.70** -39.9973 -37.7915 -35.9303 -3*. 3207 -32.9026 -31.6351 -30.4893

Page 98
TABLE 8 (CONTINUED)

0.0600 0.06*0 0.0650 0.0700 0.0750 0.0800 0.0900 0.1000 0.1100 0.1200

T \

IK)

0.000 3.0581 3.1832 3.2140 3.3651 3.5119 3.6546 3.9292 4.1913 4.4424 *.6839

0.001 3.0580 3.1832 3.2140 3.36=11 3.5118 3.6545 3. 9?92 4.1913 4.4424 4,6839

0.002 3.0561 3.1832 3.2140 3.3651 3.5118 3.6545 3.9292 4.1912 4.4424 4.6838

0.003 3.0579 3.1831 3.2139 3.3650 3.5117 3.6544 3.9291 4.1912 4.4423 4.6838

0.00* 3.0578 3.1«30 3.2137 3.3649 3.5116 3.6543 3.9290 4.1911 4.4422 4.6837

0.006 3.0574 3.1826 3.2134 3.3645 3.5113 3.6540 3.9287 4.]908 4.4420 4.6834

0.008 3.0569 3.1821 3.2129 3.3641 3.5108 3.6536 3.9J83 *«l904 4.4416 4.6831

0.010 3.056? 3. 1815 3.2123 3.3635 3.5102 3.6530 3.9?78 4. ]699 4.441 1 4.6827

0.012 3.0554 3.1807 3.2115 3.3627 3.5095 3.6523 3.9?71 4.)893 4.4406 4.6821

0.01* 3.0544 3.1797 3.2106 3.3618 3.5087 3.6515 3.9?64 4. l 886 4.4399 4.6815

0.016 3.0533 3.1787 3.2095 3.3608 3.5077 3.6506 3.9255 4.1878 4.4391 4.6808

0.018 3.0520 3.1774 3.2083 3.3597 3.5066 3.6495 3.9245 4,ib69 4.4383 4.6799

0.020 3.0506 3.1761 3.2069 3.3584 3.5054 3.6483 3.9?34 4.1859 4.4373 4.6790

0.025 3.0464 3.1720 3.2029 3.3545 3.5017 3.6448 3.9201 4.1828 4,4344 4.6763

0.030 3.0411 3.1*70 3.1980 3.3498 3.4972 3.6405 3.9161 4.1790 4,4308 4.6729

0.035 3.0349 3.1611 3.1921 3.3442 3.4918 3.6353 3.9113 4.1746 4.4266 4.6689

0.0*0 3.027? 3.15*1 3.1852 3.3377 3.4856 3.6293 3.9 58 4.J694 4.4218 4.6643

0.0*5 3.0194 3.1*62 3.1774 3.3302 3.4785 3.6225 3.8995 4.]635 4.4162 4.6591

0.050 3.0100 3.1372 3.1685 3.3218 3.4704 3.6148 3.8924 4.]568 4.4100 4.6532

0.060 2.9878 3.1160 3.1475 3.3019 3.4515 3.5967 3.8757 4.1413 4.3954 4.6394

0.070 2.9606 3.0902 3.1219 3.2777 3.4284 3.5747 3.8555 4.1225 4,3778 4.6228

0.080 2.9283 3.0594 3.0915 3.2489 3.4011 3.5487 3.8316 4.1004 4.3571 4.6034

0.090 2.8906 3.0234 3.0560 3.2154 3.3693 3.5184 3.8039 4. 748 4.3332 4.5809

0.1O0 2.8473 2.9823 3.0153 3.1769 3.3328 3.4837 3.7721 4.0454 4.3059 4.5552

0.120 2.7443 2.8841 2.9182 3.0850 3.2455 3.4005 3.6960 3.9751 4.2404 4.4939

0.1*0 2.6195 2.7647 2.8002 2.9730 3.1390 3.2988 3.6027 3.8888 4.1600 4.4186

0.160 2.473* 2. 62*" 2.6618 2.8*14 3.0134 3.1788 3.4923 3.7864 4.0645 4.3289

0.180 2.307? 2.4652 2.5037 2.6907 2.8695 3.0409 3.3649 3.A680 3.9537 4.2248

0.200 2.1218 2.2869 2.3270 2.5219 2.7077 2.8856 3.2211 3.5339 3.8280 4.106*

0.250 1 .580» 1 .7649 1.8095 2.0256 2.2308 2.4264 2.7933 3.1330 3.4505 3.7*95

0.300 0.9404 1.1448 1 .1944 1.4334 1.6596 1.8745 2.2757 2.6452 2.9888 3.3109

0.350 0.2128 6.4384 0.4930 0.7561 1.004* 1.2397 1.6773 2.0786 2.4502 2.7972

0.400 -0.592s -0.3448 -0.2850 0.0029 0.2741 0.5305 1.0061 1.4406 1.8416 2.21*9

0.450 -1 .4673 -1 .1972 -1.1320 -0.8186 -0.5240 -0.2458 0.2669 0.7376 1.1691 1.5697

0.500 -2.405o -2.1122 -2.0415 -1.70?? -1.3837 -1.0833 -0.5286 -0.0247 0.4380 0.8666

0.550 -3.4003 -3.0843 -3.0081 -2.6425 -2.2997 -1.9768 -1.3815 -0.8418 -0.3472 0.1101

0.600 -4.448T -4.1090 -4.0272 -3.6350 -3.2677 -2.9220 -2.2855 -1.7095 -1.1824 -0.6959

0.650 -5.545? -5.1823 -5.0949 -4.6759 -4.2838 -3.9151 -3.2370 -2.6242 -2.0642 -1.5*81

0.700 -6.687* -6. 3009 -6.2078 -5.7618 -5.3447 -4.9528 -4.2327 -3.5827 -2.9896 -2.4434

0.750 -7.8720 -7.4617 -7.3629 -6.8897 -6.4475 -6.0322 -5.2698 -4.5824 -3.9558 -3.3794

0.800 -9.0964 -8.6621 -8.5576 -8.0572 -7,5896 -7.1508 -6.3458 -5.6208 -4.9604 -4.3534

0.850 -10.358? -9.8999 -9.7897 -9.2618 -8.7689 -8.3064 -7.4586 -6.A956 -6.0013 -5.3636

0.900 -11.655* -11.1730 -11.0569 -10.5015 -9,9831 -9.4969 -8.6061 -7.8051 -7.0765 -6.4080

0.950 -12.9860 -12.4794 -12.3576 -11.774* -11.2306 -10.7206 -9.7866 -8.9473 -8.1844 -7.4848

1.000 -14,3*8* -13.8176 -13.6900 -13.0793 -12.5096 -1] .9757 -10.9985 -10.1207 -9.3234 -8.5925

1.100 -17.1627 -16.5833 -1 6.4440 -15.7777 -15.1566 -14.5747 -13.5104 -12.5554 -11.6888 -10.8951

1.200 -20.0877 -19.4594 -19.3085 -18.586* -17.9135 -17.2835 -16.1317 -15. 991 -14.1628 -13.3059

1.300 -23.11*4 -22.4372 -?2.2745 -21.4964 -20.7717 -20.0932 -18.8538 -17.743? -16.7368 -15.8164

1.400 -26.235? -25.5089 -?5.3344 -24.5003 -23.7235 -22.9966 -21.6690 -20.4802 -19.4035 -18.4194

1.500 -29,*436 -28.6681 -?8.*819 -27.591K -26.7626 -25.9870 -24.5712 -23.3039 -22.1567 -21.1085

Page 99
0.1300

TABLE 8 (CONTINUED)

u, (J/MOLE)

0.1400 0.1500 0.1600 0.1800 0.2000 0.2250 0.?500 0.2750 0.3000

T \

(K) 0.000 4.9167 5.1418 5.3598 5.5713 5.9769 6.3617 6.8172 7.?479 7.6566 8.0455

0.001 4.9167 5. 1418 5.3598 5.5713 5.9769 6.3617 6.8172 7.?479 7.6566 8.0455

0.002 4,9167 5.1418 5.3598 5.5713 5.9769 6.3617 6.8172 7.?479 7.6566 8.0455

0.003 4.9166 5.1417 5.3597 5.5711 5.9768 6.3616 6.B]72 7.?479 7.6565 8.0455

0.004 4.916b 5.1416 5.3597 5.571? 5.9767 6.3616 6.8]71 7.?478 7.6565 8.0454

0.006 4.9161 5.1414 5.3594 5.5710 5.9766 6.3614 6.8)69 7.?476 7.6563 H.0453

0.008 4.9160 5.1411 5.3591 5.5707 5.9763 6.3611 6.8167 7.?*74 7.6561 8.0451 0.010 4.9156 5.1407 5.3588 5.570? 5.9759 6.3608 6.«164 7.?471 7.6559 H.0448

0.012 4.915] 5.1402 5.3583 5.5699 5.9755 6.3604 6.»160 7.p4ft8 7.6555 8.0445

0.014 4.9145 5.1396 5.3577 5.5693 5.9750 6.3599 6.8)56 7,?464 7.6551 8.0441 0.016 4.9138 5.1390 5.3571 5.5687 5.9745 6.3594 6.8151 7.?459 7.6547 8.0437

0.018 4.9130 5.1382 5.3564 5.5680 5.9738 6.3588 6.8145 7,?454 7.6542 8.0432

0.020 4.9121 5.1374 5.3556 5.5673 5.9731 6.3581 6.8139 7.?44R 7.6536 8.04?7

0.025 4.9095 5.1349 5.3532 5.5650 5.9709 6.3561 6.8120 7.?430 7.6520 8.0411

0.030 4.9063 5.1318 5.3502 5.5621 5.9683 6.3536 6.8097 7.?409 7.6499 8.0392

0.035 4,9025 5.1282 5.3468 5.5588 5.9652 6.3507 6.8o70 7.?3R3 7.6475 8.0369

0.040 4.898] 5.1240 5.3427 5.5549 5.9616 6.3473 6.8039 7.?353 7.6447 H.0342

0.045 4.893] 5.1192 5.3382 5.5505 5.9575 6.3435 6.8003 7.?3?0 7.6415 8.0312

0.050 4.8875 5.1139 5.3331 5.5456 5.9529 6.3392 6.7963 7.?2R2 7.6380 8.0278

0.060 4.87*4 *.1014 5.3211 5.534] 5.9423 6.3292 6.7R70 7.?195 7.6297 8.0199

0.070 4.8587 5.0865 5.3068 5.5204 5.9296 6.3173 6.7759 7.?091 7.6199 8.0106

0.080 4.8403 5.0690 5.2901 5.5044 5.9147 6.3035 6.7ft30 7.1970 7.6085 7.9998 0.090 4.819] 5.0486 5.2709 5.4860 5.8977 6.2876 6.7483 7.]833 7.5955 '.9875 0.100 4.7949 5.0258 5.2490 5.4651 5.8785 6.2696 6.7317 7.1677 7.5809 7.9736 0.120 4.737] 4.9711 5.1970 5.4154 5.8328 6.2271 6.6925 7.1311 7.5465 7.9411 0.1*0 4.666] 4.9039 5.1331 5.3546 5.7769 6.1754 6.6448 7.0868 7.5049 7.9018 0.160 4.5815 4.8?39 5.0570 5.2820 5.7103 6.1137 6.5882 7.0342 7.4557 7.8554 0.180 4.483? 4.7307 4.9684 5.1974 5.6327 6.0418 6.5221 6.9730 7.3984 7.8015

0.200 4.371? 4.6244 4.8672 5.1007 5.5438 5.9594 6.4464 6.9028 7.3328 7.7397 0.250 4.0326 4.3021 4.5595 4.8063 5.2723 5.7070 6.2140 6.6868 7.1308 7.5496 0.300 3.614ft 3.9026 4.1768 4.4388 4.9316 5.3890 5.9)98 6.4127 6.8737 7.3072 0.350 3.1233 3.4315 3.7241 4,0029 4.5252 5.0080 5.5657 6.fi8l5 6.5621 7.0125 0.400 2.5647 2.8943 3.2065 3.5033 4.0574 4.5675 5.1546 5.6954 6.1976 6.6670

0.450 1 .944] 2.2962 2.6288 2.9445 3.5322 4.0712 4.6895 5.2571 5.7826 6.2724

0.500 1.2665 1.6417 1.9956 2.3308 2.9534 3.5227 4.1738 4.7696 5.3197 5.8312

0.550 0.5360 0.9350 1.3107 1 .6660 2.3246 2.9253 3.6103 4.?356 4.8114 5.3456

0.600 -0.2435 0.1798 0.5777 0.9537 1.6491 2.2820 3.0020 3.6576 4.2601 4.8179

0.650 -1 .0687 -0.6209 -0.2002 0.1967 0.9297 1.5955 2.3514 3.6381 3.6680 4.2502

0.700 -1.9368 -1.4640 -1.0203 -0.602? 0.169) 0,8684 1.6608 2.3794 3,0374 3.6445

0.750 -2.845? -2.3471 -1.8801 -1 .4404 -0.6304 0.1028 0.«324 1.A835 2.3701 3.0027

0.800 -3.7915 -3.2679 -2.7774 -2.3159 -1.4667 -0,6990 0.1682 0.9522 1.6679 2.3264

0.850 -4.773ft -4.2243 -3.7102 -3.2267 -2.3378 -1.5354 -0.6300 0.1873 0.9325 1.6174

0.900 -5.789R -5.2146 -4.6766 -4.1709 -3.2421 -2.4046 -1.4607 -0.6096 0.1655 0.8771

0.950 -6.8381 -6.2370 -5.6749 -5.1470 -4.1780 -3.3050 -2.3223 -1.4371 -0.6319 0.1067

1.000 -7.9175 -7.2901 -6.7038 -6.1535 -5.1440 -4.2354 -3.2134 -2.2939 -1.4582 -0.6923

1.100 -10.1628 -9.4827 -8.8478 -8.252? -7.1610 -6.1805 -5.0794 -4.0904 -3.1930 -2.3719

1.200 -12.5159 -11.7827 -11.0987 -10.4575 -9.2840 -8.2307 -7.0497 -5.9904 -5.0305 -4.1533

1.300 -14.968? -14.1818 -13.4483 -12.7613 -11.5048 -10.3783 -9.U65 -7.9862 -6.9632 -6.0293

1.400 -17.5130 -16.6728 -15.8897 -15.1565 -13.8165 -12.6163 -11.2732 -10.()714 -8.9846 -7.9935

1.500 -20.1436 -19.2495 -18.4166 -17.6370 -16.2132 -14.9388 -13.5140 -12.?401 -11.0892 -10.0404

Page 100
TABLE 9 THE ENTHALPY OF HE3 IN HE4

H3 (J/MOLE)

0.0001 0.0002 0.0005 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060 0.0080

T \

(K) 0.000 -2.10606 -2.08000 -2.02153 -1.94785 -1 83391 -1.74107 -1.66024 -1.58761 -1.52114 -1 40192

0.001 -2.1002* -2.07619 -2.01943 -1.9465? -I 83307 -1.74043 -1.6&971 -1.58716 -1.52073 -1 40159

0.002 -2. ,18653 -2.06591 -2.01329 -1.94256 -1 83056 -1.73850 -1.65811 -1.58578 -1.51951 -1 40058

0.003 -2.0696? -2.05173 -2.00368 -1.93611 -1 82640 -1.73531 -1.65547 -1.58349 -1.51748 -1 39889

0.004 -2.05134 -2.03543 -1,99146 -1.92742 -1 82066 -1.73087 -1 .65178 -1.58030 -1.51464 -1 39654

0.006 -2.01285 -1.99965 -1.96198 -1.90465 -1 80476 -1.71839 -1.64135 -1.57124 -1.50658 -1 38984

0.006 -1.97317 -1.96171 -1.92854 -1 .87679 -1 78385 -1.70151 -1.62706 -1.55876 -1 .49543 -1 38053

0.010 -1.93291 -1.92268 -1.89284 -1.84562 -1 75903 -1.68084 -1.60928 -1.54308 -1.48134 -1 36870

0.012 -1.B9231 -1.88302 -1.85576 -1.81222 -1 73125 -1.65706 -1.58844 -1.5?449 -1.46451 -1 35445

0.014 -1.85150 -1.84294 -1.81775 -1.77727 -1 70120 -1.63074 -1.56500 -1.5fl333 -1.44521 -1 33793

0.016 -1.8)054 -1.B0258 -1.77910 -1.74118 -1 66940 -1.60235 -1.53937 -1.47995 -1.42368 -1 31931 0.018 -1.7694s -1.76202 -1.73997 -1.70425 -1 63624 -1.57229 -1. 51190 -1.45465 -1.40022 -1 29877

0.020 -1.72834 -1.72130 -1.70048 -1.66666 -1 60200 -1.54086 -1.48287 -1.42769 -1.37504 -1 27650

0.025 -1.62525 -1,61905 -1.60065 -1.57065 -1 51286 -1.45774 -1.40501 -1.35448 -1.30596 -1 21438

0.030 -1.52195 -1,51636 -1.49977 -1.47267 -1 42023 -1.36993 -1.32158 -1.27500 -1 .23009 -1 14483 0.035 -1.41850 -1.41340 -1.39823 -1.37341 -1 32528 -1.27894 -1.23424 -1.19105 -1.14927 -1 06962

0.040 -1. 71497 -1.31025 -1.29623 -1.27328 -1 22869 -1.18567 -1.14406 -1.10379 -1.06475 -0 99006

0.045 -1.21136 -1.20697 -1.19391 -1.17251 -1 13091 -1.09070 -1.05177 -1.0t401 -0.97736 -0 90711

0.050 -1.10771 -1.10359 -1.09134 -1.07127 -1 03222 -0.99445 -0.95783 -0.9?228 -0.88774 -0 82144

0.060 -0.90029 -0.89661 -0,88568 -0.86776 -0 83287 -0.79910 -0.76633 -0.73448 -0.70349 -0 64389

0.070 -0.69278 -0.68944 -0,67953 -0.66329 -0 63168 -0.60108 -0.57138 -0.54251 -0.51440 -0 46030

O.ORO -0.48520 -0.48214 -0.47305 -0.45817 -0 42923 -0.40122 -0.37404 -0.34762 -0.32190 -0 27241 0.090 -0.27757 -0,27474 -0.2*634 -0.25259 -0 22586 -0.20002 -0.1^496 -O.I5O6] -0.12691 -0 08133

0.100 -0. 06991 -0.06727 -0.05945 -0.04666 -0 02182 0.00218 0.02543 O.O4B0I 0.06997 11218

0.120 0.14549 0.34782 0.35470 0.36595 38774 0.40874 0.42905 0.44874 0.46786 50452

0.140 0.76096 0.76304 0.76921 0.77925 79866 0.81731 0.83531 0.85273 0.66960 90186

0.160 1.1764S 1.17837 V. 18394 1.19301 1 21050 1.22725 1.2*338 1.25894 1 .27398 1 30266

0.1R0 1.59203 1.59376 1.59884 1.60711 1 62300 1.63817 1.65274 1.66676 1.68028 1 70595

0.200 2.O0761 2.00920 2.01387 2.02145 2 03599 2.04983 2.06307 2.07578 2.08800 2 11112 0.250 3.r4663 3.04795 3.05182 3.05807 3 06996 3.08117 3.09182 3.10196 3.11163 3 12972

0.300 4.n857? 4.08684 4.09012 4.09538 4 10531 4.U459 4.12331 4.13154 4.13932 4 15367

0.350 5.12485 5.12582 5.12864 5.13313 5 14154 5.14931 5.15653 5.16328 5.16958 5 18100 0.400 6.1640? 6.16486 6.16730 6.17118 6 17836 6.18491 6.19093 6,19647 6.20157 6 21063

0.450 7.?032fl 7.20394 7.20608 7.20944 7 21561 7.22115 7.22616 7.23070 7.23482 7 24191 0.500 8.?424n 8.24305 8.24493 8.24786 8 25317 8.25785 8.26201 8.26571 8,26899 8 27441 0.550 9.?8161 9.28219 9.28384 9.28641 9 29097 9.29491 9.29834 9.30131 9.30387 9 30786

0.600 10.32084 10,32135 10.32280 10.32504 10 32895 10.33226 10.33505 10.33738 10.33931 10 34205

0.650 11.36007 11.36052 11.36180 11.36375 11 36710 11.36983 11.37206 11.37384 11.37520 11 37684

0.700 12.39930 12.39970 12.40084 12.40253 12 40536 12.40760 12.40932 12.*l060 12.41147 12 41212

0.750 13.43854 13.43890 13.43989 13.44136 13 44373 13.44551 13.44679 13.44761 13.44804 13 44781

0.800 14.47779 14.47810 14.47897 14.48023 14 48219 14.48356 14.48443 14.48485 14.48487 14 48383

0.850 15.51704 15.51731 15.51807 15.51914 15 52073 15.52172 15.52221 15.5 ? 226 15.52192 15 52015

0.900 16.55629 16.55653 16.55718 16.55808 16 55932 16.55997 16.56012 16.55984 16.55915 16 55672

0.950 17.5955=; 17.59576 17.59631 17.59705 17 .59797 17.59831 17.59815 17.59755 17.59655 17 59351

1.000 18.63480 18.63498 18.63545 IS. 63604 18 .63667 18.63672 18.63627 18.63538 18.63410 IB .63048 1.100 20.71333 20.71345 20.71376 20.71409 20 71419 20.71372 20.71275 20.71135 20.70955 20 70492

1.200 22.79186 22.79194 22.79211 22.79220 2? 79185 22.79092 22.78950 22.78764 22.78540 22 77988

1.300 24.87039 24.87043 24.87048 24.87037 24 86962 24.86828 24.86646 24.86421 24.86157 24 85527

1.400 26.Q4893 26.94893 26.94887 26.94858 26 94747 26.94578 26.94360 26.94100 26.93801 26 93100

1.500 29.S2747 29,02744 29.02728 29.02683 29 .02540 29.02330 29.02Q89 29.01796 29.01466 29 00702

Page 101
TABLE 9 (CONTINUED)

H3 (J/MOLE)

0.0100 0.0150 0.0200 0.0250 0.0300 0.0350 0.0400 0.0*50 0.0500 0.0550

T \

(K) 0.000 -1 ,79641 -1 ,07331 -0.88986 -0.73383 -0.59844 -0.47941 -0.37382 -0.27953 -0.19495 -0.11881

0.001 -1 ,29612 -1 .07308 -0.86967 -6.73367 -0.59830 -0.47928 -0.37370 -0.2794? -0.19484 -0.11871

0.002 -1 ,59524 -1 ,07241 -0.88912 -0.73318 -0.59786 -0.*7S89 -0.37334 -0.27908 -0.19453 -0.11842

0.003 -1 ,79379 -1 .07129 -0.88818 -6.73238 -6.59715 -0.*782* -0.37274 -0.27853 -0.19401 -0.11793

0.004 -1 ,29175 -1 .06972 -0.88688 -6.73125 -0.59614 -0.*7733 -0.37190 -0.27775 -0.19328 -0.11724

0.006 -1 ,2859=, -1 ,06525 -0.88317 -0.72802 -0.59327 -0.*7472 -0.36951 -0.27553 -0.19120 -0.11528

0.008 -1 ,27787 -1 ,05902 -0.87797 -0.72352 -0.58925 -0.47108 -0.36616 -0.27241 -0.18828 -0.1125*

0.010 -1 .76757 -1 .05103 -Q. 87132 -6.71774 -0.58410 -0.46640 -0.36186 -0. 2*842 -0.18454 -0.10901

0.012 -1 ,7551" -1 ,04133 -0.86321 -0.71069 -0.57782 -0.46070 -0.35661 -0.26354 -0.17998 -0.10*70

0.014 -1 ,24057 -1 ,02994 -0.85368 -0.70239 -0.570*1 -0.45397 -0.35041 -0.25779 -0.17*58 -0.09962

0.016 -1 72409 -1 01692 -0.84274 -0.69286 -0.56189 -0.44622 -0.3*329 -0.25116 -0.16837 -0.09377

0.018 -1 7057R -1 00233 -6.83043 -6.68210 -6.55227 -0.43747 -0.33523 -0.24366 -0.16135 -0.0871*

0.020 -1 7857* -0 ,98622 -n .81678 -0.67015 -6.5*157 -0.42773 -0.32624 -0.23530 -0.15351 -0.07975

0.025 -1 l292q -0 ,93983 -0.77710 -0.63522 -0.51018 -0.39910 -0.29982 -0.2T069 -0.130*2 -0.05796

0.030 -1 06502 -0 88*71 -6.73012 -0.59350 -0.*72*8 -0.36458 -0.26788 -0.18089 -0.102*2 -0.03150

0.035 -0 ,9947n -0 82512 -0.67670 -0.54559 -0-*2891 -0.32450 -0.23067 -0.U609 -0.06967 -0.00052

0.040 -0 91956 -0 75911 -6.61772 -0.49215 -0.37996 -0.27925 -0.18851 -0.1065* -0.03237 0.03*84

0.045 -0 O4059 -0 68859 -6.55396 -0.*3385 -0.32617 -0.22924 -0.1*172 -0.06252 0.00926 0.07438

O.OSO -0 75852 -0 ,61431 -6.48607 -0.37128 -0.26806 -0.17492 -0.09067 -0.0i*32 0.05*97 0.11788

0.060 -0 ,*872? -0 ,45675 -0.3*016 -0.23534 -0-1*069 -0.05500 0.02274 0.0933* 0-15751 0.21584

0.070 -0 ,40881 -0 .29007 -0.18365 -0.08778 -0.00107 0.07758 0.1*901 0.21397 0.27304 0.32674

0.080 -0 22528 -0 ,11660 -6.01911 0.06877 0.1*828 0.22039 0.28589 0.34543 0.39956 0.**873

0.090 -0 i3795 06205 6.15164 0.23230 6.30538 0.37151 0.*3l50 0.48596 0.53538 0.58018

0.100 15731 24471 6.32732 0.*0165 0.*6S75 0.52942 0.58433 0.63*05 0.67904 0.71971

0.120 53927 61896 6.68982 0.75317 0.80999 0.86108 0.90702 0.94829 0.98530 1.01842

0.140 Q3234 1 00181 1.06307 1.11741 1.16570 1.20867 1.2*693 1.28092 1.31101 1.3375*

0.160 1 32964 1 ,39068 1 .44396 1 .49070 1.53179 1.56791 1.59955 1.6?720 1.65125 1.67198

0.180 1 72995 1 78394 T. 83046 1.&7073 1.90563 1.93580 1.96176 1.9P393 2.00265 2.01826

0.200 2 13265 2 18053 2.22123 2.25592 2.28543 2.310*2 2.33139 2.34875 2.36282 2.37388

0.250 3 14630 3 ,18216 3.21128 3.23*79 3.25350 3.26801 3.27881 3.28629 3.29077 3.29253

0.300 4 16656 4 ,19342 4.21383 4.22889 4.23937 4. 24588 4.2*888 4.24875 4.24579 4.2*028

0.350 5 19101 5 ,21081 5.22*37 5.23275 5.23673 5.23689 5.23367 5.2?745 5.21854 5.20718

0.400 6 71831 6 23239 6.2*037 6.24333 6.2*200 6,23695 6.22864 6.21743 6.20361 6.187*3

0.450 7 7476=; 7 ,25697 7.26031 7.25873 7.25296 7.24357 7.23099 7.21558 7.19763 7.17740

0.500 8 77851 8 28379 8.28319 8.27775 8.26820 8.25510 8.23888 8,2i988 8.10841 8.17*70

0.550 9 31054 9 31234 9.30834 9.29956 9.28675 9.270*3 9.2&105 9.2^895 9.20**2 9.17769

0.600 10 34340 10 34225 16.33527 10.32358 10.30790 10.28877 10.26662 10.24180 10.21*57 10.18519

0.650 11 37718 1 1 37325 11.36364 11.34938 11.33116 11.3095* 11.28494 11.25769 11 .22809 11.19636

0.700 12 ,41140 12 40516 12.39320 12.37663 12.35615 12.33231 12.30551 12.27610 12.24436 12.21052

0.750 13 44630 13 43781 13.*237* 13.*0510 13.38258 13.35673 13.32796 13.29660 13.26294 13.22720

0.800 1* 48153 14 47109 14.45511 14.43459 14.41022 1*. 38255 14.35199 14.31887 14.283*6 14.24599

0.850 15 51713 15 50491 15.*8718 15.*6495 15.43890 15.*0957 15.37737 15.34264 15.30563 15.26660

0.900 16 55303 16 53918 16.51986 16.*9606 16.*68*7 16.43762 16.40392 16.36770 16.32924 16.28876

0.950 17 5892] 17 57386 17.55307 17.52782 17.*9881 17.46656 17.43148 17.30389 17.35*08 17.31227

1.000 18 ,*256? 18 60888 18.58673 18.56015 18.52982 18.*9627 18.45092 18.4? 107 18.38001 18.33697

1.100 20 ,69905 20 67982 20.65523 20.62625 20.59356 20.55769 20.51904 20.47793 20.43463 20.38937

1.200 22 ,77313 22 75173 22.72501 22.69394 22.65919 22.62129 22.58063 22.53754 22.49229 22.44509

1.300 74 04774 24 82443 24.79583 24.76290 24.72634 24.68664 24.64421 24.50937 24.55239 24.50347

1.400 26 ,02278 26 ,89776 26.86749 26.83292 26.79473 26.75343 26.70942 26.66302 26.61449 26.56405

1.500 ?8 ,9981b 28 97163 28.93985 28.90379 28.86415 28.82141 28.77598 28.77818 78.67826 28.62644

Page 102
TABLF 9 (CONTINUED)

H3 (J/MOLE)

0.O6OO 0.06*0 0.0650 0.0700 0.0750 0.0800 0.0900 0.]000 O.UOO 0.1200

T \

K)ono -0 r50l3 00000 0.01191 0.06799 11867 0.16443 0.24281 0.30584 0.35561 ,39377

.001 -0 o5004 ,00009 0.01200 0.06807 11875 0.16451 0.2*289 0.30591 0.35567 .39383 002 -0 f\4976 00036 0. 01226 Q.0683? 11899 0.16474 0.24310 0.3J611 0.35587 .39402

.003 -0 04930 00080 0.01270 0.06875 11939 0.16513 0.24346 0.3o645 0.35619 .39*32

.004 -0 04865 00143 0.01332 0.06934 11996 0.16567 0.24397 0.36693 0.35663 .39474

.006 -0 0467Q .00321 0. 01509 0.07103 12158 0.16723 0.24542 0.3o828 0.35791 .39596

.008 -0 0441a 00571 0.01756 0.07339 12384 0.16941 0.24744 0.3T018 0.35970 ,39766

010 -0 '4085 00B92 0.02074 0.07643 12675 0.17220 0.25004 0.3)262 0.36201 39984

,012 -0 ^3677 ,01284 ii. 02463 0.08013 13031 0.17562 0.2&322 0.3)560 0.36482 ,40251

014 -0 o319^ 01747 0.02921 0.08451 13451 0.17965 0.25698 0.31912 0.36814 40566

016 -0 02640 02280 0.03449 0.08956 13934 0.18430 0.26130 0.32318 0.37197 ,40929

018 -0 O2012 02884 0.04047 0.09528 14482 0.18957 0.26620 0.3?778 0.37631 41341

.020 -0 nl 31

03558 0.04715 0.10165 15094 0.19545 0. 27168 0.33291 0.38115 ,41800 025 00756 05546 0.06684 0.12048 16899 0.21281 0.28784 0.34Bo8 0.39S47 43160

.030 03267 07962 0.09078 0.14338 19096 0.23394 0.30753 0.36656 0.41293 ,44816

035 n 06212 10797 0.11887 0.17027 21677 0.25879 0.33070 0.38832 0.43349 ,46769

040 o9577 14039 0.15101 0.2010* 6 24635 0.28728 0.35729 0.41331 0.45712 49014

045 1 334ft 17675 0.16705 0.23563 27960 0.31932 0.38723 0.44148 0.48377 51547

050 17500 21688 0.22685 0.27385 31639 0.35481 0.42044 0.47276 0.51339 54364

060 p6S8t 30770 0.31695 0.36056 40003 0.43563 0.49628 0.54434 0.58127 ,60829

070 ?755^ 41129 0.41979 0.45986 49606 0.52864 0.58390 0.62729 0.66015 ,68356

0«0 49335 52600 0.53375 0.57026 60314 0.63263 0.68?30 0.7?077 0.74927 76882

090 62074 65036 0.65738 0.69037 71995 0.74636 0.79040 0.8?386 0.84787 ,86337

1"0 75639 78307 0.78938 0.81894 84531 0.86867 0.90714 0.93559 0.95508 ,96647

.120

.140

1

1

?479* 36077

1

1

,06920 37717

i. 07418

1 .38097

1 .09732

1.3.9833

1 11759 1.13516

1.42532

1.16?86 1.44303

1.18152

1.4^247

1 .19208

1 .45449

1

1

.19529

1 41306 .44979

.160 1 68966 1 70175 1 .70451 1.71672 1 72649 1.73396 1.74256 1.74350 1.73756 1 .72539

.180 2 o309o 2 .03926 2.04107 2.04869 2 05401 2.05717 2.05754 2.05072 2.03744 2 01834

.200 2 38221 2 38705 2.38801 2.39149 2 39279 2.39206 2.38497 2.3J108 2.35109 2 .32559

250

300

3

4

2917Q

23242

3

4

28956

22460

3.28878

4.22243

3.2836? 4.21046

3

4

27647

19666

3.26748 4.18115

3.24447

4.14547

3.2]541 4.10414

3.18094

4.05781

3 14159

4 .00702

.350 5 T9359 5 18125 5.17797 5.16047 5 14123 5.12038 5.07427 5.02288 4.96684 4 90659

400 6 l'691o 6 15303 6.14882 6.12673 6 10297 6.07767 6.02286 5.9ft3o2 5.89873 5 83048

.450 7 15508 7 .13585 7.13086 7.10489 7 07731 7.04824 6. 98A04 6. 9)899 6.R4767 6 .77257

.500 8 1489«, 8 12702 8.12136 8.09206 8 06120 8.02888 7.96630 7.88703 7.80964 7 72858

.550 9 14897 9 12468 9.11844 9.08624 9 05251 9.01736 8.94323 8.86452 8.78180 8 69553

.600 10 15386 10 12750 10.12074 10.08599 10 04974 10.01210 9.93305 9.84954 9.76211 9 67123

.650 11 l627o 1 1 13450 11.12728 11 .09027 11 05177 11.01191 10.92849 10.84070 10.74907 10 65406

.700 12 17478 12 14494 12.13731 12.09826 12 05775 12.01590 11.92857 11.83692 11.74152 11 64280

.750 13 T895B 13 15826 13.15026 13.10937 13 06704 13.02340 12.93251 12.83739 12.73857 12 63649

.800 14 ?0667 14 17399 14.16566 14.12310 14 07913 14.03384 13.93974 13.84145 13.73952 13 63438

.850 15 22572 15 19181 15.18317 15.13908 15 09360 15.04682 14.94976 14,84858 14.74380 14 63586

.900 16 24645 16 21140 16.20248 16.15700 16. 11013 16.06198 15.96221 15.8^836 15.75096 15 64044

.950 17 26864 17 ,23255 17.22337 17.17660 17 12845 17.07903 16.97676 16.87045 16.76063 16 64773

1 .000 18 2921? 18 25506 18.24564 18.19767 18 14834 18.09774 17.99316 17.8P457 17.77250 17 65739

1 .100 20 34233 20 30354 20.29368 20.24357 20 19210 20.13940 20.03064 19.91795 19.80185 19 68276

1 .200 22 39613 22 35582 22.34559 22.29359 22 24026 22.18570 22.07330 21.95702 21.83737 21 71479

1 .300 ?4 4528? 24 41117 24.40060 24.34693 24, 29196 24.23577 24.12013 24.06067 23.87789 23 75222

1 • 400 26 51188 26 46903 26.45816 26.40301 26. 34656 26.28891 26.17039 26.04808 25.92250 25 79406

1 .500 28 5729? 28 52898 28.51784 28.46136 28, 40358 28.34462 28.22350 28.09863 27.97052 27 83959

Page 103
T4PLF 9 (CONTINUED)

H3 (J/MOLE)

(K) 0.000

0.1300 0.1400 0.1500 0.1600 0.1800 0.2000 0.2250 0.2500 0.2750 0.3000

0.42167 0.44040 0.45089 0.45391 0.44012 0.4033* 0.33005 0.23100 0.11009 -0.02960

0.001 0.42173 0.44046 0.45094 0.45396 0.44016 0.40338 0.33009 0.23104 0.11013 -0.02956

O.on? 0, 42190 0.44062 0. 45110 0.454)1 0.44031 0.40352 0.33021 0.23116 0.11024 -0.07945

0.0O3 0.42219 0.44090 0.45137 0.45437 0.44054 0.40374 0.33042 0.23136 0.11043 -0.02928

0.00* 0.42259 0.44129 0.45174 0.45473 0.44088 0.40405 0.33071 0.23163 0.11069 -0.029O3

0.006 0.42375 0.44239 0.45280 0.45575 0-44183 0.40495 0.33155 0.23242 0.11143 -0.02^32

0.00H 0.42537 0.44394 0.45428 0.45717 0.44316 0.40620 0.33?72 0.23351 0.11247 -0.07733

0.010 0.42745 0.44593 0.45619 0. 45901 0.44487 0.40781 0.33422 0.23493 0.11381 -0.02606

0.012 0.47999 0.44B36 0.45852 0.46125 0.44696 0.40977 0.33605 0.23665 0.11544 -0.07451

0.014 0.43299 0.45123 0.46128 0.46390 0.44943 0.41709 0.33822 0.23869 0.11737 -0.07267

0.016 0.43645 0.45454 0.46446 0.46696 0.45228 0.41477 0.3*072 0.24104 0. 11960 -0.07055

0.018 P. 44Q3B 0.45829 0.46805 0.4704? 0.45551 0.41781 0.34355 0.24370 0.12212 -0.01815

0.020 0.4447ft 0.46248 0.47208 0.47429 0.45912 0.47120 0.3*671 0.24668 0.12494 -0.01547

0.025 0.45771 0.47487 0.48397 0.48573 0.46979 0.43122 0.35607 0.2*549 0.13327 -0.00753

0.030 0.47351 0.48999 0.49R47 0.49970 0.48281 0.44347 0.36750 0.26624 0.14346 0.00216

0.035 0.49212 0.50780 0.51558 0.51616 0.49818 0.45791 0.38099 0.27894 0.15548 0.01360

0.040 0.51354 0.52830 0.53526 0.53511 0.51586 0.47454 0.39653 0.29356 0.16933 0.02679

0.045 0.53771 0.55145 0.55750 0.55653 0.53586 0.49336 0.*1*11 0.3i011 0-18501 0.04172

0.050 0.56461 0.57723 0.58226 0.58039 0.55815 0.51433 0.43371 U.3?857 0.20251 0.05839

0.060 0.62641 0.63648 0.63923 0.63530 0.60950 0.56269 0.4 7 894 0.37119 0.24290 0.09687

0.070 0.69847 0.70568 0.70585 0.69957 0*66966 0.61943 0.53207 0.4?12B 0.29041 0.14216

0.080 0.78026 0.78434 0.7B168 0.77283 0.73842 0.68433 0.59291 0.4 7 871 0.34493 0.19415

0.0°0 0.B71U 0.87192 0.B6625 0.85464 0.81536 0.75710 0.66125 0.54330 0.40629 0.25272

O.IOO 0.9705? 0.96785 0.95902 0.94451 0.90009 0.83741 0.73681 0.614R? 0.47433 0.31772

0.120 1 .1918) 1 .18719 1 .16693 1 .14644 1 .09124 1.01915 0.90B38 0.77764 0.62954 0.46625

0.14(1 1 ,43894 1 .42747 1 .40080 1.3743? 1.30821 1.22645 1.10501 0.96493 0.B0861 0.63S05

0.160 1.70754 1.68447 1 .65659 1.62425 1 .54740 1.45599 1.32381 1.17422 1 .00942 0.83126

0.180 1 .9939? 1.96463 1 .93085 1.89290 1.80565 1.70482 1.56?o* 1.4n297 1.22966 1.04379

0.200 2.?9508 2.25998 2.22066 2.17741 2.08026 1.97035 1.81727 1.64890 1.46715 1.27362

0.250 3.S9779 3.04994 2.99835 2.94331 2.82385 2.69322 2.51626 2.3?6o? 7.12419 1.91220

0.300 3.95219 3.89369 3.83182 3.76684 3.62843 3.47998 3.2«217 3.07253 2.85263 2.62376

0.350 4,84255 4.77507 4.70447 4.63100 4.47635 4.31255 4.09667 3.87007 3.63422 3.39032

0.400 5.75867 5.68365 5.60567 5.52497 5.35630 5.17914 4.94745 4.70595 4.45603 4.198B0

0,450 6. (,9405 6.61247 6.52810 6.44118 6.?6050 6.07174 5.82615 5.57U6 5.30901 5.03991

0.500 7.64425 7.55697 7.46701 7.3746? 7.18332 6,98444 6.72671 6.46035 6.18674 5.90697

0.550 8.60608 8.51379 8.41892 8.32171 8.12103 7.91309 7.64454 7.36789 7.08436 6.79504

0.600 9.57726 9.48052 9.3&128 9.27978 9.07074 8.85473 8.57645 8.29047 7.99809 7.70025

0.650 10.55604 10.45533 10.35218 10.24684 10.03030 9.80703 9.52001 9.2?562 8.92511 R. 61951 0.7C0 11.54114 1 1.43684 11.33017 11.22136 10«99805 10.76821 10.47326 10.17123 9.86337 9.55068

0.750 12.53153 12.42398 12.31411 12.20214 11 .97268 11.73687 11.43470 11.1?571 10.81113 10.49194

0.800 13.52640 13.41589 13.30310 13.18826 17.95318 12.71191 12.40312 12.0B775 11.76700 11.44186

0.850 14.5251? 14.41189 14.29643 14.17895 13.93871 13.69242 13.37755 13.05630 12.72987 12.39923

0.900 15.52717 15.41)44 15.29351 15.17360 14.92859 14.67767 14.35719 14.03051 13.69882 13.36310

0.150 16.53211 16.41406 16.29385 16.17170 15.92229 15,66708 15.34]39 15.0f|967 14.67310 14.33265

1.000 17.53959 1 7.41940 17.29707 17.17283 16.91932 16.66012 16.32960 15.99319 15.65207 15.30722

1.100 19.56103 19,43697 19.31083 19.1828? 18.92193 IB. 65554 18.31627 17.97138 17.62204 17.26921

1.200 21.58963 21.46217 21.33268 21.20136 20.93398 20.66126 20.3H28 19.96192 19.60534 19.2*547

1.3C0 23.6240(1 23.49353 23.3&107 23.22682 22.95368 22.67533 22.32151 21.96250 21.59946 21.23331

1.400 25.66312 25.52996 25.39484 25.25796 24.97966 24.69627 24.33632 23.97135 23.60251 23.23074

1.500 27.70619 27.57061 27.43309 27.29384 27.01088 26.72295 26.35746 25.9fl7H 25.61303 25.23616

Page 104
TABLE 10 THE OSMOTIC PRESSURE OF H£3 IN HE* AND THE EXPRESSION -[^(X, T) -U4

*(T=0)] OSMOTIC PRESSURE P OSM

-[W4

(X. T) -U

4 '(T=0)] U4

X • 0.0001 X - 0.0002 X 0.0005 X 0.0010

T (K) 0.000

0.001 0.002

0.003

0.004 0.006

0.008

0.010 0.0]2

0.01*

0.016

0.018

o.oao 0.025

0.030 0.035

0.040

0.045

0.050

0.060 0.070

0.080

0.090

0. 100 0.1?0

0.140

0.160

0.180

0.200

0.250

0.300

0.350 0.4OO

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800 0.850

0.900 0.950

1.000

1.100

1.200

1.300

1.400

1.500

P OSM

(TORR) 4.850-004

5.5o 9 -004 7.002-004

8.840-004

1 .083-003 1.5Q2-003

1.933-003 2.371-003

2.813-003

3.257-003

3.7n2-003

4.149.003

4.596-003

5.718-003

6.841-003

7.966-003 9.093-003

1.022-002

1.135-002

1 .360-002 1.5R6-002

1.812-002 2.038-002

2.264-002

2.715-002

3.167-C02

3.619-002

4.071-002 4.5?3-002 5.653-002

6.784-002

7.914.002 9.044-002

1.017-001

1.130-001

1.244-001

1.357-001

1.470-001

1 .5S3-001 1.696-001

1.809-001

1.922-001 2.035-001 2.148-001

2.261-001

2.4B7-001

2.713-001

2.9T9-001

3.165-001 3.391-001

U4 U/MOLE)

1 .783-006 2.026-006

2.575-006

3.250-00A

3.982-006

5.521-006

7.108-006

8.719-006

1.034-005

1.198-00!! 1.361-005

1 .526-005 1.690-005 2.103-005

2.516-005

2.930-005

3.345-005 3.761-005 4.177-005

5.011-005 5.848-005

6.690-005

7.537-005

8.391.005

1.013-004

1.191-004

1 .375-004 1.568-004

1 .772-004 2.345-004

3.046-004

3.932-004 5.068-004

6.533-004 8.412-004

1.0«0-003 1.381-003

1.757-003 2.227-003

2.827-003

3.612-003 4.669-003

6.122-003 8.140-003

1.094-002 2.002-002

3.618-002

6.319-002

1.061-001

1 .713-001

P OSM

(TORR) 1.534-003

1.620-003

1.843-003

2. 152-003 2.506-003 3.285-003

4.110-003

4,959-003 5.822-003

6.693-003

7.571-003 8,454-003

9.339-003

1.156-002

1.380-002

1.604-002

1.828-002 2.053-002

2.278-002 2.728-002

3.178-002

3.629-002 4,080-002

4.532-002

5.435-002

6.338-002

7.241-002

8.145-002

9.048-002

1.131-001 1.357-001

1.583-001

1.809-001 2.035-001 2.261-001

2.487-001 2.713-001

2.939-001

3.165-001

3.391-001 3.617-001

3.843-001 4.069-001

4.295-001

4.521-001

4.973-001

5.425-001

5.878-001

6.33O-001 6.782-001

U4

(J/MOLE) 5.642-006

5.956-006

6.778-006 7.913-006

9,216-006

1.208-005

1. 511-005

1. 823-005 2.141-005

2.461-ooS

2.784-005

3.109-005

3.434-005 4.252-005

5.0^4-005

5.898-005

6.724-005

7.551-005

8.379-005

1.004-004

l.lTfl-004 1.337-004

1,505-004

1,673-004 2.012-004

2.357-004 2.707-004

3.066-004

3.436-00*

4,424-00*

5.5*0-004

6.842-004

8.394-00*

1.027-003

1.257-003

1.537-003

1.880-003 2.297-003 2.809-003

3.*5o-003

*. 277-003 5.375-003

6.870-003

8.929-003

1.177-002 2.09*-002

3.717-002 6.*27-002

1.072-001 1.726-001

P OSM

(TORR) 6.978-003

7.093-003

7.426-003 7.948-003 8.612-003

1.021-002

1.203-002 1.397-002

1,599-002

1.806-002 2.016-002

2.228-002

2.443-002

2.986-002

3,534-002 4.086-002

4.641-002 5.197-002

5.754-002

6.872-002

7.993-002

9.116-002

1.024-001 1.136-001

1.362-001

1.587-001

1.812-001 2.038-001

2.264-001

2.828-001

3.392-001

3.957-001 4.521-001

5.086-001

5.651-001

6.216-001

6.780-001

7,345-001

7.910-001

8.475-001 9.040-001

9.605-001

1.017*000

1.073*000 1.130*000

1.243*000 1.356*000 1*69*000

1.582*000

1,695*000

U4

(J/MOLE) 2.566-005

2.608-005

2.731-005 2.923-005

3.167-005

3.756-005 4.425-005

5.138-005

5,879-005

6.639-005

7.412-005

8.194.005

8.983-005

1.098-004

1.300-004 1.503-004

1.707-004

1.911-004 2.116-004

2.528-004

2.941-004 3.355-004

3.770-004

4.185-004 5.O21-004

5.861-004

6.709-00*

7.565-004 8.432-004

1.066-003

1.302-003

1.557-003

1.837-003 2.149-003 2.503-003

2.908-003

3.376-003 3.917-003

4.554-003

5.320-003

6.271-003

7.494-003 9.113-003

1.130-002 1.426-002 2.368-002

4,017-00?

6.751-002

1.107-001 1.763-001

P OSM

(TORR) 2.181-002

2.196-002

2.238-002

2,308-002

2.403.002

2.650-002

2.953-002

3.292-002

3.654-002

4.03*-002

*. 426. 002 4.828.002

5.236-002

6.279.002

7.344.002 8.423.002

9.511-002

1.061-001

1.171-001 1.392-001 1.614-001

1.837-001 2.060-001

2.284-001

2.732-001

3.182-001 3.631-001

*.Q81-O0l

4.531-001

U4

(J/MOLE) 8.020-005

8.073-005

8.231-005

6.488-005 8.836-005

9.7*5-005

1.086-004

1.210-004

1.344-004

1.483-004

1.628-004 1.775-004

1.925-004 2.309-004

2.701-004

3.097-004 3.497-004

3.900-004

4.305-004 5.118-004

5.936-004

6.757-004 7.580-004

8.405-004

1.006-003 1.172-003

1*3*0-003

1.508-003

1.677-003 5.658-001 2.107-003

6.785-001

7,913.001 9.0*1-001

1.017*000

1.130*000 1.2*3*000

1.356*000

1.468.000 1.581*000

1.69**000

1.807*000

1.920*000 2,033,000

2.1*6*000

2.259.000

2,*8**000

2.710*000

2.936.000

3.162*000

3.388*000

2.550-003

3.012-003

3.499-003 4.018-003

4. 580-003 5.192-003 5.867-003

6.616-003

7.459-003

8.433-003 9.591-003

1.102-002

l.?85-002

1.524-002

1. 841-002 2.824-002

*. 515-002 7.290-002

1.165-001

1.825-001

P OSM

(TORR) 6.769-002

6.787-002

6.8*1-002

6.931-002 7.056-002

7.*01-002

7.855-002

8.393-002

8.996-002

9.648-002

1.034-001

1.106-001

1.180-001

1.374-001

1.575-001 1.781-001

1.991-001 2.203-001 2.417-001

2.850-001

3.287-001 3.727-001

4.168-001 4.611-001

5.500-001

6.393-001

7.287-001

8.183-001 9.079-001

1.132*000

1.357*000

1.582*000

1.807*000 2.033*000

2.258*000

2.483*000

2.709*000

2.934*000

3.160*000

3.385*000

3.611*000

3.836*000 4.062*000

4,287*000

4,513*000

4.964*000

5.415*000

5,866*000

6.317*000 6.768*000

0.0020

U4

(J/MOLE) 2.489-004

2.496-004

2.516-004

2.549-004

2,595-004

2. '21-00* 2.888-004

3.086-004 3.308-004

3.548-00*

3.801-00*

4.066-004 4.339-004

5.051-004

5.791-004

6.549-004

7.320-004

8.101-004

8.889-004

1.048-003 1.209-003

1.371-003

1.533-003

1.696-003 2.024-003

2.353-003

2.684-003

3.016-003 3.349-003

4.191-003

5.046-003 5.920-003

6.820-003

7.753-003

8. '28-003

9. '54-003 1.084-002

1. 200-002

1.326-002 1.465-002 1.622-002

1.807-002 2.031-00?

2.311-002

2.670-002

3. ?36-002 5,509-002

8.368-002

1,281-001

1. 950-001

Page 105
TABLE ]0 (CONTINUED)

X » 0.0030 X = 0.0040 X a 0.0050 X s 0.0060 X * O.oOBO

T

(K) 0.000

0.001 0.002

0.003 0.00*

0.006

0.008

0.010

0.012

0.01* 0.016 0.018

0.020 0.025

0.030 0.035

0.040 0.045

0.050

0.060

0.070

0.080

0.090

0.100 0.120 0.140

0.160

0.180

0.200

0.250

0.300 0.350

0.400

0.450

0.500 0.550

0.600

0.650

0.700 0.750

0.800 0.850

0.900

0.950

1.000

I. 100 1.200

1.300

1.4 1.500

P OSM

(TOPR)

1 .306-001 1.3o8-001

1.315-001

1.325-001 1.339-001

1.380-001

1.415-001 1.5n2-001

1.579-001

1.665-001

1.757-001

1.855-001

1.957-001 2.228-001

2.513-001

2.809-001 3.H3-001

3.422-001

3.735-001 4.371-001

5.015-001 5.665-001

6.320-001 6.978-001

8.351-001 9.631-001

1.096*000

1.230*000

1.364*000

1.700*000 2.036*000

2.373*000

2.710*000

3.047*000

3.384*000 3.722*000

4.060*000

4.397*000 4.735*000

5.073*000

5.4"iO*000 5.748*000

6.086*000

6.424*000

6.762*000

7.438*000

8.114*000

8.790*000

9.466*000

1.014*001

U4 (J/MOLE) 4.803-004

4.811-004

4.834-004

4.872-004 4.925-004

5.074-004

5.276-004

5.523-004

5.807-004

6.122-004

6.461-004

6.821-004

7.196-004 8.191-004

9.241-004

1.033-003

1.145-003

1.258-003

1.373-003 1.607-003

1.844. 2.083.

2.324.

2.567.

3.054.

3.544. 4.036-

4.531- 5.027-

6.277-

003 003

003 003

003 003 003

003

003

003 7.542-003

8.827-003

1.014-002

1.148-002

1.287-002

1.431-002

1.581-002

1.738-002

1.906-002 2.086-002 2.284-002

2.510-002 2.775-002

3.097-002

3.497-002 4.646-002

6.501-002

9.443-002

1.397-001 2.074-001

P OSM

(TORR) 2.076-001

2.079-001

2.085-001

2.097-001

2.113-001

2.158-001

2.220-001

2.297-001

2,387-001 2.488-001

2.599-001

2.718-001

2.844-001

3.181-001

3.543-001

3.921-001 4.312-001

4.712-001

5.119-001

5.949-001 6.795-001

7.650-001

8.513-001

9.382-001

1.113*000 1.289*000

1 .466*000 1.644*000

1.822*000 2.266*000

2.715*000

3.163*000

3.611*000

4.060*000

4.509*000

4.959*000 5.408*000

5.858*000

6.307*000

6.757*000

7,207*000

7,657*000

8.107*000 8.557*000

9.007*000

9.907*000

1.081*001

1.171*001

1.261*001

1.351*001

U4 (J/MOLE) 7.634-004

7.643-004 7.668-004

7.710-004

7.769-004 7.935-004

8.162-004

8.445-00*

8.776-00* 9.1*9-00*

9.557-00*

9.995-00*

1.0*6-003

1.170-003

1.303-003

l.**2-003

1.586-003 1.733-003

1.882-003 2.188-003

2,*99-003 2.813-003

3.131-003

3,*5o-003

*. 095-003 4.743-003

5.396-003

6.051-003

6.709-003

8.365-003

1.004-002 1.173-002

1.345-002

1.521-002 1.701-002

1.886-002 2.077-002 2.275-002

2.484- o2 2.705-002

2.945-002

3.212-002

3,518-002

3.881-002 4.323-002 5.554-002

7.492-002

1.052-001

1.513-001 2.197-001

P OSM

(TORR) 2.967-001

2.970-001

2.977-001

2,990-001

3,007-001

3.056-001

3.123-001 3.208-001

3.308-001

3.423-001

3.549-001 3,686-001

3,832-001 4.228-001

4.658-001

5.112-001

5,58*-001

6.070-001 6.567-001

7.58*-001 8,623-001

9.678-001

1.07**000

1.182*000

1 ,399*000 1.618*000 1.838*000 2.059*000

2.280*000

2.836*000

3.393*000 3.952*000

*. 512*000 5,072*000

5,632*000

6.193*000 6,75**000

7.315*000

7.877*000

8,*39*000 9.000*000

9.562*000

1.012*001 1.069*001

1.125*001

1.237*001

1,350*001

l.*62*001

1.575*001 1.687*001

U4 (J/MOLE) 1.091-003

1.092-003 1.095-003

1.099-003

1.106-003 1.124-003

1.1*8-003

1.180-003

1.216-003 1.258-003

1.305-003

1.355-003

l.*09-003 1.555-003

1.713-003

1.880-003 2.053-003 2.232-003

2.415-003

2.789-003

3.171-003

3.559-003

3.951-003

*. 3*7-003 5.1*6-003

5.951-003

6.762-003

7.577-003

8.395-003

1.0*5-002 1.253-002

l.*63-002

1.676-002

1.893-002 2.11*-002 2.340-002

2.572-002 2.812-002

3.061-002

3.323-002

3.604-002

3.912-002

*. 260-002

*. 664-002 5.1*7-002

6.*60-002

8.*8l-002

1.159-001 1.628-001 2.321-001

P OSM

(TORR) 3.966-001

3.969-001

3.977_00l 3.990-001

*. 008-001

*. 060-001

*. 132-001

*. 223-001

*. 332-001 *.*57-ool

*. 597. ool

*. 7*9-001

*. 912-001 5.360-001

5.852-001

6.376-001 6.925-001

7.*92-00l 8,07*-00l 9.270-001

1.050*000

1.175.00U

1.301*000

l.*29*000

1.686*000 1.9*8*000 2.211*000

2.*75*000

2.7*0*000

3,404*000

4.072*000

4.741*000

5.411*000

6.082*000

6.754*000

7.426*000

8.098*000

8.771*000

9.444*000

1.012*001

1.079*001

1.146*001 1.21**001

1.281*001

1.3*8*001

1.483*001 1.618*001

1.753*001 1.868*001 2.023*001

U4 (J/MOLE) 1.458-003

1.459-003

1.462-003 1.467-003

1.474-003

1.493-003 1.519-003

1.553-003

1.593-003

1.639-003

1.690-003

1.746-003 1.806-003

1.971-003 2.152-003

2.345-003

2.546-003

2.755-003 2.969-003

3.409-003

3.860-003 4.320-003

4.785-003

5.256-003

6.206-003

7.167-003

8.134-003

9.107-003

1.008-002

1.254-002

1.503-002

1.753-002 2.007-002

2.264-002

2.526-002

*. 793-002 3.066-002

3.347-002

3.637-002

3.940-002 4.262-002

4.611-002

5.000-002

5.446-002

5.969-002

7.365-002

9.468-002

1.266-001 1.743-001 2.444-001

P OSM

(TORR) 6.244-001

6.247-001

6.256-001

6.270-001

6.291-001 6.348-001

6.428-001

6.530-001 6.652-001

6.795-001

6.955-001

7.132-001 7.324-001

7.860-001

8.460-001

9.110-001

9,797-001

1.051*000

1.125*000 1.279*000

1.437*000

1.600*000

1.765*000

1.932*000 2.272*000

2.615*000

2.962*000

3.310*000

3.661*000

4.542*000

5.427*000

6.315*000

7.206*000

8.098*000

8.991*000 9.884*000

1.078*001

1.167*001 1.257*001

1.346*001

1.436*001

1.526*001 1.615*001

1.705*001 1.795*001

1.974*001

2.153*001 2.333*001

2.512*001 2.692*001

U4

(J/MOLE) 296-003

297-003

300-003

306-003 313-003

334-

364- *01-

446-

498-

557- 623-

693-

890-

111- 350-

602-

866-

138-

?02-

003

003 003

003

003

003

003

003 003

003 003

003

003 003

003 286-003 883-003

491-003

106-003 354-003 618-003

089-002 218-002

347-002

673-002

001-002 332-002

667-002

005-002 348-002

697-002

052-002

414-002

T86-002 171-002 575-002

006-002 477-002

00*-002 610-002

169-002

144-001 479-001

973-001

691-001

Page 106
TABLE 10 (CONTINUED)

0. 01 00 X * 0.0150 X 0.0200 X 0*0290 X 0.0300

T P OSM U4 P OSM U4 P OSM U4 P OSM U4 P OSM U4

(K) (TORR) (J/MOLE) (TORR) (J/MOLE) (TORR) (J/MOLE) (TORR) (J/MOLE) (TORR) (J/MOLE) 0.000 8.845-001 3.252-003 1.647*000 6.056-003 2.532*000 9.310-003 3.506*000 1.289-002 4.545*000 1.671-002

0.001 8.848-001 3.254-003 1.647*000 6.057-003 2.532*000 9.312-003 3.506*000 1.289-002 4.546*000 1.671-002

0.002 8.858-001 3.257-003 1.648*000 6.061-003 2.534.000 9.316-003 3.508*000 l.?90-002 4.547*000 1 .672-002

0.0O3 8.873-001 3.263-003 1.650*000 6, 068-003 2.535.000 9.323-003 3.510*000 1.291-002 4,549*000 1 .673-002

0.00* 8,855-001 3.271-003 1.653*000 6.0^7-003 2.538*000 9.333-003 3.513*000 1.292-002 4.552*000 1.674-002

0.00* 8.957-001 3.294-003 1.660*000 6.103-003 2.546*000 9.362-003 3.521*000 1.295-002 4.561*000 1.677-002

0.008 9.044-001 3.325-003 1.670*000 6,l4o-003 2.557*000 9.403-003 3.533*000 1.299-002 4.574*000 1.682-002

o.oio 9.154-001 3.366-003 1,683*000 6.187-003 2.571*000 9.454-003 3.548*000 1.305-002 4.590*000 1 .688-002

0.012 9.288-001 3.415-003 1.698*000 6.244-003 2.588*000 9.518-003 3.567*000 1.312-002 4. 610'000 1.695-002

0.01* 9.444-001 3.472-003 1.716*000 6.311-003 2.609*000 9.592-003 3.589*000 1.320-002 4.633*000 1.704-002

0.016 9.621-001 3.538-003 1.737.000 6.387-003 2.632*000 9.677-003 3.614*000 1.329-002 4.660*000 1.714-002

0.018 9.818-001 3.610-003 1.761.000 6.473-003 2.658*000 9,774-003 3,642*000 1.339-002 4,691.000 1.725-002

0.020 1.003*000 3.689-003 1.786.000 6.568-003 2.687*000 9.880-003 3.674*000 1.351-002 4.725*000 1.737-002

0.025 1. 0*4. 000 3.913-003 1.861.000 6.842-003 2.772*000 1.019-002 3.767*000 1.385-002 4.824.000 1.774-002

0.030 1.133.000 4.167-003 1,948.000 7.162-003 2.872*000 1.056-002 3.877*000 1.426-002 4.943.000 1.818-002

0.035 1.269*000 4.445-003 2,045*000 7.520-003 2.986*000 1.098-00? 4.005*000 1.473-002 5.082*000 1.869-002

0.0*0 1.290*000 4.743-003 2.151*000 7.911-003 3.112*000 1.144-00? 4,147*000 1.525-002 5.238*000 1.926-002

0.045 1.375*000 5.056-003 2.265*000 8.329-003 3.248*000 1.194-002 4.302*000 1.582-002 5.409*000 j.989-002

0.050 1.464*000 5.382-003 2.385*000 8.769-003 3.394*000 1.248-002 4,469*000 1.643-002 5.594*000 2.057-002

0.060 1 .648*000 6.061-003 2.639*000 9.7 -003 3.706*000 1.363-002 4,832*000 1.777-002 6.001*000 2.207-002

0.070 1.841*000 6.769-003 2,908*000 1.0 e 9-002 4,042*000 1.486-002 5.227*000 1.922-002 ' 6.448*000 2.371-002

0.080 2.039*000 7.497-003 3.187*000 1.172-002 4.395*000 1.616-002 5.645*000 2.076-002 6.927*000 2.547-002

0.090 2.241*000 8.241-003 3,476*000 1.278-002 4.761*000 1.751-00? 6.083*000 2.237-002 7.430*000 2.732-002

0.100 2.446*000 8.996-003 3,771*000 1.387-002 5.139*000 1.890-00? 6.537*000 2.404-002 7.954*000 2.925-002

0.120 2.864*000 1.053-002 4,375*000 1.609-002 5.917.000 2.176-002 7,479*000 2.750-002 9.050*000 3.328-002

0.140 3.288-000 1.209-002 4,993*000 1.836-002 6.719*000 2.471-002 8.455*000 3.109-002 1.019*001 3. 748-002

0.160 3.717.000 1.367-002 5.621*000 2.067-002 7.538*000 2.772-002 9.457.000 3.478-002 1.152*001 4.235-002

0.180 4,149.000 1.526-002 6.257*000 2.301-002 8,4o4.000 3.091-002 1.050.001 3.863-002 1.260*001 4.634-002

0.200 4,584.000 1 .687-002 6,897.000 2.537-002 9,208.000 3.387-002 1.151.001 4.233-002 1.379*001 5.072-002

0.250 5.679.000 2.091-002 8,516.000 3.134-002 1.134.001 4.172-002 1.414.001 5.201-002 1.691*001 6.219-002

0.300 6.780*000 2.499-002 1.015.001 3.737-002 1.349.001 4.967-002 1. 680»00l 6.184-002 2.008*001 7.388-002

0.350 7.886*000 2.910-002 1.179*001 4.347-002 1.567*001 5.770-002 1.950*001 7.]8o-002 2.329*001 8.573-002

0.400 8.995*000 3.325-002 1.344*001 4.96i-oo2 1.785*001 6.581-002 2.221*001 8.J84-002 2.652*001 9.769-002

0.*50 1.011*001 3.744-002 1.510*001 5.580-002 2.004*001 7.398-00? 2.494*001 9.197-002 2.977*001 1.098-001

0.500 1.122*001 4.168-002 1.676*001 6.205-002 2.224*001 8.222-002 2.767*001 1-022-001 3.304*001 1.219-001

0.550 1.233*001 4.598-002 1,842*001 6.836-002 2.445*001 9.052-002 3.042.001 1.125-001 3.632*001 1.342-001

0.600 1.345.001 5.034-002 2,008*001 7.473-002 2,666.001 9.890-002 3.317*001 1.228-001 3.961*001 1.465-001

0.650 1.457.001 5.478-002 2.175.001 8.119-002 2.887.001 1.074-001 3.592.001 1.333-001 4,290*001 1.590-001

0.700 1.568.001 5.931-002 2.342*001 8.775-002 3,108.001 1.159-001 3.868.001 1.439-001 4.620*001 1. '15-001 0.750 1.680*001 6.398-002 2.509.001 9.445-002 3,330.001 1.246-001 *. 144. 001 1.546-001 4.951*001 1.842-001

0.800 1.792*001 6.883-002 2.676*001 1 .013-001 3.552*001 1.335-001 4.420*001 1.655-001 5.281*001 1.971-001

0.850 1.9n4*001 7.396-002 2.843*001 1.085-001 3.774*001 1.427-001 4.697*001 1.767-001 5.613*001 2.103-001

0.900 2.015*001 7.948-002 3.010*001 1.160-001 3.996*001 1.523-001 4.974*001 1.883-001 5.944*001 2.239-001

0.950 2.127*001 8.557-002 3.177*001 1.2*2-001 4.218*001 1.625-001 5.251*001 2.004-001 6.276*001 2.381-001

1.000 2.239*001 9.245-002 3.344*001 1.33l-ool 4.441*001 1.734-001 5.528*001 2.134-001 6.608*001 2.531-001

1.100 2.463*001 1.097-001 3.679*001 1.544-noi 4,885*001 1.987-001 6.083.001 2.428-001 7.272*001 2.865-001

1.200 2.687*001 1.340-001 4.014*001 1.828-001 5.331*001 2.312-001 6.638.001 2.793-001 7.937*001 3.270-001

1.300 2.911*001 1 .692.001 4.349.001 2.220-001 5,776.001 2.745-001 7.194.001 3.266-001 8.603*001 3.784-001

1.400 3.135*001 2.202-001 4,684*001 2.771-001 6.222.001 3.337-001 7.750.001 3.899-001 9.269*001 4.457-001

1.500 3.359*001 2.936-001 5.019.001 3.546-001 6,667.001 4.152-001 8.306.001 4.755-001 9.935*001 5.354-001

Page 107
TABLE 10 (CONTINUED)

X .0350 X « .0400 X .0450 X a .0500 X = .0550

T P OSM U4 P OSM u* P OSM U4 P OSM U4 P OSM U4

(K) (TOPR) (J/MOLE) (TORR) < J/MOLE

>

(TORR) (J/MOLE) (TORR) (J/MOLE) (TORR) f J/MOLE) 0.000 5.631*000 2.0^0-002 6,748*000 2.481-002 7,885*000 2.899-002 9.031*000 3.321-002 1.018*001 3 ,742-00?

0.001 5.631*000 2.071-002 6,749*000 2.462-002 7.886*000 2.900-002 9.032*000 3.321-002 1.018*001 3 743-002

0.002 5.633*000 2.071-002 6.750*000 2.482-002 7,887*000 2.900-002 9.034*000 3.322-002 1.018*001 3 743-002

0.003 5.635*000 2.072-002 6.753*000 2.483-002 7.890*000 2,901-002 9.036*000 3.323-002 1.018*001 3 744-002

0.00* 5.638*000 2.073-002 6,756*000 2.484-002 7.894*000 2.902-002 9,040*000 3.324-002 1.019*001 3 746-002

0.006 5.648*000 2.077-002 6,766*000 2.488-002 7.904*000 2.906-002 9.051.000 3.328-002 1.020*001 3 ,750-002

0.008 5.6*1*000 2.082-002 6.780*000 2.493-002 7.918*000 2.912-002 9,066*000 3.333-002 1.021*001 3 .755-002 0-010 5.678*000 2. 88-002 6.798*000 2.500-002 7.937*000 2.918-002 9.085*000 3.341-002 1.023*001 3 763-002

0.012 5.699*000 2.096-002 6.820*000 2.508-002 7.960*000 2.927-002 9.109*000 3.349-002 1.026*001 3 772-002

0.01* 5.7?4*000 2.105-002 6,846*000 2.517-002 7.987*000 2.937-002 9.]37*000 3.360-002 1.029*001 3 782-002

0.016 5.752*000 2.115-002 6.876*000 2.528-002 8.018*000 2.948-00? 9.169*000 3.371-002 1.032*001 3 ,795-002 0.018 5.784*000 2.127-002 6,909*000 2.541-002 8.053*000 2.961-002 9.206*000 3.385-002 1.036*001 3 809-002

0.020 5.820*000 2.140-002 6.947*000 2.554-002 8.092*000 2.976-002 9.246*000 3.400-002 1.040*001 3 824-002

0.025 5.9?6*000 2.179-002 7.058*000 2.595-002 8.208*000 3.018-002 9.366*000 3.444-002 1.052*001 3 870-002

0.030 6.053*000 2.226-002 7,192*000 2.6*4-002 8,348*000 3.070-002 9.512*000 3.498-002 1.068*001 3 925-002

0.035 6.2ol*000 2.280-002 7.348*000 2.702-002 8.512*000 3,130-002 9.684*000 3.561-002 1.085*001 3 ,991-002 0.0*0 6.368*000 2.342-002 7,526*000 2.767-002 8.699*000 3.199-002 9.879*000 3.633-002 1.106*001 4 066-002

0.0*5 6.554*000 2.410-002 7,724*000 2.84o-on2 8.908*000 3.275-002 1.010*001 3.713-002 1.128*001 4 149-002

0.050 6.755*000 2.484-002 7,940*000 2.919-002 9.137*000 3.360-002 1.03**001 3.801-002 1.154*001 4 242-002

0.060 7.2ol*000 2.648-002 8.420*000 3.096-002 9,649*000 3.548-002 1.088*001 4.000-002 1.210*001 4 450-002

0.070 7.695*000 2.829-002 8.956*000 3.293-002 1.022*001 3.759-002 1.1*9*001 4.225-002 1.275*001 4 687-002

0.080 8.2?7*000 3.025-002 9.539*000 3.507-002 1.085.001 3.990-00? 1.216*001 4.471-002 1,346*001 4 948-002

0.090 fi. 792*000 3.233-002 1.016*001 3.736-002 1.152*001 4,238-002 1.288*001 4.737-002 1.422*001 5 230-002

0.100 9.382*000 3.450-002 1.081*001 3.975-002 1.223*001 4,498-00? 1.365*001 5.017-002 ] .504*001 5 530-002

0.120 1.062*001 3.906-002 1.219*001 4.482-002 1.374*001 5.053-002 1.528*001 5.617-002 1.679*001 6 ,174-002 0.140 1.192*001 4.385-002 1.365*001 5.018-002 1.53**001 5.64?-002 1.702*001 6.257-002 1.666*001 6 862-002

0.160 1.339*001 4.923-002 1.527*001 5.615-002 1.712*001 6.297-002 1.895*001 6.968-002 2.074*001 7 ,626-002

0.180 1.468*001 5.397-002 1.673*001 6.151-002 1,875*001 6.894-002 2.073*001 7.625-002 2.268*001 8 341-002

0.200 1.6o5*001 5.903-002 1.828*001 6.723-002 2.048*001 7.530-002 2.263*001 8.322-002 2.474*001 9 099-002

0.250 1.964*001 7.225-002 2.234*001 8.216-002 2.*99*001 9.191-00? 2.759*001 1.015-001 3.015*001 1 109-001 0.300 2.331*001 8.576-002 2.649*001 9.746-002 2.962*001 1.090-001 3.270*001 1.203-001 3.573*001 1 314-001

0.350 2.702*001 9.947-002 3.071*001 1.130-001 3,*34*001 1.264-001 3.791*001 1.395-001 4.142*001 1 524-001

0.400 3.078*001 1.133-001 3,498*001 1.288-001 3.911*001 1.44Q-001 4.319*001 1.590-001 4.720*001 1 737-001 0.450 3.455*001 1.273-001 3.927*001 1.447-001 4.393*001 1.618-001 4,851*001 1.787-001 5.303*001 1 953-001

0.500 3.835*001 1.414-001 4.359*001 1.607-001 4.877*001 1.797-001 5.367*001 1.985-001 5.891*001 2 170-001 0.550 4.216*001 1.556-001 4,793*001 1.769-001 5.363*001 1.978-001 5.926*001 2.185-001 6.482*001 2 390-001 0.600 4.598*001 1.700-001 5.229*001 1.931-001 5.852*001 2.161-001 6.466*001 2.387-001 7.076*001 2 611-001 0.650 4.981*001 1.844-001 5.665*001 2.095-001 6.342*001 2.344-001 7.011*001 2.590-001 7.672*001 2 833-001 0.700 5.365*001 1.989-001 6.103*001 2.260-001 6.833*001 2.529-001 7.556*001 2.795-001 8.270*001 3 057-001 0.750 5.750*001 2.136-001 6.541*001 2.427-001 7.325*001 2.716-001 8.102*001 3.001-001 8.870*001 3 283-001 0.800 6.135*001 2.285-001 6.980*001 2.596-001 7.818*001 2.904-001 8.649*001 3.210-001 9.471*001 3 512-001 0.850 6.520*001 2.437-001 7.420*001 2.768-001 8.312*001 3.096-001 9.196*001 3.421-001 1.007*002 3 U3-001

0.900 6.9o6*001 2.593-001 7.860*001 2.9**-001 8.807*001 3.292-001 9.745*001 3.637-001 1.068*002 3 979-001

0.950 7.292*001 2.755-001 8.301*001 3.126-001 9.302*001 3.494-001 1.029*002 3.859-001 1.128*002 4 221-001

1.000 7.679*001 2.925-001 8.742*001 3.316-001 9.797*001 3.704-001 1.084*002 4.089-001 1.188*002 4 471-001

1.100 8.453*001 3.299-001 9.625*001 3.730-001 1.079*002 4.158-001 1.195*002 4.584-001 1.309*002 5 006-001

1.200 9.227*001 3.745-001 1.051*002 *. 216-001 1.178*002 4.685-001 1.305*002 5.150-001 1.431*002 5 612-001

1.300 1.000*002 4.299-001 1.139*002 4.811-001 1.278*002 5.320-001 1.415*002 5.825-001 1.552*002 6 328-001

1.400 1.078*002 5.012-001 1.228*002 5.564-001 1.377*002 6.114-001 1.526*002 6.660-001 1.674*002 7 203-001

1.500 1.155*002 5.949-001 1.317*002 6.542-001 1.477*002 7.132-001 1.637*002 7.718-001 1.795*002 8 302-001

Page 108
TABLE 10 (CONTINUED)

X * .0600 X = .0640 X x .0650 X = .0700 X • O750

T P OSM U4 P OSM U4 P OSM U4 P OSM U4 P OSM U4

(K) (TORR) (J/MOLE) (TORR) (J/MOLE) (TORR) (J/MOLE) (TORR) (J/MOLE) (TORR) (J/MOLE) 0.000 1.132*001 4.161-002 1.222*001 4.492-002 1.244*001 4.574-002 1.354*001 4.980-002 1.462*001 5 376-002

0.001 1.132*001 4.161-002 1.222*001 4.492-0ft2 1.244.001 4.575-002 1.354*001 4.980-002 1.462*001 5 376-002

0.003 1.132*001 4.162-002 1.222*001 4.493-002 1,244*001 4.575-002 1.355*001 4.981-002 1.462*001 5 377-002

0.003 1.132*001 4.163-002 1.222*001 4.494-002 1,245*001 4.576-002 1,355*001 4.982-002 1 .463*001 5 378-002

0.004 1.133*001 4.164-002 1.223*001 4.496-002 1.245*001 4.578-002 1.355*001 4. <>84-002 1.463*001 S 380-002

0.006 1.134*001 4.169-002 1.224*001 4.500-002 1.246*001 4.582-002 1.357*001 4.988-002 1.464*001 5 384-002

0.00B 1.135*001 4.175-002 1.225*001 4.506-002 1.248*001 4.588-002 1.358*001 4.994-002 1.466*001 5 391-002

0.010 1.137*001 4.182-002 1.228*001 4.514-002 1.250*001 4.596-002 1.360*001 5.002-002 1.468*001 5 399-002

0.012 1.140*001 4.191-002 1. 230*001 4.523-002 1.253*001 4.606-002 1 .363*ool 5.012-002 1.471*001 5 409-002

o.oi* 1.143*001 4.202-002 1.233*001 4.534-002 1.256*001 4.617-002 1.366*001 5.024-002 1.474*001 5 421-002

0.016 1.146*001 4.215-002 1.237*001 4.547-002 1.259*001 4.630-002 1.370*001 5.037-002 1.478*001 3 434-002

0.018 1.150*001 4.229-002 1.241*001 4.562-002 1.263*001 4.645-002 1.374*001 5.052-002 1.482*001 5 450-002

0.020 1.155*001 4.245-002 1.245*001 4.578-002 1.268*001 4.661-002 1.379*001 5.069-002 1.487*001 5 467-002

0.025 1.167*001 4.293-002 1.258*001 4.627-002 1.281*001 4.710-002 1.392*001 5.119-002 1.501*001 5 518-002

0.030 1.183*001 4.350-002 1,274*001 4.686-002 1.297*001 4.769-002 1.409*001 5.180-002 1.518*001 5 581-002

0.035 1.201*001 4.418-002 1.293*001 4.755-002 1.316*001 4.839-002 1.428*001 5.252-002 1.538*001 S 655-002

0.040 1.222*001 4.495-002 1.315*001 4.834-002 1.338*001 4.919-002 1.451*001 5.334-002 1.561*001 5 739-002 0.045 1.246*001 4.582-002 1.339*001 4.924-002 1.362*001 5.008-002 1.476*001 5.427-002 1.587*001 5 834-002

0.050 1.272*001 4.678-002 1.366*001 5.023-002 1.389*001 5.108-002 1.504*001 5.529-002 1.616*001 5 940-002

0.060 1.331*001 4.895-002 1.427*001 5.247-002 1.451*001 5.334-002 1.567*001 5.763-002 1.681*001 6 181-002

0.070 1.399*001 5.144-002 1.497*001 5.503-002 1.521*001 5.592-002 1.640*001 6.031-002 1.757*001 6 459-002

0.080 1.474*001 5.418-002 1.574*001 5.788-002 1.599*001 5.880-002 1.722*001 6.331-002 1.841*001 6 770-002

0.090 1.555*001

1.641*001 5.716-002

6.033-002

1.658*001 1.748*001 6.098-002

6.429-002

1.684*001

1.775*001 6.192-0026.527-002

1.811*001 6.658-002

7.008-002

1,934*001 2.033*001

7

7 110-002

0.100 1.906*001 476-002

0.120 1.8?7*001 2.027*001

6.720-002

7.454-002

1.944*001 2.153*001

7.147-002

7.918-002

1.972*001 2.184*001

7.252-002 8.032-002

2.114*001

2.338*001

7.771-002

8.595-002

2.251*001 e 275-002

0.140 2.486*001 9 141-002

0.160 2.249*001 8.271-002 2.386*001 8.775-002 2.420*001 8.900-002 2.587*001 9.511-002 2.748*001 1 011-001

0.180 2.459*001 9.042-002 2.608*001 9.590-002 2.645*001 9.725-002 2.826*001 1.039-001 3.001*001 1 104-001

0.200 2.681*001 9.859-002 2.843*001 1.045-001 2.883*001 1.060-001 3.079*001 1-132-001 3.270*001 1 202-001

0.250 3.265*001 1.201-001 3.461*001 1.273-001 3.509*001 1.291-001 3.747*001 1.378-001 3.979*001 1 463-001

0.300 3.869*001 1.423-001 4.101*001 1.509-001 4,159*001 1.530-001 4.442*001 1.634-001 4.718*001 1 735-001 0.350 4.486*001 1.651-001 4.757*001 1.750-001 4.824*001 1.775-001 5.155*001 1.896-001 5.478*001 2 015-001

0.400 5.114*001 1.882.001 5,424*001 1.996-001 5.500*001 2.024-001 5.880*001 2.164-001 6.252*001 2 301-001

0.450 5.748*001 2.116-001 6,098*001 2.245-001 6.185*001 2.277-001 6.615*001 2,435-001 7,037*001 2 590-001

0.500 6.387*001 2.353-001 6.77B*001 2.497-001 6.875*001 2.532-001 7.356*001 2.709-001 7,829*001 2 ,883-001 0.550 7.030*001 2.591-001 7,463*001 2.750-001 7.571*001 2.790-001 8.103*001 2.986-001 8.627*001 3 178-001

0.600 7.677*001 2.832-001 8.152*001 3. 006-001 8.270*001 3.049-001 8.854*001 3.264-001 9.431*001 3 476-001

0.650 8.3a6*001 3.074-001 8.843*001 3.264-001 8.972*001 3.311-001 9.60 9 *00l 3.545-001 1.024*002 3 777-001

0.700 8.977*001 3.317-001 9.537*001 3.523-001 9.676*001 3.574-001 1.037*002 3.828-001 1.105*002 4 079-001

0.750 9.630*001 3.563-001 1.023*002 3.785-001 1.038*002 3.840-001 1.113*002 4.113-001 1.186*002 4 384-001

0.800 1.028*002 3.811-001 1.093*002 4.049-001 1.109*002 4,108-001 1.189*002 4.401-001 1.268*002 4 691-001

0.850 1.094*002 4.063-001 1.163*002 4.316-001 1.180*002 4.379-001 1.265*002 4.692-001 1.350*002 5 002-001

0.900 1.160*002 4,318-001 1.233*002 4.587-001 1.251*002 4.654-001 1.342*002 4.987-001 1.432*002 5 317-001

0.950 1.226*002 4.580-001 1.303*002 4,865-001 1.322.002 4.936-001 1.418*002 5.289-001 1.514*002 5 ,639-001

1.000 1.291*002 4.850-001 1.373*002 5, 151-001 1.394*002 5.226-001 1,495*002 5.599-001 1.596*002 5 ,969-001 1.100 1.423*002 5.425-001 1.514*002 5.758-001 1.537*002 5.841-001 1.649*002 6.255-001 1.761*002 & 665-001

1.200 1.556*002 6.072-001 1.655*002 6.437-001 1.680*002 6.529-001 1.803*002 6.982-001 1.926*002 7 433-001

1.300 1.688*002 6.828-001 1.796*002 7.226-001 1.823*002 7.325-001 1.958*002 7.819-001 2.091*002 8 310-001

l.*00 1.821*002 7.743-001 1.938*002 8.174-001 1,967*002 8.281-001 2.112*002 8.816-001 2.257*002 9 348-001

1.500 1.953*002 8.883-001 2.079*002 9.346-001 2.111*002 9.461-001 2.267*002 1.004*000 2.423*002 1 061*000

Page 109
TABLE 10 (CONTINUED)

X » 0.0800 X = 0.0900 X 0.1000 X = 0. 1 100 X x 0.)H00

T P OSM U4 P OSM ua P OSM U4 P OSM U4 P OSM U4

<K> (TORR) (J/MOLE) (TORR) U/MOLE) (TORR) (J/MOLE) (TORR) U/MOLE) (TORR) (J/MOLE) 0.000 1.567*001 5.760-002 1.764*001 6.487-002 1.944*001 7.147-002 2.102*001 7.730-002 2.237*001 8.224-002

0.001 1.567*001 5.760-002 1.764*001 6.487-002 1.944*001 7.147-00? 2.103*001 7.730-002 2.237*001 8.225-00?

0.003 1.567*001 5.761-002 1,765*001 6.488-002 1.944*001 7.148-002 2.103*001 7.731-002 2.237*001 8.226-002

0.003 1.567*001 5.762-002 1.765*001 6.489-002 1.945*001 7.149-002 2.103*001 7.732-002 2.238*001 8.227-002

0.00* 1.568*001 5.764-002 1.765*001 6.491-002 1,945*001 7.151-002 2.104*001 7.734-002 2.238*001 8.229-002

0.006 1.569*001 5.769-002 1.767*001 6.496-002 1.946*001 7.156-002 2.105*001 7.739-002 2.240*001 8.234-002

0.008 1.571*001 5.775-002 1.769*001 6.502-002 1.948*001 7.163-002 2.107*001 7.746-002 2.242*001 8.242-002

0.010 1.573*001 5.784-002 1.771*001 6.511-002 1.951*001 7.172-002 2.110*001 7.756-002 2.245*001 8.252-002

0.012 1 .576*001 5.794-002 1.774*001 6.522-002 1.954*001 7.183-002 2.113*001 7.767-002 2.248*001 8.263-002

0.01* 1.579*001 5.806-002 1.777*001 6.535-002 1.957*001 7.197-002 2.116*001 7.781-002 2.252*001 8.278-002

0.016 1.583*001 5.820-002 1.781*001 6.549-002 1.962*001 7.212-002 2.121*001 7.797-002 2.256*001 8.294-002

o.oia 1.587*001 5.836-002 1.786*001 6.566-002 1.966*001 7.229-002 2.126*001 7.815-002 2.261*001 8.312-002

0.020 1.592*001 5.854-002 1.791*001 6.584-002 1.971*001 7.248-002 2.131*001 7.835-002 2.267*001 8.333-002

0.025 1.6 6*001 5.906-002 1.806*001 6.639-002 1,987*001 7.305-002 2.147*001 7.894-002 2.283*001 8.394-002

0.030 1.6?4*001 5.970-002 1.824*001 6.706-002 2.006*001 7,375-002 2.167*001 7.966-002 2.304*001 8.468-002

0.035 1.644*001 6.045-002 1.845*001 6.785-002 2.028*001 7.457-002 2.190*001 8.051-002 2.328*001 8.557-002

0.040 1.668*001 6.132-002 1.870*001 6.876-002 2.054*001 7.552-002 2.217*001 8.J49-002 2.357*001 g.667-002

0.045 1 .694*001 6.230-002 1.898*001 6.978-002 2.083*001 7.658-002 2.247*001 8.?60-002 2.387*001 8. '74-002 O.O^O 1.7?4*001 6.339-002 1.929*001 7.092-002 2.115*001 7.777-002 2.281*001 8.384-002 2.421*001 8.901-002

0.060 1.791*001 6.587-002 2.000*001 7.353-002 2.190*001 8. 051-002 2.358*001 8.668-002 2.501*001 9.195-002

0.070 1.869*001 6.873-002 2.082*001 7.656-002 2,276*001 8.369-002 2,448*001 9.001-002 2.595*001 9.541-002

O.ORO 1.957*001 7.195-002 2.175*001 7.998-002 2.374*001 8.729-002 2,551*001 9.378-002 2.702*001 9.935-002

0.090 2.053*001 7.548-002 2.277*001 8.374-002 2.484*001 9.131-002 2.666*001 9.800-002 2.822*001 1. 038-001 0.100 2.166*001 7.928-002 2.389*001 8.783-002 2.600*001 9.561-00? 2.789*001 1.025-001 2.951*001 1.085-001

0.120 ?. 383*001 8.762-002 2.633*001 9.682-002 2.861*001 1.052-001 3.065*001 1.127-001 3.243*001 1.192-001

0.140 2.630*001 9.669-002 2.901*001 1.067-001 3.149*001 1.158-001 3.372*001 l.?40-001 3.567*001 1.311-001

0.160 2.9n4*001 1.068-001 3,200*001 1.177-001 3.471*001 1.276-001 3.716*001 1.366-001 3.931*001 1 . 445-001

0.180 3.171*001 1.166-001 3,494*001 1.285-001 3,790*001 1.394-001 4.059*001 1.492-001 4,298*001 1.580-001

0.200 3.455*001 1.270-001 3.806*001 1.399-001 4.130*001 1.519-001 4.426*001 1.627-001 4,691*001 1. ?25-001 0.250 4.2n5*001 1.546-001 4.635*001 1.704-001 5.036*001 1.852-001 5.406*001 1.988-001 5.744*001 2.112-001

0.300 4.988*001 1.835-001 5,505*001 2.025-001 5.991*001 2.203-001 6,445*001 2.370-001 6.864*001 2.524-001

0.350 5.794*001 2.131-001 6.403*001 2.355-001 6.980*001 2.567-001 7.523*001 2.767-001 8.030*001 2.953-001

0.400 6.616*001 2.434-001 7.321*001 2.694-001 7,993*001 2.940-001 8.629*001 3.174-001 9.230*001 3.395-001

0.450 7.451*001 2.742-001 8.254*001 3.037-001 9.023*001 3.320-001 9.757*001 3.590-001 1.045*002 3.846-001

0.500 8.294*001 3.054-001 9.198*001 3.386-001 1.007*002 3.706-001 1.090*002 4.012-001 1.170*002 4.304-001

0.550 9.144*001 3.368-001 1.015*002 3.738-001 1.112*002 4,095-001 1,206*002 4.439-001 1.295*002 4.769-001

0.600 9.999*001 3.685-001 1.111*002 4.094-001 1.219*002 4.489-001 1.322*002 4,870-001 1.422*002 5.238-001

0.650 1.086*002 4.005-001 1.207*002 4.452-001 1.326*002 4.886-001 1.440*002 5.306-001 1.550*002 5.712-001

0.700 1.172*002 4.327-001 1.304*002 4.813-001 1.433*002 5.285-001 1.558*002 5,744-001 1.679*002 6.189-001

0.750 1.259*002 4.651-001 1.402*002 5.176-001 1.541*002 5.688-001 1.677*002 6.187-001 1.809*002 6.671-001

0.800 1.346*002 4.978-001 1.500*002 5.543-001 1.650*002 6.094-001 1.796*002 6.632-001 1.939*002 7.156-001

0.850 1.433*002 5.309-001 1.598*002 5.913-001 1.758*002 6.504-001 1.916*002 7.082-001 2.069*002 7.646-001

0.900 1.5?0*002 5.644-001 1.696*002 6.288-001 1.867*002 6.920-001 2.036*002 7.538-001 2.200*002 8.142-001

0.950 1.608*002 5.986-001 1,794*002 6.670-001 1,977*002 7,342-001 2.156*002 8.000-001 2.331*002 8.644-001

l.oon 1.696*002 6.336-001 1,893*002 7.060-001 2.086*002 7.772-001 2.276*002 8.470-001 2.463*002 9.155-001

1.100 1.871*002 7.072-001 2,091*002 7.877-001 2.306*002 8.670-001 2.518*002 9.450-001 2.727*002 1.022*000

1.200 2.048*002 7.881-001 2.289*002 8.767-OOI 2.527*002 9.641-001 2.761*002 1.050*000 2.992*002 1.135*000

1.300 2.224*002 8.799-001 2.487*002 9.767-001 2.747*002 1.072*000 3.00**002 1.167*000 3.258*002 1 .260*000

1.400 2.4ol*002 9.877-001 2.686*002 1.093*000 2.969*002 1.196*000 3.248*002 1.299*000 3.524*002 1.400*000

1.500 2.578*002 1.118*000 2.886*002 1.231*000 3.190*002 1.343*000 3.492*002 1.454*000 3.791*002 1.564*000

Page 110
TABLE 10 (CONTINUED)

0.1300 X = 0.1400 0.1500 0.16Q0 X 0.1800

T

<K) P OSM

(TORR) U4 (J/MOLE)

P OSM

(TORR) U4 (J/MOLE)

P OSM

(TORR) U4 (J/MOLE)

P OSM

(TORR) U4

(J/MOLE)

P OSM

(TORR) U4 (J/MOLE) 0.300 7.248*001 2.665-001 7.594*001 2.792-001 7 ,902*001 2.905-001 8.170*001 3.003-001 8.578*001 3.152-001

0.350

o.+oo 0.450

0.500

8.5nl*001

9.792*001

1.111*002

1 .245*002

3.126-001

3.601-001 4.088-001

4.582-001

8.933*001 1.032*002

1.173*002

1.317*002

3.285-001

3.794-001

4.315-001

4.846-001

9

111

326*001 080*002 231*002

,385*002

3.429-001

3.971-001

4.527-001 5.094-001

9.677*001 1.124*002

1.284*002

1.448*002

3.558-001

4-133-001

4.723-001

5.326-001

1.025*002

1.199*002

1.378*002

1.561*002

3.768-001 4.408-001

5.067-001 5.741-001

0.550 0.600

0.650

0.700 0.750

1.381*002 1.519*002

1.657*002

1.796*002

1.9-57*002

5.084-001

5.591-001

6.103-00) 6.620-001 7.141-001

1,463*002 1.611*002

1.760*002

1.910*002 2.060*002

5.384-001 5.929-001

6.48O-O01

7.036-001

7.596-001

11

122

541*002

,699*002

,858*002

,019*002

,180*002

5.669-001

6.252-001

6.841-001

7.436-001

8.035-001

1.614*002

1.782*002

1.952*002 2.123*002

2.296*002

5.938-001

6.559-001

7.187-001

7,820-001

8.459-001

1.747*002

1.936*002 2.127*002

2.319*002 2.513*002

6.427-001

7.123-001 7.827-001

8.539-001

9.258-001

0.800 2.077*002 7.666-001 2.212*002 8.161-001 2 ,343*002 8.640-001 2.469*002 9.104-001 2.709*002 9.982-001

0.850

0.9 0.950

1-000

2.219*002

2.361*002

2.5o3*002

2.646*002

8.196-001

8.731-001

9.274-001

9.826-001

2.364*002 2.517*002

2.671*002 2.824*002

8.731-001

9.307-001

9.89 -00l 1.0*8*000

2

2

2

2

,5o6*002

.670*002

.834*002

,999*002

9.250-001

9.867-001

1.0*9*000 1.112*000

2.643*002

2.818*002 2.994*002

3.170*002

9.754-001

•.•0*1*000

1« 108*000 l»l75*000

2.905*002

3.102*002

3.300*002 3.499*002

1.071*000

1.145*000 1.220*000

1.296*000

1.100 1.200

1.300

1.400 1.500

2.932*002

3.219*002

3.5n8*002

3.796*002 4.086*002

1.097*000

1.219*000

1.352*000

1.501*000

1 .672*000

3.133*002

3.443*002

3,754*002 4.066*002

4.378*002

1.171*000

1.301*000 1.442*000

1.599*000

1.779*000

3

3

34

4

,330*002

,663*002

,997*002

.331*002

,667*002

1.243*000

1.382*000

1.531*000

1.697*000

1.885*000

3.524*002

3.879*002

4.236*002

4,594*002

4.952*002

1.314*000

1.461*000

1.619*000 1.793*000

1.990*000

3.898*002

4.300*002

4.702*002

5,107*002 5.512*002

1.452*000

1.615*000

1. 790*000 1.981*000 2,195*000

TABLE 10 (CONTINUED)

X = .2000 X x .2250 X = • 2500 X = .2750 X = .jOOO

T P OSM U4 P OSM U4 P OSM U4 P OSM U4 P OSM U4

<K) (TORR) (J/MOLE) (TORR) (J/MOLE) (TORR) (J/MOLE) (TORR) (J/MOLE) (TORR) (J/MOLE) 0.300 8.807*001 3.236-001 8.821*001 3.240-001 8.510*001 3.124-001 7.846*001 2.878-001 6.801*001 2.493-001

0.350 1.064*002 3.910-001 1.085*002 3.987-001 1.074*002 3.942-001 1.026*002 3.766-001 9.409*001 3.449-001

0.4 1.256*002 4.614-001 1.298*002 4.770-001 1.308*002 4.803-001 1.282*002 4.704-001 1.217*002 4.464-001

0.450 1.453*002 5.341-001 1.519*002 5.581-001 1.552*002 5.697-001 1.548*002 5.681-001 1.506*002 5.523-001

0.500 1.656*002 6.086-001 1.746*002 6.414-001 1.802*002 6.618-001 1.823*002 6.690-001 1.805*002 6.619-001

0.550 1.862*002 6.846-001 1,977*002 7.265-001 2.058*002 7.561-001 2.104*002 7.724-001 2.111*002 7.745-001

0.600 2.071*002 7.617-001 2.212*002 8.131-001 2.319*002 8.521-001 2.391*002 8.779-001 2.425*002 8.895-001

0.650 2.283*002 8.399-001 2,450*002 9.009-001 2.584*002 9.496-001 2,683*002 9.851-001 2.743*002 1 .007*000

0.700 2.497*002 9.189-001 2.691*002 9.898-001 2.852*002 1.048*000 2.978*002 1.094*000 3.066*002 1.125*000

0.750 2.713*002 9.987-001 2.934*002 1.080*000 3.123*002 1.148*000 3.276*002 1.204*000 3.393*002 1.246*000

0.800 2.930*002 1.079*000 3.179*002 1.170*000 3.396*002 1.249*000 3.578*002 1.315*000 3.723*002 1.368*000

0.850 3.148*002 1.161*000 3.426*002 1.262*000 3.671*002 1.351*000 3.882*002 1.428*000 4.056*002 1.491*000

0.900 3.368*002 1.243*000 3.674*002 1.354*000 3.948*002 1.454*000 4.188*002 1.541*000 4.392*00^ 1,615*000

0.950 3.589*002 1.326*000 3.923*002 1.44fi*000 4,226*002 1.558*000 4,495*002 1.656*000 4.729*002 1.741*000

1.000 3.810*002 1.410*000 4.173*002 1.543*000 4.505*002 1.664*000 4.805*002 1.772*000 5.069*002 1,868*000

1.100 4.256*002 1.582*000 4.677*002 1.736*000 5.068*002 1.879*000 5.428*002 2.010*000 5.753*002 2.128*000

1.200 4.703*002 1 .763*000 5.184*002 1.939*000 5,635*002 2.103*000 6.055*002 2.256*000 6.443*002 2.396*000

1.3 5.153*002 1 .955*000 5.693*002 2.152*000 6,204*002 2.339*000 6.686*002 2.515*000 7.137*002 2.678*000

1.400 5.6o5*002 2.164*000 6.204*002 2.383*000 6.776*002 2.592*000 7.320*002 2.790*000 7.834*002 2.976*000

1.500 6.057*002 2.395*000 6.717*002 2.637*000 7.351*002 2.868*000 7.957*002 3.089*000 8.535*002 3.298*000

Page 111
TABLE 11 THE SPECIFIC HEAT OF THE TOTAL HE3 - HE* SOLUTION

C (J/MOLE-K)

T x

(K) 0.000

0.001 0.002

0.003

0,00*

0.006 0.008

0.010 0.012

0.01*

0.016

0.018 0.020

0.025 0.030

0.035

0.0*0 0.0*5

0.050

0.060 0.070

0.080

0.090

0.100

0.120

0.1*0

0.160

0.180 0.200

0.250 0.300

0.350

0.400

0.*50

0.500

0.550

0.600

0.650

0.700

0.750 0.800

0.850 0.900

0.950

1.000

1.100

1.200

1.300

l.*00

1.500

0.0001

0.000*000 6.509-00*

9,4*9.00*

1.066.003

1.12*-003

1.177-003

1.201-003 1.21*-003

1.222-003 1.227-003

1.231-003

1.23*-003

1.236-003

1.2*0-003

1.2*3-003 1.2*5-003

1.2*8-003

1.251-003

1.25*-003 1.262-003

1.273-003

1.2B7-003

1.305-003 1.328-003

1.387-003

l.*71-003

1.581-003 1.723-003

1.900-003 2.523-003

3.453-003

*. 750-003 6.475-003

8.691-003

1.1*6-002 l.*B*-002

1.898-002 2.563-002

3.69*-002

5.612-002 8.718-002

1.3*6-001 2.031-001

2.970-001

4.203-001 7.706-001

1.292*000 2.046*000

3.115*000

4.532*000

0.0002

000*000 928.004

516.003 853-003

0*0-003 227-003

315-003

36*-003 39*-003

*l*-003

429-003 39-003

**7.003

*61-003 70-003

77-003

83-003

87-003

92-003

503-003 515-003

530-003

5*9-003

572.003

632-003

716-003

827-003 969-003

1*6-003 770-003

699-003

996-003

722.003

937-003

270-002

608-002

022-002

688-002 819-002

736-002

842-002

359-001

0*3-001 982-001

215-001

718-001 293»000

0*7*000

116*000 533*000

0.0005

0.000*000

1.25*-003 2,402-003

3,316-003

3,976-003

*. 780-003 5.21*-003 5.*73-003

5.6*0-003

5.755-003

5.838-003

5,899-003 5.9*7-003

6,027-003

6,077-003

6,111-003

6.136-003 6,155-003

6.170-003

6.196-003 6.218-003

6.2*0-003

6.26*-003

6,291-003

6,356-003

6.444-003 6,557-003

6,701-003

6.879-003

7.505-003 8.435-003 9.733-003

1.1*6-002

1.367-002

1.6*4.002

1,962-002 2.396-002

3.061-002 .192-002

6.109-002

9.21*-002

1.396-001 2.080-001 3.019-001 .252-001

7.753-001

1.296*000 2.050*000

3.119*000 .535*000

0.0010

0.000*000

1.593-003 3.139-003 *.57*-oo3

5,828-003

7.703-003

8.924-003 9.727-003

1.028-002 1.067-002

1.0 9 7-002 1.119-002

1.136-002

1.166-002 1.165-002

1.197-002

1.206-002 1.213-002

1.218-002

1.226-002

1.232-002

1.236-002

1. 2^1-002

1.2*5-002

1.253-002

1.263-002 1.275-002

1.290-002 1.309-002

1.372-002 l.*65-002

1.595-002 1.768-002

1.990-002 2.266-002

2,60*-002

3.018-002 3.683-002 .813-002

6.729-002

9.833-002

1.^57-001 2.1*1-001

3,o8o-001

*. 312-001 7.812-001

1.302*000 2.055*000

3,l2**000

*. 539*000

0.0020

0.000*000 2.016-003

*. 010-003 5.956-003

7.821.003

1.115-002

1.382-002

1.586-002

1.7*1-002

1.860-002

1.952-002 2.02*-002

2.083-002 2.187-002

2,255-002 2.301-002

2.33*-002

2.359-002

2.379-002 2.*06-002

2,*26-002

2.**0-002 2.*51-002

2.*60-002 2,*76-002

2.*9l-002

2.507-002

2.52*-002 2.5**-002

2.611-002

2.706-002

2.837-002

3.011-002

3.233-002

3,5io-002

3.848-002

4.261-002 .926-002

6.055-002

7.969-002

1.107-001

1.581-001 2.264.001 3.201-001 .32-001

7.929-001

1.313*000 2.066*000

3.133*000 4.547*000

0.0030

0.000*000 2.314-003 .613.003

6.882.003 9,101-003

1.329-002

1.700-002 2.010-002

2.263-002

2.468-002 2.635-002

2.771-002

2,883.002

3,088-002 3.226-002

3.321-002

3.392-002

3. 5-002

3.^86-002

3.5^5-002

3.586-002

3.615-002

3.637-002

3.655-002

3.683-002 3.706-002

3.728-002

3. 7^9-002 3.773-002

3.844-002 3.943-002 .076-002

*. 251-002

*. 7^-002

.751-002

5.089-002

5.503-002

6.167-002

7.296-002

9.208-002

1.231-001

1.704-001 2.387-001 3.323-001

4.553-001 8.0^6-001

1.324*000 2.076*000

3.142*000 4.555*000

0.0040

0.000*000

2.552-003 5.09+-003 7.M2-003

1.010.002

1. 89.Oo2 1.932-002 2.32^-002

2.666-002

2.951-002

3.1«2-Oo2

3,395.002

3,566.002

3.888.002 .109.002

.268-002

.385-002 . 7^-002

.$3-002 ^-002

.71+-002

.763-002

.801-002

,831-0o2

.875-002

.910-002

.939-002

.966-002

.99^-002

5.073-002

5.176-002 5.311-002

5. 88.002

5.712-002

5.991-002

6.329-002

6.7^3-002

7.407-002

8.535-002

1»0^5-001

1.354-001

1.827-001

2. "509.001 3,^*-00l

.673.001

8.162-001

1.335*000 2.087*000

3,152*000

4,563*000

0.0050

000*000 755-003

50T-003

229-003

093-002 620-002

119-002 578-002

990-002

3^9-002 658-002

926-002

156-002 603-002

917-002

1*6-002 319-002 51-002

554-002

706-002 811-002

886-002

9*3-002 987-002

053-002

101-002

1*0-002

175-002 208-002

296-002 04-002

5^4-002

723-002

9^9-002

228-002 568-002

982-002

6^6-002 774-002

168-001 478-001 95o-001

631-001

566-001

793-001

279-001 3*6*000

097*000

161*000 571*000

0.0060

0.000*000 2,933-003

5,858.003 8.768-003

1.166-002

1.732-002 2.277-002

2.790-002

3.259-002

3.683-002

*. 056-002 4,384-002

*. 672-002 5.2*5-002

5.659-002

5.965-002 6.198-002

6.379-002

6.523-002

6.733-002 6.878-002

6,983-002 7.063-002

7.125-002

7.215-002

7.280-002

7.331-002

7.375-002 7.*15-002

7.51*-002

7.629-002

7.773-002

7.955-002

8.183-002

8.464-002

8.804-002

9.220-002 9.884-002

1.101-001

1.292-001

1.601-001 2.073-001 2.754-001

3.687-001

*. 913-001 8,396-001

1.357*000 2.107*000

3.170*000 .579*000

0.0080

,000*000 ,239-003

,472-003 ,693-003

,290-002 ,923-002

,5*1-002 136-002

,699-00? ,22*-002 f07-OO2 1*5-002 538-002

353-002

973-002 7-002

,814-002 104-002 338-002

687-002

,929-002 107-002

,2*1-002

,3*6-002 ,98-002

605-002 685-002

751-002 808-002

,935-002

,007-001

,022-001 ,0*1-001

,065-001 ,093-001 127-001

,169-001 ,236-001

,3*8-001

,539-001

,8*7-001 ,318-001 ,998-001 ,930-001

,153-001 ,629-001

,380*000 128*000

189*000

,595*000

Page 112
TABLE 11 (CONTINUED)

C (J/MOLE-K)

T N

(K) 0.000

0.001 0.002

0.003 0.00*

0.006 0.008

0.010 0.012

0.014

0.016

0.018

0.020

0.025

0.030

035

• 0*0

.0*5 050

060 0.070

0.080 0.090

0.100

0.120 0.1*0

0.160

0.180

0.200

0.250 0.300

0.350

0.*00

0.450 0.500

0.550

0.600 0.650

0.700

0.750

0.800 0.850

0.900

0.950

1.000 1.100

1.200

1.300

1.400 1.500

o.nloo

0.000*000

3.500-003 6.955-003

1 .0*8-002 1.395-002 2.084-002

2.760-0Q2

3.419-002 4.054-002

4.659-002

5.2?6-0l)2 5.756-002

6.2*3-002

7.281-002 8.102-002

8.750-002

9.264-002 9.676-002

l.OOl-OOl

1.052-001

1.088-001

1.114-001 1.134-001

1.150-001

1.173-001

1.188-001 1.200-001

1.210-001 1.217-001

1.234-001

1.249-001 1.2*6-001

1.286-001

1.310-001 1.339-001 1.374-001

1.416-001

1.482-001

1.595-001

1.785-001 2.0O3-001 2.564-001

3.2*2-001 4.172-001

5.393-001

8.862-001

1 . *P2«000 2.149*000

3.2o8*000

4.611*000

0.0150

0.000*000 4.035-003

8.067-003

1 .209-002 1.611.002 2.410-002

3.202-002

3.982-002 4.748-002

5.495-002

6.219-002

6.915-002 7.578-002

9.085-002

1.036-001

1.142-001

1.231-001 1.305-001

1.367-001

1.464-001

1.534-001

1.587-001

1.628-001

1 .660-001

1 .707-001 1.740-001 1.764-001

1 .783-001 1.797-001

1.826-001

1.848-001

1 .870-001 1.893-001

1.920-001 1.951.001

1.987-001 2.030-001 2.0'7-001

2.210-001 2.400-001

2.707-001

3.175-001 3.851-001

4.776-001 5.992-001

9.4**-001

I .458.000 2.201*000

3.25**000

*. 650*000

0.0200

0.000*000 .70-003

8.937-003

1.340-002

1,786-002 2.674-002

3.556-002 .30-002

5.294-002

6.144-002 6.978-002

7.792-002 8.582-002

1.043-001 1.209-001

1.352-001

1.476-001 1.582-001

1.674-001

1.821-001 1.931-001 2.015-001 2.081-001

2.134-001

2.212-001 2.267-001

2.307-001

2.338-001 2.362-001

2.406-001

2.439-001

2.467.001

2.495-001

2.525-001 2.558-001

2.596-001

2.640-001 2.709-001

2.822-001

3.012-001

3.318-001

3.785-001 .58-001

5.379-001

6.589-001

1.002*000 1.513*000 2.253*000 3.301*000 .690*000

0.0250

0.000*000 ,8^3-003

9.685-003

1.452-002

1.935-002 2.899-002 3.858-002 .811-002

5.756-002

6.690-002

7.611-002 8.517-002

9. 05-002

1.153-001

1.348-001

1.524-001

1.679-001

1.816-001

1.936-001 2.134-001 2.287-001

2. 06-001

2.500-001 2.576-001

2.691-001 2.771-001

2.831-001

2.876-001 2.912-0ol

2.976-001 3.020-001

3.057-001

3.091-001 3.125-001

3,161-001

3.202-001 3.248-001

3.318-001

3. 32-001

3.622-001

3.928-001 .393-001

5.063-001 5.980-001

7.184-001

1.060*000

1 .568*000 2.304*000

3.347*000 .729*000

0.0300

0.000*000 5,175-003

1.035-002

1.552-002 2.068.002

3.099-002 .126-002

5,148-002 6.163-002

7.169-002 8.165-002

9.148-002

1.012-001

1.246.001

1, 66.001

1.668-001 1.853-001 2.017-001

2.164-001

2. 12-001

2.608-001

2.764-001 2.889-001

2.990-001

3.i*5-001

3.255-001

3.336-001

3.398-001

3. 7-001

3.S35-001

3.594-001 3.640-001

3.681.001 3.720.001

3.760-001

3.804-001 3.852-001

3.924-001 .039-001

.230-001

.535-001

.999-001

5.666.001

6.580-001

7.778-001

1.118*000

1 ,624.000 2.356*000 3.393*000 .768*000

0.0350

0.000*000

5, 75-003

1.095-002

1.642-002 2,189.002 3.280-002 .368-002

5.452-002

6.529-002

7.600-002 8,661-002

9.712-002

1.075-001

1.328-001

1.569-001

1.795-001

2. 004-001 2.194-001

2.366-001

2.661-001

2.899-001

3.093-001

3.250-001 3.379-001

3.577-001

3.719-001

3.825-00] 3.906-001 3.970-001

4.0B3-001

4.160-001

4.217-001

4.266-001

4.311-001

4,356-001 4.402-001

4.454-001 4.527-001

4.644-001

4.835-001

5.140-001

5.603-001 6.268.001

7.178-001

8.371-001 1.176*000

1.679*000 2.407*000

3.440*000

4.807*000

0.0400

0.000*000 5.752-003

1.150-002

1.725-002 2.299.002

3.447-002 4.591-002

5.731-002

6.866-002

7.994-002 9.115-002

1.023-001

1.133-001

1.403-001

1.662-001

1.90»-001 2.137-001

2.351-001

2.547-001 2.886-001

3.166-001 3.397-001 3.587.001

3.745-001

3,988.001

4.165-001 4.298-001

4.399-001

4.480-001

4.623-001

4.717-001 4,788-001

4.846.001 4.897.001

4.947.001

4.998-001

5.052-001 5.128-001

5.246-001

5.439-001

5.744-001

6.205-001 6.868.001

7.774.001 8.962-001

1.233*000

1 .734*000 2.459*000

3.486.000 4.846*000

0.0450

000*000 009-003

202-002 802-002 402.002

601-002

797-002

99 -002 178-002 360-002 535-002

Q70-001

186-001 471-001

746-001

010-001 259-001 493-001

710-001

092-001

412-001

680-OOI

903-001

090-001 381-001

593-001

755-001 880-OOI

977-001

152-001 268-001

352-001 420-001

479-001 535-001 59o-001

648-001 726-001

846-001

040-001 345-001

806-001

466-001

369-001

552-001 29l»000

789*000

510*000 532*000 885*000

0.0500

0.000*000 6.250-003

1.250-002

1.874-002 2.499.002

3.746-002

4.991-002

6.233-002

7.470-002

8.702-002 9.928-002

1.115-001

1.236-001

1 .534-001 1.824-001 2.104-001

2.371-001

2.623-001

2.860-001

3.282-001

3.640-001

3.943-001

4.199-001

4.416-001 4,756-001

5.007-001

5.197-001

5.347-001 5.464-001

5.673-001 5.811-001

5.911-001

5,990-001

6.057-001 6.119-001

6.179-001

6.240-001 6.322-001

6.444-001

6.639-001

6.945-001

7.405-001

8.063-001 8.962-001

1.014*000

1.348*000

1.844*000 2.561*000

3.578*000 4.924*000

0.0550

.000*000 ,477-003

,295-002

,943-002

,590-002

,883-002 174-002

,461-002 745-002

,025-002 030-001

157-001

,282-001

,593-001

,897-001 191-001

,474-001 743-001

,997-001

,457-001

,853-001 190-001

,479-001

,725-001 115-001

,405-001

,627-001

,801-001 ,9*0-001 185-001

,347-001

,464-001

,554-001 ,630-001

,699-001 764-001 830-001 915-001

040-001

,236-001

,542-001 ,002-001

,659-001

,554-001 073*000

,405*000

,898*000

,612*000 ,623*000 ,963*000

Page 113
TABLE 11 (CONTINUED)

C (J/MQLE-K)

T(K)

0.0600 0.06*0 0.0650 0.0700 0.0750 0.0800 0,0*00 O.loOO 0.1100 0.1200

0.000

0.001 0.002

0,003

0.00*

0.006

0.008

0.010 0.012

0»01*

0.016

0.018

0.020 0.025

0.030 0.035

0.0*0 0.0*5

0.050 0.060

0.070

0.080

0,090

0.100

0.120

0.1*0

0.160 0.180

0.200

0.250

0.300

0.350 0.*00

O.*5o

0.500

0.550

0.600 0.650

0.700

0.750

0.800

0.850 0.900

0.950

1.000 1.100

1.200

1.300

1.400 1.500

O.on0*ooo

6. 693-003 1.339-002 2.008-002

2.676-002

*. 013-002 5.3*7-002

6.679-002

8.006-002

9.330-002

1.065-001 1.196-001

1.327-001

1.6*9-001 1.966-001 2.273-001

2.570-001 2.855-001

3.125-001

3.621-001

*. 051-001 *.*?3-001

*. 7*3-001 5.018-001

5.*59-00l 5.790-001

6.0A*-00l 6.2**-001

6.*05-001

6.689-001 6.877-001

7.011-001

7.11*-00l 7,200-001

7.276-001

7.3*7-001 7.*17-001

7.505-001

7.633-001

7.831-001 8.138-001 8,597-001

9.252-001

] . 01**000 1.131*000

l.*62*000

1.953*000 2.663*000

3.669*000 5.002*000

0.000*000 6,858-003

1.372-002 2.057.002 2.7*3-002

*. 112-002 5.*80-002

6.8*5-002

8. 206-002 9.56*-002

1 .092-001

1 .226-001

1 .360-001

1 .6*2-001 2.018-001

2.336-001

2.6*3-001

2.939-001

3.222-001

3.7**-001 4.202-001

4.599-001

*.9**-001 5.2*2-001

5.72*-001

6.089-001 6.369-001

6.590-001 6.769-001

7.086-001

7.295-001 7.***-001

7.559.001

7.653-001 7.735-001

7.811-001

7.885-001

7.976-001 8.106-001

8.306-001

8.61*-001 9.073-001

9.726-001

1 .062*000 1.178.000

1.508*000

1.997*000 2.70**000

3.706*000 5.033*000

0.000*000 6,899-003

1.380-002 2,069.002

2.759-002

*. 136-002 5.512-002

6.885-002 8.255-002

9.621-002

1.098-001

l,23*-00l

1,369-001 1.703-001 2.030-001

2.351-001 2.661-001

2.960-001 3.2*5-001

3.773-001

*. 238-001

*. 6*2-001 .993-001

5.297-001 5.789-001

6.162-001 6.**9-001

6.676-001

6.859-001

7.18*-001

7.399-001

7.552-001

7.669-001

7,765-001

7,8*9-001

7.926-001

8.001-001

8.094-001

8.22*-001

8.*2*-001

8.732-001 9.191-001

9,8*5-001

1.073*000

1.190*000

1.519*000 2.007*000

2.71**000

3.715*000

5.0*1*000

0.000*000 7.096-003

l.*19-002 2.128-002

2.838-002

*. 255-002 5.670-002

7.0 8 3-002 8.*93-O02

9.899-002

l.l3o-001

1.270-001

1.409-001 1.753-001 2.092-001

2.*2*-001

2.7*7-001

3.059-001

3.359-001

3.916-001

*,*1*-001

*. 850-001 5.231-Qol

5.563.001

6.106-001

6.521-001 6.8*3-001

7.0 9 8-001 7.303-001

7.673-001

7.915-001 8.088-001

8.220-001 8.327-001

8.*19-001

8.503-001 8.583-001

8.679-001

8.813-001

9.015-001

9.325-001

9.783-001

1.0***000

1.132*000 1.2*8*000

1.576*000 2.062*000

2.765*000 3.760*000

5.079*000

0.000*000 7.285-003

l.*57-002 2.185-002

2.913-002

*. 369-002 5.822-002

7.273-002

8.722-002

1.017-001

1.161-001

1.3o*-001

l.**7-001

1.802-001 2.151-001

2.*94-001

2.829-001

3.154-001

3.466-001

•.052-001

*. 581-001 5.0*7-001 S,*58-001

5.818-001 6.M1-001

6.869-001 7.226-001

7.509-001

7.739-001

8.15*-001 8,*25-001

8.619-001 8,766-001

8,885-001

8.985-001 9.076-001

9.162-001

9.263-001

9.*00-001

9.605-001

9.915-001

1.037*000 1.102*000

1.191*000

1.306*000

1.633*000 2.116*000 2.816*000

3.806*000 5.118*000

0.000*000 7.*67-003

1.*93-002 2.2*0-002

2.986-002 *.*78-00?

5.968-002

7.*56-002

8.9*1-002

1.0*2-001

1.190-001

1.337-001

1,*8*-001

1,8*9-001

2. 208-001 2.561-001

2.907-001

3.2*3-001

3.569-001

*. 181-001 .739-001

5.235-001

5, 67*. 001 6.062-001

6.705-001

7.206-001 7.599-001

7.911-001 8.165-001

8.626-001

8.929-001

9.1*5-001 9.308-001

9.*38-001 9.5*9-001

9.6*7-001 9.739-001

9.8**-001 9.985-001

1.019*000

1.050*000

1.096*000 1.161*000

1.2*9.000

1.36**000

1.689*000 2.170*000

2.866*000

3.851*000 5.156*000

0.000*000

7,fll*-003 1.563-002 2.3**-O02

3.125-002

*. 686-002 6.2*6-002

7. 803-0Q2 9.359-002

1.091-001

1.2*6-001

1. 00-001

1.55*-0ol

1.937-001 2.315-001

2.683-001

3.05*-001

3. 12-001

3.760-001 ,*22-Ool

5.032-001

5. 586.O0I 6.080.001

6,520-001 7.262-001

7.8*8-001 8.31*-001

8. 688-0Q1 8.993-001

9.550-001 9.919-001

1.018*000

1.038*000 1.05**000

1.067*000

1.078*000

1.088*000

1.100*000

1.115*000 1.136*000 1.168*000

1.2l**000

1.278*000

1.366.000

l.*80.000

1.802*000 2.279*000

2.967*000

3.9*2*000

5.233*000

000*000

139-003 628-002 **l-002

255-002

88i-002

506-002

13Q-002 75i-002

137-001 298-001 *59-001

620-001

020-001 415-001

«06-001

191-001 569-001 93R-001

6**-001

302-001

908-001

454-001 946-001

782-001 454-001

99^-001

*3l-001

789-001 0*5*000

089*000

120*000

1*3*000

162*000

177*000

l9o*000 202*000

215*000

230*000 252*000

284*000

33o*000

395*000 482*000

595*000

914*000

386*000

068*000

032*000

309*000

0.000*000 8.4*7-003

1.689-002

2, 53*. 002 3.378-002 5.066-002

6.753-002

8.438-002

1. 012-001

1. 180-001 1.348-001

1.515-001

1.682-001 2.098-001

2.510-001

2.917-001

3.320-001

3.715-001 4.103-001

*. 851-001 5.553-001

6.20*-001

6.802-001 7.3*2-001

8.270-001

9,026-001 9.6*1-001

1.01**000 1.056*000

1.132*000 1.183*000

1.220*000 1.2*7*000

1.269*000

1.286*000

1.301*000

1.3l**000

1.328*000

1.3*5*000

1,368*000

1.400*000

1 ,4*6*000 1.511*000

1,598*000

1,710*000 2.026*U00

2.494*000

3.168*000

4.122*000 5.386*000

,000*000 7*0-003 /8-002

,622-002

,*95-002 2*2-002

988-002

732-002 0*7-001 221-001

,395-001 ,568-001 7*1-001

,172-001 ,599-001

,023-001 ,**1-001

,85*-001 ,259-001 ,0*+-001 787-001

,481-001 126-001

713-001

731-001

,569-001 ,026*000 ,082*000 129*000

,216*000 ,276*000

,318*000

,349*000 ,374*000

,394*000 ,11*000

,426*000

,4*1*000

,459*000

,482*000

,515*000

,562*000 ,626*000 713*000

,82**000 138*000

,601*000

,268*000 212*000 *62*000
TABLE! 11 (CONTINUED)

C (J/MOLE-K)

0.1300 0.1400 0.1500 0.1600 0.1800 0.2000 0.2250

T \

(K)

0.000 0.000*000 0.000*000 0.000*000 0.000*000 0.000*000 0.000*000 0.000*000

0.001 9.020-003 9.288-003 9,547-003 9.797-003 1.027-002 1.072-002 1.126-002

0.002 1.804.002 1 .858-002 1.909.002 1.959-002 2.055.002 2.145-002 2.252.002

0.003 2.706-002 2.786.002 2,864-002 2.939-002 3.082.002 3.217-002 3.378,002

0,004 3,60^-002 3.715.002 3,818.002 3,918-002 4.109.002 4.289.002 4,503-002

0.006 5.410-002 5.571-002 5.727-002 5.877-002 6.163-002 6.434-002 6.754-o 2 0.008 7.212-002 7.427-002 7.634-002 7.834-002 8.216-002 8.577-002 9.005-002

0.010 9.012-002 9.281-002 9.540-002 9.79 -002 1.027-001 1.072-001 1.125-001

0.012 L081-OQ1 1 .113-001 1.144-001 1.175-001 1.232-001 1.286-001 1.350-001

0.014 1.261-001 1.298-001 1.335-001 1.370-001 1.437-001 1.500-001 1. 575-001

0.016 1.440-001 1 .483-001 1.525-001 1.565-001 1.641-001 1.714-001 1.799.001

0.018 1.619-001 1 .668-001 1.714-001 1.760-001 1.846-001 1.927-001 2.02*-00)

0.020 1.798-001 1.852.001 1.904-001 1.954-001 2.050-001 2.141.001 2.246.001

0.025 2.243-001 2.311-001 2.376-001 2.439-001 2.559-001 2.673-001 2.807-001

0.030 2.685-001 2.767.001 2,846-001 2.921-001 3.066.001 3.203-001 3.364.001

0.035 3.123-001 3.219-001 3.312-001 3.401-001 3.570-001 3.730-001 3.919-001

0.040 3.557-001 3.668-001 3.774-001 3.876-001 4.071-001 4.254-001 4.471-001

0-045 3.985-001 4.111-001 4.231-001 4.347-001 4.568-001 4.775-001 5.020-001

0.050 4.4O7-001 4.548-001 4.683-001 4,813-001 5.060-001 5.292-001 S. 566-001

0.060 5.227-001 5.401-001 5.567-001 5.726-001 6.028-001 6.310-001 6.643-001

0.070 6.008-001 6.218-001 6.417-001 6.608-001 6.968-001 7.304-001 7.a98_0o1

0.080 6.743-001 6.991-001 7.226-001 7.451-001 7.874-001 8.267-001 8.726-001

0.090 7.430-001 7.716-001 7.988-001 8.249-001 8.738.001 9.192.001 9. 720.001

0.100 8.062-001 8.392-001 8,704-001 9.000-001 9,557-001 1.008*000 1.068*000

0.120 9.1*7-001 9.580-001 9,974-001 1 ,0 3 5.000 1.106*000 1.171.000 1.246*000

0.140 1.008*000 1.058*000 1.105*000 1.150*000 1.235*000 1.314*000 1.406*000

0.160 1.085*000 1.141*000 1.195*000 1.247*000 1.346*000 1.438*000 1 .^46*000

0.180 1.148*000 1.211*000 1.272*000 1.330*000 1.441*000 1.546*000 1.666.000

0.200 1.201*000 1.269*000 1.336*000 1.400*000 1.523*000 1.639*000 1.776*000

0.250 1.299*000 1.379*000 1.457*000 1.534*000 1.681*000 1.821*000 1.989.000

0.300 1.366*000 1.454*000 1.541*000 1.626*000 1.791*000 1.951*000 2.142*000

0.350 1.414*000 1 .509*000 1.602*000 1.694*000 1.872*000 2.046*000 2.255*000

0.400 1.450*000 1,549*000 1.647*000 1.744*000 1.934*000 2.118*000 2.342*000

0.450 1.478*000 1.581*000 1.683*000 1.783*000 1.981*000 2.174*000 2.410*000

0.500 1.501*000 1.607*000 1.711*000 1,815*000 2.019*000 2.219*000 2,465*000

0.550 1.520*000 1.628*000 1.735*000 1.841*000 2.050*000 2.256*000 2.509*000

0.600 1.537*000 1.647*000 1.756*000 1.864*000 2.077*000 2.288*000 2.547*000

0.650 1.553*000 1 .665*000 1.775*000 1.885*000 2.102*000 2.316*000 2.580*000

0.700 1.572*000 1.685*000 1.796*000 1.907*000 2.127*000 2.345*000 2.613*000

0.750 1.596*000 1.710*000 1.823*000 1.935*000 2.157*000 2.377*000 2.648*000

0,800 1.630*000 1.744*000 1.857*000 1.970*000 2.194*000 2.416*000 2.690*000

0.850 1.677*000 1.791*000 1.905*000 2.018*000 2.243*000 2.466*000 2.742*000

0.900 1.741*000 1.856*000 1,969*000 2.083*000 2.308*000 2.531*000 2.808*000

0.950 1.827.000 1.941*000 2.055*000 2.168*000 2.393*000 2.616*000 2.892*000

1.000 1.938*000 2.051*000 2.164*000 2.277*000 2.501*000 2,723*000 2.998,000

1.100 2.249*000 2.360*000 2.470*000 2.580*000 2.799*000 3.017*000 3.287*000

1.200 2.707*000 2.814*000 2.920*000 3.025*000 3.236.000 3.445*000 3.704.000

1.300 3.368*000 3.467*000 3.566*000 3.665*000 3.862*000 4.057*000 4.300*000

1.400 4.302*000 4.391*000 4.480*000 4,568*000 4.745*000 4.920*000 5.138*000

1.500 5.537*000 5.613*000 5.688*000 5.763*000 5.912*000 6.060*000 6.244*000

0,2500

000*000

177-002 353-002 53o-002

706-002

059-002

411-002

176-001 411-001

646-001

88]-001

115-001 35o-001

935-001

51R-001

099-001 677-001

25?-001

825-001 957-001

069-001

156-001 021*000

124*000 316*000

49i*000

646*000

783*000

904*000

147*000 325*000 45p*000

560*000

64o*000

704*000

757*000

801*000 840*000 878*000

917*000

961*000

015*000 082*000

166*000 27i»000

554*000 962*000

541*000

355*000 427*000

0.2750

0.000*000

1.225.002 2.450-002

3,676-002

4,901.002

7.350-002

9.800-002

1.225-001

1,470-001

1.714-001

1.959-001 2.203-001

2.447-001

3.056-001

3,664.001 4.270-001

4.873-001

5.474-001

6.072-001

7.256-001 8.421-001

9.565-001

1.068.000

1.177.000

1.382.000

1.570*000

1.740*000

1.891*000 2.026*000

2.299*000

2.502*000

2.654*000

2.771*000

2.864*000

2.939*000

3.000*000

3.051*000 3.096*000

3.139*000 3.181*000

3.229*000

3.285*000 3.353*000

3,438*000 3.542*000

3.820*000

4.218*000 4.781*000

5.569*000

6.608*000

0.3000

,000*000

,272-002

,544-002

,816-002 088-00?

,631-002

,017-001

,272-001

,526-001 '80-001 034-001

,287-001 541-001

174-001 805-001

,435-001

,062-001

,687-001

,309-001 ,542-001 759-001

,955-001 113*000

,227*000

,444*000 ,645*000

,829*000

,994*000 141*000

,444*000

,671*000

,844*000 ,978*000

,083*000 169*000

,240*000

,298*000

,349*000 ,396*000

,443*000

,494*000

,552*000

,622*000 '07*000 810*000

084*000

,472*000

,019*000 783*000

?88*000

Page 115
TABLE 12 THE ENTROPY OF THE TOTAL HE3 - HF4 SOLUTION

S (J/MOLE-K)

T \

(K) 0.000

0.001 0.003

0,003

0.004

0.006

0.008 0.010 0.012

0.01*

0.016

0.018

0.020 0.025

0.030 0.035

0.0*0 0.0*5

0.050 0.060

0.070

0.080 CO^O

0.100

0.120

0.1*0

0.160

0.180

0.200

0,250 0.300

0.350

0.400 0.*50

0.500

0,550

0,600

0.650

0.T00

0.750

0.800

0.850 0.900

0.950

1.000

1.100

1.200

1.300

l.*00

1.500

O.oOOl

0.000*000 7.128-00*

1.271-003

1.681-003

1.946-003 2.*6*-003

2.806-003

3.075-003

3.298-003

3.486-003

3.650-003 3.796-003

3.926-003

*. 203-003 *.*28-003

*.6?0-003 .786-003

*.93*-0o3

5.066.003

5.295-003

5.*90-003

5.661-003

5.8i*-003

5-953-003

6.200-003

6.*)9-003

6.623-003

6.81 7-003 7.00?-003

7.493-003

8.030-003

8.655-003

9.396-003

1.0?8-002 1.13*-002

1.258-002 l.*0*-002

1.580-002

1.808-002 2.122-002 2.576-002

3.238-002 •190-002

5. 527-002

7.351-002

1.288-001 2.168-001

3.*«l-00l

5.367-001 7.980-001

0.0002

0.000*000

9.212-00*

1.751-003 2.*37-003

2.998-003

3.866-003

*. 520-003 5.0*3-003

5.*77-003

5.8*7-003

6.171-003

6.*57-003

6.715-003

7.263-003 7.712-003

8.09*-003

8.425-003 8.717-003 8.980-003

9. 35-003

9.822-003

1.016-002

1 .0*6-002 1.073-002

1.120-002 1.161-002

1.198-002

1.232-002

1.26*. 002 1.3*1-002

l.*17-002

1 .*99-002

1 .590-002 1.693-002 1.812-002

1.9*8-002 2.105.002

2.291.002 2.527.002

2.851.002

3.312-002

3.981-002

*. 941-002

6.285-002

8.11*-002

1 .366-001 2.2*6-001

3.561-001

5.**7.001

8.061-001

0.0005

0,000*000

1.26*-003 2.*95-003

3.651-003

*. 701-003 6,*83-003

7.923-003

9.117-003

1.013-002

1.101-002 1.178-002

1.2*7-002

1,310-002

l.***-002

1.55*-002

1.648-002 1.730-002

1,802-002

1,867-002

1.980-002 2.075-002

2.158-002

2.232-002

2.298-002

2.414-002

2.512-002

2.599-002

2.677-002 2.7*8-002

2.908-002

3,053-002

3,192-002 3.333-002

3.480-002 3.638-002

3.810-002

3.999-002

*. 215-002 *.*79-002

*. 828-002 5.31*-002

6.005-002 6.986-002

8.350-002

1.020-001

1.577-001 2,*61-001

3.778-001

5,667-001

8.282-001

0.0010

0.000*000

1.598-003 3.l8o-003

*. 729-003 6.222-003 8.966-003

1.136-002

1.3*5-002

1.527-002

1.689-002

1.833-002

1.964-002 2.082-002

2.339-002

2.554-002

2.737-002

2.898-002

3.0*0-002

3.168-002 3.391-002

3.581-002 3.7*6-002

3.89!-oo2

*. 022-002

*. 250-002 *.***-002 .613-002

4.764-002

*. 901-002 5.200-002

5.*57-002 5.693-002

5.916-002

6.137-002

6.3&0-002 6,592-002

6,835-002

7.101-002

7,*ll-002

7,803-002

8.329-002

9.058-002

1.007-001

1.1*7-001

1.335-001 1.898-001 2.787-001

*. 108-001 6.001-001

8.619-001

0.0020

0.000*000 2.019-003

*. 030-003 6.026.003

7,997-003

1.182-002

1.541-002

1.872-002 2.176-002

2.*5*-002

2.708-002

2.942-002 3.159-002

3.636-002 .041-002

4.392-002

*. 702-002 4.978.002

5.228-002

5.664-002 6.037-002

6.362-002 6.650-002

6.908-002

7.358-002

7.741-002

8.075-002

8.371-002

8,638-002 9.212-002

9.696-002

1.012-001

1.051-001

1.088-001

1.123-001 1.158-001

1.194-001

1.230-001

1.270-001

1.318-001

1.379-001 l.*59-001

1.568-001

1.714-001

1.908-001 2.*83-001

3.381-001

*. 711-001 6.611.001

9.236.001

0.0030

0.000*000 2.316.003

*. 626. 003 6.927.003

9.212.003

1.371-002

1.805-002 2.219-002

2.609-002

2.973-00?

3.31*-00?

3.633-002

3.931-002 .598-002

5.174-002

5.67P-00? 6.127-002

6.529-002

6.895-002

7.536-002 8.086-002

8.566-002 8.993-002 9.378-002

1.005-001

1.062-001 1.111-001

1.155-001

1.195-001

1.280-001

1.351-001

1. 12-001

1.468-001

1.519-001 1.568-001

1.615-001 1.661-001

1.707-001 1.756-001

1.813-001

1.881-001

1.969-001 2.085-001

2.238-001 2.438-001

3.02*-001

3.933-001 5.271-001

7.178.001

9.809-001

0.0040

0.000*000 2.554-0O3

5.103-003

7.646.003

1.018-002 1.519-002 2.009-002 2.483-002

2. 938-002 3.371-002

3.782-002 *.l70-Oo2

*. 536-002 5.369-002 6.099-002

6.7*5-002 7.323-002

7.8**-0o2 8.319-002 9.157-002

9. 879-002

1.051-001

1»107-001

1.158-001

1.2*7-001 1.322-001

1.3B8-001

1.4*6-001

l.*99.0ol

1. 611-001 1.70*-001

1.785-001

1.857-001

1.923-001

1.985-001 2.0*3-001

2.100-00) 2.156-001

2.215-001 2,280-001

2.356-001

2.452-001

2.574-001 2.73*-001

2.9*0-001

3.538-001

4. 456.001 5,803.001 7.718-001

1.035*000

0.0o5o

000*000

75*. 003 50A-003

255-003

099-002 6*3-002

l7fl-002 701-002

208-002

697-002

165-002 611-002

037-002

016-002

884-OO2

66Q-002

359-002 993-002

573-002

O60-OOI

1*9-001 227-001

2 9 7-001 359-001 *69-001

563-001

6*5-001 717-001

782-001

922-001

038-001

137-001 226-001

306-001

381-0OI ASi-001

519-001

585.001

653-001

726-001

flll-OOl 914-001

0*3-001

209-001

*22-001

031-001

959-001

315-001

237-001

08fi*000

0.0060

0.000*000 2.933-003

5,864-003

8.790-003

1.171-002 1.751-002 2.325-002

2.889-002

3,440-002

3.975-002 4.491-002

4.988-002

5.466-002

6.573-002

7.568-002 8.464-002

9.277-002

1.002-001 1,070-001

1.191-001

1.296-001

1.388-001

1.471-001

1.546-001

1.676-001

1,788-001 1.886-001

1.972-001 2.050-001

2.217-001

2.355-001

2.473-001

2.578-001

2.673-001

2.761-001 2.843-001

2.921-001

2.998-001

3.075-001

3.156-001 3.2*9-001

3.359-001

3.496-001 3.669-001

3.887-001

*, 507-001 5.**6-001

6.810-001 8,739-001

1.139*000

0*0080

.000*000

,239-003

,477-003 '10-003 294-002

,937-002

,575-002

.206-002 ,829-002

,439-002

,035-002

,615-002 178-002

,505-002 '21-002

,833-002

,085-001 179-001

,266-001

,421-001

,557-001

,677-001 '85-001

,883-001

,055-001

,202-001

,331-001 ,6-001

,5*9-001 '69-001

,951-001 107-001

,2*5-001

,369-001 ,483-001

,588-001

,688-001 '84-001

,879-001

,978-001

,087-001

,212-001

,363-001 ,548-001 '80-001

,422-001

,381-001 '62-001 '06-001

,237*000

Page 116
TABLE 12 (CONTINUED)

S (J/MOLE-K)

T \

(K)

0.000

0.001 0.002

0.003 0.00*

0.006 0.008

0.010 0.012

0.01* 0.016

0.018

0.020 0.025

0.030 0.035

0.0*0 0.0*5

0.050

0.060

0.0T0 0.080

0.0«0

0.100

0.120

0.1*0

0.160 0.180

0.200

0.250 0.300

0.350

O.*00

0.*50 0.500

0.550

0.600 0.650

0.700 0.750 0.800

0.850

0.900

0.950

1.000

1.100

1.200

1.300

1.400 1.500

o.nioo

0.000*000 3.500-003

6.999-003

1.0*9-002

1.399-002

?. 095-002 2.787-002

3.474-002 *-15*-002

4.825-002 5.484-002

6.131-002

6.763-002

8.272-002 9.675-002

1.097-001

1.218-001 1.3?9-001

1 .413-001 1.620-001 1.785-001

1.912-001 2.065-001

2.185-001

2.397-001 2.579-001

2.738-001 2.880-001

3.008-001

3.282-001

3.508-001 3.702-001

3,872-001

*. 025-001 *.16*-00l

*. 293-001 4.415-001

*. 530-001 *.6**-00l .760-001

*.8S*-00l 5.02*-00l

5.189-001

5.388-001

5.632-001

6.2O7-001

7.275-OQl

8.67*-00l

1. 063*000

1. 330*000

0.0150

0.000*000

*. 035-003 8.070-003

1 .210-002 1.613-002 2.*18-002 3.220-002

*. 018-002

*• 812-002 5.600-002

6.382-002

7.155-002

7.918.002

9.775-002

1.155-001

1.323-001

1 .481-001 1-631-001 1.771-001 2.030-001 2.261-001

2.469-001

2.659.001

2.832-001 3.139-001

3.405-001

3.639-001

3.8*8-001 4.036-001

4.4*1-001

4.775-001 5.062-001

5.313-001 5.538-001

5.742-001

5.929-001

6.104-001

6.269-001

6.*28-001

6.586-001

6.750-001

6.927-001

7.127-001

7.359-001 7.633-001

8.35*-001 9.382-001

1.082*000

1 .282*000 1.552*000

0.0200

0.000*000 *.*70-003

8.939-003

1.341-002

1.787-002 2.679-002

3.569-002

4.457-002 5.341-002

6.221-002

7.096-002 7.965-002 8.827-002

1.094-001

1. 300-001 1.497-001 1,686-001

1.866-001 2.038-001 2.356-001

2.646-001

2.909-001

3.151-001 3.373-001

3.769-001

*. 115-001 .20-001

*.69*-001 .941-001

5.*73-00l

5.915-001

6.293-001

6.62*-001

6.920-001

7.188-001 7,*33-001

7.661-001

7.875-001 8,079-001

8.280-001

8.483-001 8.697-001

8,932-001

9.196-001

9.502-001

1.028*000

1.136*000

1.28**000

l.*87*000

1.761*000

0.0250

0.000*000

*, 8*4-003 9.686-003

l.*53-002

1.937-002 2.90*-002

3.869-002

*. 833-002 5.794-002

6.751-002

7.705-002 8.654-002 9.597-002

1.1*3-001

l.*2o-001

1.6*2-001

1.855-001 2.061-001

2.259-001

2.630-001 2.971-001

3.285-O01

3.574-001

3.8*1-001

*. 322-001

*. 7*3-001 5.117-001 5.*53-001

5.758-001

6.415-001

6.962-001 7.430-001

7,8*1-001

8.207-001

8,538-001

8.8*1-001

9.121-001 9.384-001

9.633-001

9.876-001

1.012*000

1.037*000 1.06**000

1.09**000

1.127*000

1.211*000

1.323*000

l.*76*000

1.683*000

1,959*000

0.0300

0.000*000 5.175-003

1.035.002

1.552-002 2.069-002

3.103-002

*. 135-002 5.166-002

6.19*-002

7,220-002

8.2*2-002 9.261-002

1.028.001 1.279-001

1.526-001 1.767-001 2.002-001

2.230-001

2.*50-001

2.867-001

3.255-001 3.613-001

3,946-001

4,256-001

*. 816-001 5.309-001

5.750-001

6.1*6-001

6.507-001

7.286-001 7.936-001

8.*9*-001

8.983-001 9.*18-001

9,812-001

1.017*000

1.051*000

1.082*000

1.111*000 1.1*0*000

1.168*000

1.197*000

1.227*000

1.260*000 1.297*000

1.386*000

1.503*000

1.660*000

1.871*000 2.150*000

0.0350

0.000*000 5,*75.003

1.095-002

1.6*2-002 2.190-002

3.284-002 .376-002

5,*68-002

6.557-002

7.6*^-002 8.728-00? 9.809-002

1.089.001 1.356-001

1.620-001 1.879-001 2.132-001 2.379-001

2.620-001 3.078-001

3.507-001

3.907-001 .280-001

.630-001

5.264-001 5.827-001

6.331-001 6.786-001

7.201-001

8.100-001

8.852-001 9,*97-001

1.006*000

1.057*000

1.103*000 1.1*^*000

1.183*000 1.219*000

1.253*000 1.285*000

1.317*000

1.350*000

1.38^.000

1.^20*000

l.*60*000

1.55^*000 1.677*000

1.838*000 2.052*000

2.334.000

0.0^00

0.000*000 5.752.003

l.l50-Oo2

1.725-002 2.300-002

3,^5o-Oo?

*. 598-002 5.7*5-002

6.890-002 8.033-002

«.l7*-00?

1.031-001

1.1*5.001 1,*27-001

1.705-001 1.980-001 2.250-001

2.51*-001 2.772-Ojl

3.?68-Ool 3.73*-Ool .173-001

*. 58*.00l .971-001

5.676.001

6.305-001

6.870-001

7.182-Ofll 7.850-001

8.866-001

9.718-001 1.0*5*000

1.109.000 1.167,000

1.219*000

1.266*000

1.310*000 1.350*000

1.389*000

1.426*000

1,462*000

1.498*000

1.535*000 1.57**000

1.617*000 1.717*000

1.8*5*000 2.010*000

2.228*000

2.513*000

0.0450

000*000

009-003 202-002

802-002 03-002

60^-002 eO^-002

003-002

200-002

395-002 588-002

078-001

197-001 »9?-001 785-001

074-001

359-001 638-001

912-001

4*1-001

9*3«001

416-001

863-001

284-001

057-001 749-001

374-001

94J-001

460-001 591-001

054*000

136*000 208*000

272*000

33fl*000 383*000 32*000

478*000

520*000

561*000

601*000

6*1*000

682*000 724*000

770*000 876*000

008*000

178*000 399*000

687*000

0.0500

0.000*000 6,250-003

1.250-002

1.875-002 2.500-002

3.749-002

4.997-002 6.244-002

7.490-002

8.734-002

9,976-002

1.122-001 1,245-001

1.553-001 1.859-001 2.161-001

2.460-001

2.753-001

3.042-001

3.602-001 4,136-001

4.642-001 5.122-001

5.576-001

6.412-001

7.165-001 7.847-001

8.468-001

9.038-001

1.028*000 1.133*000

1.223*000

1.303*000

1.374.000

1.438*000

l.*96*000

1.550*000

1.601*000

1.648*000

1.693*000 1.737*000

1.780*000

1.824*000

1.870*000

1.919*000 2.030*000

2.167*000

2.341*000

2.566*000 2,857*000

0.0550

0.000*000 6,*77-003

1,295-002 1.9*3-002 2.591-002

3.885-002

5.179-002 6.*72-002

7. f6*-002 9.05^-002

1.03^-001

1 .163-001 1,291-001

1 .611-001 1.928-001 2.2O-001

2.55^-001

2.861-001

3.16+-001

3.752-001 .315-001

.852-001

5.363-001

5.848-001

6. ^6-001

7.557-001

8 .29^-001 8.967-001 9.566-001

1. 09^*000

,208*000

,307*000

,39^*000

.472*000

.542*000

.606*000 .665*000

, 720*000

. 772*000 .821*000

.869*000 .916*000

.963*000 2.012*000 2.064*000

2.181*000

2.323*000

2.501*000

2. 730*000 3,024*000

Page 117
TABLE 12 (CONTINUED)

S (J/MOLE-K)

0.0600 0.0640 0.0650 0.0700 0.0750 O.OROO 0.0900 O.loOO

T \

(K) 0.000 0.000*000 0.000*000 0.000*000 0.000*000 0.000*000 0.000*000 0.000*000

0.001 6.493-003 6.858-003 6.899-003 7,096-003 7,285-003 7,*67-003 7.81*-003

0.002 1.359-002 1.372-002 1,380-002 l.*19-002 l.*57.002 l.*93.002 1,563.002

0.003 2.00 8 -002 2,057-002 2.070-002 2.129-002 2.185-002 2.2*0-002 2.3**-002

0.00* 2.677-002 2.7*3-002 2,759-002 2,838-002 2.9l*-002 2.987-002 3.125-002

0.006 *. 015-002 4.114-002 *. 138-002 *. 257-002 .370-002 *.*8o-002 *. 687-002

0.008 5.352-002 5.484-002 5.517-002 5.675-002 5.826-002 5.972-002 6.2*9-002

0*010 6.688-002 6.854-002 6.894-002 7.0 9 2"002 7.2«l-002 7.*6+-002 7.810-002

0.012 8.0?3-002 8.222-002 8.271-002 8.508-002 8.735-002 8.954-002 9.371-002

0.01* 9.357-002 9.599-002 9.6*6-002 9.923-002 1.019-001 1.0++-001 1.093-001

0.016 1.069-001 1.095-001 1.102-001 l.l3*-001 1.16*-001 1.193-001 1.2*9-001 0.018 1.202-001 1.232.001 1.239-001 1,275-001 1.309-001 1.3+2.001 l.*0*-001

0.020 1.335-001 1 .368.001 1,376-001 1.*16-001 1,*5*-001 1. +90-001 1.560-001

0.025 1.665-001 1.707.001 1.718-001 1.767-001 1.815-001 1.861.001 1.9*8.001

0.030 1.99*-00l 2.0*5-001 2.057.001 2.117-001 2.17*-001 2.230-001 2.335-001

0.035 2.321-001 2.380-001 2.39*-001 2.*65-00l 2.532-001 2.597-001 2.720-001

0.0*0 2.6**-00l 2.712-001 2.728-001 2.809-001 2.887-001 2.961-001 3.103-001

0.0*5 2.963-001 3.0*0-001 3.059-001 3.151-001 3.239-001 3.323-001 3. +83-001

0.050 3.278-001 3.365-001 3.386-001 3. + 89-001 3.588-001 3.682-001 3.861-0C1

0.060 3.892-001 3.999-001 *. 025-001 +.152-001 .272-001 +.388-001 +.605-001

0.070 4.484-001 4.612-001 *. 6*3-001 *.79+-O01 *. 937-001 5.075-001 5.33*-0OI

O.OBO 5.0*9-001 5.199.001 5.236-001 5. +12-001 5.580-001 5.7*1-001 6.0*2-001

0.090 5.589-001 5.761-001 5.803-001 6.006-001 6.199-001 6.383-001 6.729-001

0.100 6.10*-001 6.298.001 6,3*5-001 6.575-001 6.793-001 7.001-001 7.393-001

0.120 7.059-001 7.298-001 7.357-001 7.639-001 7.908-001 8.166-001 8.*50-001

0.1*0 7.927-001 8.210-001 8.27B-001 8.613-001 8.933-001 9.239-001 9.815-001

0.160 8.718-001 9.0*2-001 9.121-001 9.506-001 9.87*-001 1.023*000 1.089*000

0.180 9.4*1-001 9.805-001 9.89*-001 1.033*000 1.07**000 1.11**000 1.190*000

0.200 1.011*000 1.051*000 1.061*000 1.109*000 1.155*000 1.199*000 1.28J.000

0.250 1.157*000 1.206*000 1.218*000 1.276*000 1.332*000 1.386*000 l.*90*000

0.300 1.281*000 1.337*000 1.351*000 l.*18*000 1,*83*000 1.5*6*000 1,668*000

0.350 1.388.000 1 .450*000 l.*66*000 1,5*1*000 1.615*000 1.686*000 1.822*000

o.*oo l.*82*000 1.551*000 1.567*000 1 .65o»000 1.731*000 1.809.000 1.960*000

0.*5o 1.566*000 1 .6*0*000 1.658*000 1,7*8*000 1,835.000 1.919*000 2.083*000

0.500 1.643*000 1.721*000 1.7*1*000 1,836*000 1.929.000 2.020*000 2.195*000

0.550 1.712*000 1.795*000 1.816*000 1.917*000 2.015*000 2.111*000 2.297*000

0.600 1 .777*000 1.86**000 1.885*000 1.991*000 2.09**000 2.195*000 2.391*000

0.650 1 .836*000 1.927*000 1.949*000 2.060*000 2.168*000 2.27**000 2.*79*000

0.700 1.892*000 1 .987*000 2.010*000 2.125*000 2.237*000 2.3*7*000 2,561*000

0.750 1.946*000 2.0*3*000 2.067*000 2.186*000 2.303*000 2.*17*000 2.638*000

0.800 1.997*000 2.098*000 2.123*000 2.2*5*000 2.366*000 2.*83*000 2.713.000

0.850 2.048*000 2.151*000 2.177*000 2.303*000 2.*27*000 2.5*8*000 2.78b*0oO

0.900 2.099*000 2.205*000 2.231*000 2.361*000 2.*88*000 2.613*000 2.856*000

0.950 2.151*000 2.260*000 2.287*000 2.*19*000 2.550*000 2.678*000 2.927*000

1.000 2.206*000 2.317*000 2.344*000 2.*80*000 2.6l**000 2.7*5*000 3.000*000

1.100 2.3?8*000 2.****000 2.472*000 2.61**000 2.752*000 2.889*000 3,155*000

1.200 2.475*000 2.59**000 2.624*000 2.770*000 2.9l**000 3.055*000 3.331*000

1.300 2.658*000 2.780*000 2.811*000 2.961*000 3.109*000 3.255*000 3.539.000

l.*00 2.890*000 3.015*000 3,0*7*000 3.201*000 3.352*000 3.501*000 3.792*000

1.500 3.186.000 3.315*000 3,3*6*000 3,503*000 3.658*000 3.810*000 *.107*000

000*000

139-003 62P-002 **2-002

255-002

883-002 510-002

136-002 761-002

139-001 301-001

*63-001

625-001

O3o-001 33-001

835-001

235-001 632-001

028-001 809-001

575-001

323-001

051-001 757-001

100-001 035*000

152*000 260*000

362*000 588*000

782*000

952*000

10**000 239*000

363*000 475*000

579*000

676*000

767*000

852*000 934*000

013*000

091*000

169*000 2*7*000 +13*000

599*000

815*000

076*000

396*000

0.1100

0.000*000 8.++7-003

1,689.002

2. 53*. 002 3.379.002

5.067-002

6.756-002 8.**+-002

1.013-001 1.182-001

1.350-001 1.519.001

1.687.001 2,107-001

2.526-001

2.9++-001

3.360-001

3.773-001 +.185-001

5.000-001

5.801-001

6.585-001

7.351-001

8.096-001

9.520-001

1.085*000

1.210*000

1.327*000

1. +36*000

1.680*000

1.891*000 2.076*000 2.2+1*000

2.389*000

2.52**000

2.6*7*000

2.761*000

2.867*000

2.966*000

3.059*000

3.1*9*000

3.235*000 3.319*000

3,*03*000

3,*R8*000 3.66**000

3.860*000

*. 08**000

*. 352*000 .678*000

0.1200

000*000 7+0-003

r+8-002

,622-002 ,+96-002

,2*3-002

,990-002 '37-002

,0*8-001 ,223-001

,397-001 ,572-001 r+6-001

,181-001 ,615-001 ,0*7-001 ,78-001

,907-001

.33+-001 181-001

,015-001 .83+-001

,635-001 ,+16-001

,916-001 133*000

,265*000

,389*000

,506*000 ?68*00Q

,995*000 195*000

,373*000 ,53**000

,679*000 813*000

,937*000 051*000

159*000

,260*000

,357*000 ,+50*000

,5*1*000

,631*000 ?22*000

,909*000 11**000

,3*7*000 ,622*000

,953*000

Page 11

J
TABLE 12 (CONTINUED)

S (J/MQLE-K)

0.1300 O.MOO 0.1500 0.1600 0.1800 0.3000 0.2250

T \

(K) 0.000 0.000*000 0.000*000 0.000*000 0.000*000 0.000*000 0.000*000 0,000*000

0.001 9.020-003 9.288-003 9,547-003 9.797-003 1.027-002 1.072-002 1.126-002

0.002 1.8o*-002 1.858.002 1,909.002 1.959-002 2.055-002 2.145.002 2,252.002

0.003 2.706-002 2.786.002 2.864-002 2.939-002 3.082.002 3.217-002 3.378.002

0.004 3.608-002 3.715.002 3,819.002 3.919-002 4.109.002 4.290-002 4.S03.002

0.006 5.411-002 5.572-002 5.72B-002 5.878-002 6.164-002 6.434-002 6.755-002

0.008 7.214-002 7.429-002 7.636-002 7.836-002 8.218-002 8.579-002 9.006-002

0.010 9.017-002 9.2»6-002 9.545-002 9.795-002 1.027-001 1.072-001 1.126-001 0.012 1.082-001 1.114-001 1.145-001 1.175-001 1.232-001 1.287-001 lOSl-OQl

0.01* 1.262-001 1.300-001 1.336-001 1.371-001 1.438-001 1.501-001 1.576-001 0.016 1.442-001 1.485-001 1.527-001 1.567-001 1.643-001 1.715-001 1.801-001

0.018 1.622-001 1.670-001 1.717-001 1.762-001 1.848-001 1.929-00) 2.026-001

0.020 1.802-001 1.856-001 1.908-001 1.958-001 2.053.001 2.143-001 2.25U.001

0.025 2.251-001 2.318.001 2.383-001 2.4*6-001 2.565-001 2.678-001 2.B12-001

0.030 2.699.001 2.780-001 2.858-001 2.933-001 3.077-001 3.213-001 3.373.001

0.035 3.146-001 3.241-001 3.332-001 3.420-001 3.587-001 3.746-001 3.93*-Ool

0.0*0 3.591-001 3.700-001 3.804-001 3.905-001 4.097-001 4.278-001 4.493-001

0.0*5 4.035-001 4.157-001 4.275-001 4.389-001 4.605-001 4.809-001 5.051-001

0.050 4.477-001 4.613-001 4.744-001 4.87l-ool 5.112-001 5.339-001 S.A09-001

0*060 5.353-001 5.518-001 5.677-001 5.829-001 6.120-001 6.394-001 6.7l9-o l 0.070 6.218-001 6.413-001 6.599-001 6.779-001 7.120-001 7.442-001 7.822-001

0.080 7.0«9-00l 7.294-0O1 7.509-001 7.717-001 8.110-001 8.481-001 8.918-001

0.090 7.903-001 6.160-001 8.405-001 8.6*1-001 9.088-001 9.508-001 1.000*000

0.100 8.719-001 9.008.001 9.284-001 9.5*9-001 1.00S.000 1.052.000 1 .

08.000

0.120 1.029*000 1.065*000 1.099*000 1.131*000 1.193.000 1.251*000 1.318.000

0.1*0 1.177*000 1.220*000 1.261*000 1.300*000 1.373*000 1.442*000 1.523*000

0.160 1.317*000 1.367*000 1.414*000 1.460*000 1.546*000 1.626*000 1.720*000

0.1 80 1.4*9*000 1.505*000 1.560*000 1.6*2*000 1.710*000 1.802*000 1.909.000

0.200 1.572*000 1.636*000 1.697*000 1.755*000 1.866*000 1.969*000 2.090*000

0.250 1.852*000 1.932*000 2.009*000 2.083*000 2.224*000 2.356*000 2.511*000

0.300 2.095*000 2.190*000 2.283*000 2.372*000 2.541*000 2.700*000 2.888.000

0.350 2.309*000 2.419*000 2.525*000 2,628*000 2.823*000 3.008*000 3.227.000

0.400 2.500*000 2.623.000 2.742.000 2.857*000 3,077.000 3,286.000 3. 534.000

0.*50 2.673.000 2.808.000 2.938*000 3.065*000 3,308.000 3,539.000 3.814.000

0.500 2.830*000 2.976.000 3.117*000 3.254.000 3,519.000 3.771.000 4.071.000

0.550 2.974*000 3.130*000 3.281*000 3.429*000 3.713*000 3.984*000 4.308.000

0.600 3.107*000 3.272*000 3.433*000 3.590*000 3.892.000 4.182*000 4.528*000

0.650 3.231*000 3.405*000 3,574*000 3.740*000 4.06C000 4.366*000 4.733*000

0.700 3.346*000 3.529*000 3,707*000 3.880*000 4.216.000 4.539*000 4.925*000

0.750 3.456*000 3.646*000 3,832*000 4.013*000 4.364*000 4.702*000 5.107*000

0.800 3.560*000 3.757.000 3,950*000 4.139*000 4.504*000 4.856*000 5.279.000

0.850 3.660*000 3.864*000 4.064*000 4.260*000 4.639*000 5.004*000 5.444*000

0.900 3.757.000 3.968.000 4,175.000 4.377*000 4.769.000 5.1*7.000 5,*o2*0o0

0.950 3.854*000 4.071.000 4,283.000 *.*9l*000 4,896.000 5.286.000 5.756*000

1.000 3.950*000 4.173.000 4,391.000 *, 605*000 5,021.000 5.423.000 5,907*000

1.100 4.148*000 4.382.000 4.611*000 *. 836*000 5.272.000 5,695*000 6.205*000

1.200 4.3(2*000 4.606.000 4.844*000 5.078*000 5.534.000 5.975*000 6.^08*000

1.300 4.604*000 4.855*000 5.102*000 5.3*4*000 5.816*000 6.273*000 6.827*000

1.400 4.886*000 5*144*000 5.398*000 5.647*000 6.133*000 6.604*000 7.174*000

1.500 5.223*000 5.487*000 5.746*000 6.001*000 6.498*000 6.980*000 7.565*000

0.2500

000*000

l7 7 -002 353-002

53 -002 707-002

06o-002 412-002

176-001 412-001

647-001

882-001

117-001 352-001 939-001 526-001

112-001 697-001

28]-001

P64-OOI

026-001

182-001 33J-001 047*000

160*000 382*000

59fi*000 806*000

010*000 204*000

65**000

064*000 433*000

769*000

075*000

356*000 617*000

859*000

084*000 296*000

49^*000 686*000

867*000

041*000

210*000

375*000

699*000

024*000

363*000 728*000

132*000

0.2750

0.000*000

1.225-002 2.450-002

3.676-002 4.901-002

7.351-002 9.801-002

1.225-001

1.470-001

1.715-001

1.960-001 2.205-001

2.449-001

3.061-001

3.672-001 4.282-001

4.892-001

5.501-001

6.108-001

7.320-001 8.526-001

9.726-001

1,092*000

1.210*000

1.443*000

1.670*000

1.891*000 2.105*000

2.311*000 2.794*000

3.232*000

3.630*000

3.992*000 4,324*000

4.630*000 4.913*000

5.176*000 5.422*000

5.653*000 5.871*000

6.078*000 6.276*000

6.465*000 6.649*000

6.828*000

7.177*000 7.526*000

7.884*000

8.266*000

8.684*000

0.3000

,000*000 ,272-002 ,544.002

,816-002

,088-002 ,632-002

,018-001 272-001

526-001

780-001

,035-001

,289-001 ,543-001 178-001

,812-001 ,446-001

,079-001 712-001

,343-001

,603-001

,857-001 010*000

135*000

,258*000 ,501*000 739*000 971*000

196*000

,414*000 ,926*000

,392*000

,hl8*000 ,206*000

,563*000

,893*000

,198*000

, 483*000 749*000

999*000 235*000

,459*000

,672*000

,877*000 075*000

,268.000 ,643*000

,014*000

,392*000

, 791*000 ,223*000

Page 119
TABLE 13 THE enthalpy and EXCESS ENTHALPY OF THE TOTAL HF.3 - HE* SOLUTyOw

X » .0001 X .0002 X » • 0005 X .flOlO X .0020

T(K) -H (J/MOLF)

HE (J/MOLE)-H (J/MOLE)

HE (J/MOLE)

-H

(J/MOLE)

HE (J/MOLE)

-H

(J/MOLE) HE(J/MoLE)

-H (J/MOLE) HE

IJ/MOLE) 0.000

0.001 0.002

0.003

0.00*

39.05631

39.05631 39.05631 39.05630

39.05630

-0.00021

.0.00021

.0.00021

.0.00021 .0.00021

39.05261

39.05261

39.05261

39.05261 39.05260

-0.000*2

-0.000*2

-0.000*2 -0.000*2

-0.000*2

39,0*151

39,0*151 39.0*150

39.0*150

39,0*150

-0.0010*

-0.0010* -0.00103

-0.00103 -0,00103

3939

39

39

39,

02297

02297

02296

02296

02296

_O.Oo2o3

-0,0o203

-0,Oo202

-0.0fl2o2 _O.Oo202

38,98580

38,98580

38,98579 38.98579

38.98578

.0

.0

.0

-0.0

00392

00392

00391

00391 00390

0.006

0.008

0.010 0.012

0.01*

39.05630 39.05630

39.05630 39.056g9 39.05629

-0.00021 -0.00020

-0.00020

-0.00020

-0.00020

39.05260

39.05260

39.05259

39.05259

39.05258

-0.000*1

-0.000*1 -0.000*0

-0.000*0 -0.00039

39,0*1*9 39.0*1*8

39.0*1*7

39.0*146 39.0*1*5

-0.00102

-0.00101 -0.00100 -0.00099

-0.00098

39

39

3939

39

0229* 02293

02291 02289

02287

-0.00200

-0.00199

.0.00197

-0.00195

.0.00193

38.98576

3B.9857*

38.98571 38.98567

38.9856*

.0

-0

.0

-0

.0

00388 00386

00383

00380

.00376 0.016

0.018

0.020 0.025

0.030

39.05629

39.05629

39.05628 39.05628

39.05627

-0.00019 -0.00019

-0.00019 -0.00018

-0.00018

39.05258

39.05257 39.05257

39.05255

39.0525*

-0.00039

-0.0003P

-0.00038 -0.00037

-0.00036

39.0*1*3 39.0*1*2

39,0*1*1

39,0*138

39.0*135

-0.00097 -0.00095

-0.0009*

-0.00091 -0.00089

3939

39

3939

022a* 02282

02260 0227*

02268

-0.00191 -0.0q189

-0,0fll86 .0,00181 .0.00175

38.98560 38,98556

38.98552

38.985*1 38.98530

.0

.0

.0

.0

.0

.00373 00369

00365

00355 003**

0.035

0.0*0 0.0*5

0.050

0.060

39.05627 39.05626

39.05625 39.05625

39.05623

-0.00017 -0.00017

-0.00016

-0.00016 -0.0001*

39.05253

39.05252

39.05250 39.052*9

39.052*7

-0.0003*

-0.00033

-0.00032

-0.00031 -0.00029

39.0*132

39.0*129 39.0*126

39,0*123

39.0*117

-0.00086 -0.00083

-0.00080

-0.00077 -0.00072

39

39

39

3939

02262

02256

02250 022**

02232

-0.00170

-0.00164 -0.00159

-0.00153

-0.00142

38.98519

38.98507 38.98*95

38.98*83 38.98*59

.0.0

-0

.0.0

00333 00323

00312

00301 00280

0.070

0.080

0.090

0.100

0.120

39.05622

39.05621 39.05620 39.05618

39.05616

-0.00013

-0.00012

.0.00011 -0.00010

-0.00008

39.052**

39,052*2 39.05239

39.05237

39.05231

-0.00027 -0.0002*

-0.00022

-0.00020 -0.00016

39.0*110 39.0*10*

39,04098

39.0*092 39,0*079

-0.00066

-O.OOO6I -0.00055

-0.00050 -0.00039

39

39

3939

39

02220

022o7 02195

021A3

02158

-0.00131

.0.00120 .0,00110 -0.00099

-0,00078

38.98*35

38.98*11 38,98387

38.98362

38,98313

.0

.0.0

.0

.0

00258

00237

00216

00195

00153

0.1*0

0.160

0.180

0.200 0.250

39.05613

39.056)0 39.05606

39.05603

39.05592

-0.00006

-0.0000* -0.00002

0.00000

0.00005

39.05226

39.05221 39.05215

39.05209

39.05191

-0.00012

-O.OOOOS

-0.0000*

0.00000 0.00010

39.0*066

39.0*053

39.0*0*0

39.0*026

39.03990

-0.00029

-0.00019

-0.00009

0.00001 0.00025

3939

39

39

39

02132

02107

02081 02055

0i9qe

-0.00058

-0.00038 -0.00018

0.00002

O.OoOSO

38.98263

38.98213

36.98163

38.98112

38.97983

.0

.0

.0

00113

00073

0003* 00005

00101

0.300 0.350

0.*00 0.*50

0.500

39.05577

39.05S57

39.05529

39.05*91

39.05**1

0.00010 0.0001* 0.00019

0.0002* 0.00028

39.05170

39.051**

39,05110 39.05066

39.05009

0.00019

0.00029

0.0003R

0.000*7

0.00057

39.03951 39.03906 39.03853

39.03790 39,03715

0.000*9

0.00072

0.00096

0.00119

0.001*2

39

39

39

3939

0l9i8

OI841 01757

0166*

01558

0.00097

0.0ol*5

0.00191 0.00238

0.0o28*

38,97850

38.97712 38.97566

38.97*10 38.972*2

00196

00291 0038* 00*76 00568

0.550

0.600

0.650 0«7oo

0.750

39.05375

39.05291

39.05181 39.05027

39,0*799

0.00033

0.00037

0.000*2

0.000*6

0.00051

39.0*938

39.0*8*8

39.0*731 39.0*571 39.0*336

0.00066

0.00075 0*00084

0.00093

0.00101

39.03625

39,03516

39.03381 39.03202

39.029*9

0.0016*

0.00187

0.00209

0«00232

0.0025*

39

39

39

39

39

01*36

01296

01130

U0 9 20 O0636

O.Oo329

O.Oo37* 0.00*19

0.0o*63

0.00507

38.97058

38.96856

38.96628 38.96356

38.96009 0-

00659

007*9

00839

00*27 01015

0.800 0.850

0.900

0.950

1.000

39,0***6

39.03900 39.03065

39.01826

39.000*6

0.00055

0.00059 0.0006*

0.00068

0.00072

39.03978

39.03*25

39.0258*

39.01339

38.99553

0.00110 0.00119

0.00127

0.00136

0.00144

39.02571 39.02000

39,011*1 38.99877

38.98073

0.00275

0.00297

0.00318 0,00339

0.00360

39

38

38

3838

00227

.99625 98735

97**1 956o7

0.00551 0.0o59*

0,0o636

0,00678

O.Oo720

38.95539

38.9*875

38.93923

38.92569

38.90673

01102

01188

01273 01357

01**0

1.100

1.200

1.300

1-400 1.500

38.9*2)5 38.8*068

38.67610

38.*2097 38.0*138

0.00080

0.00088 0.00096

0.00103

0.00110

38.93710

38.83551 38.67082 38.M559

38.03592

0.00160

0.00176

0.00191 0.00206

0.00219

38.92195 38.82002

38.65500

38.399*7 38.0195*

0.00*01 0.00**0

0.00*78 0.0051* 0.005*8

38

3fl 38

3837

89669

79*18

62863

37260 9922*

O.O080I 0.00880 0.00955

0.0)028 0.01096

38.8*617

38.7*252 38.57588

38.31887 37.93763

0'

0<

0<

01603

01760

01911 02055 02193

Page 120
TABLE 13 (CONTINUED)

X • 0030 X • .00*0 X •0050 X a • n060 X « • 080

T -H HE -H HE -H HE -H HF -H HE

<K> (j/MOLf(J/MOLE) (J/MOLE' Ij/HOLE) (J/MOLE) (J/MOLE* (j/mole) (J/MOLE) (J/MOLE) (J/MOLE) 0.000 38.9*852 -0.00570 38.91116 -0,007*0 38,87372 -0.00902 38.83622 -0.01058 38.76101 .0.01349

0.001 38.9*852 -0.00570 38.9H16 -0.007*0 38,87372 -0.00902 38.83621 -0.01058 38.76101 .0 01349

0.002 38.9*852 -0.00570 38.91116 -0,007*0 38,87372 -0.00902 38.83621 -0,0]057 38,76101 .0 013*9

0.003 38,9*851 -0.00569 38.91115 -0,00739 38.87371 -0.00901 38.836?0 -0,01056 38,76100 .0 013*8

0.00* 38,9*850 .0.00568 38,9111* -0.00738 38,87370 -0.00900 38,63619 .0.01055 38,76099 .0 013*7

0.006 38,94848 -0.00566 38.91112 -0.00736 38,87367 -0.00898 38.83616 .0.01053 38.76096 .0 0U44

0.008 38.9*8*5 -0.00563 38.91108 -0.00732 38.8736* -0.0089* 38.63612 -0.0l0*9 38,76091 .0 013*0

0.010 38.9*841 -0.00560 38.9H0* -0.00728 38.87359 -0.00890 38.8 3 6 7 -0.0104* 38.76085 >0 0133*

0.012 38.9*837 -0.00556 38.91099 -0.0072* 38.87353 -0,0088* 38.836 1 -0.01038 38.76079 .0 ,01328 0.01* 38,9*832 -0.00551 38.91093 -0.00718 38.873*7 -0,00878 38,83594 -0.01032 38,76071 .0 01321 0.016 38.9*827 -0.005*6 38,91087 -0.00712 38,873*0 -0.00872 38.83587 -0.01024 38.76062 .0 01312 0.018 38.9*822 -0.005*1 38.91081 -0. 00706 38.87332 -0.0086* 38.83578 -0.0]016 38.76052 .0 01303

0.020 38.9*8 16 -0.00536 38.9107* -0.U0700 38.8732* -0.00857 38.835 6 9 -O.O1O08 38,760*1 -0 01293

0-025 38.9*8 1 -0.00521 38.91055 -0.00682 38.87302 -0.00836 38.

3 5** -0.0o 9 85 38.76011 -0 01265

0.030 38.9*785 -0.00507 38.91035 -0.00663 38.87279 -0.0081* 38.63517 -0.0o 9 59 38.75978 -0 0123*

0.035 38.9*769 -0.00*91 38.9101* -0.006** 38.87253 -0.00791 38.83*88 -0,00932 38.759*2 .0 01201 0.0*0 38.9*7«;2 -0.00*76 38,9o992 -0.0062* 38.87227 -0.00767 38.83*57 -0,0o 9 04 38.7590* .0 01166

0.0*5 38,9*735 .0,00*60 38.90970 -0.00603 38,87200 .0,007*2 38.83*26 -0,0o876 38,75864 .0 01130

0.050 38,9*7l8 -0.00*** 38,909*8 -0.00583 38,87173 -0,00717 38.6339* .0,00847 38.75823 .0 01093

0.060 38.9*683 -0.00*13 38.9o9o2 -0.005*2 38.87116 -0.00666 38.83327 .0,00787 38.75737 .0 01018

0.070 38.9*6*7 -0.00381 38,90855 -0.00500 38.87059 -0.00616 38.83259 -O.Oo727 38.756*9 .0 009*0

0.080 38.9*611 -0.00350 38.90807 -0.00*59 38.87000 -0.00565 38.83190 -0.00667 38.75559 -0 00862

0.090 38.9*575 -0.00318 38.90760 -0.00*18 38.869*1 -0.00514 38.83120 -O.Oo607 38.75*67 -0 00783

0.100 38.9*538 -0.00287 38.9 7ll -0.00377 38.86881 -0.00463 38.830*9 -0.065*6 38.75374 -0 00705

0.120 38.9**65 -0.00226 38.9061* -0.00296 38.86761 -0.00363 38.629 5 -0.00427 38. 75186 -0 005*8

0.1*0 38,9*391 -0.00166 38.90516 -0.00216 38.86639 -0.00263 38.82760 -0.00309 38.74995 -0 00392

0.160 38.9*317 -0.00106 38.90*18 -0.00137 38.86517 -0.00165 38.8261* -0.00192 38,74802 .0 00238

0.180 38.9*2*2 -0.000*7 38.90319 -0.00059 38,8639* -0.00068 38.82*67 .0.00076 38.74607 .0 00085

0.200 38.9*167 0.00011 38.90219 0.00019 38.86270 0.00028 38.82319 0.00039 38,74412 00067

0.250 38.93976 0.00155 38.89968 0.00210 38.85958 0.00266 38.819*6 O.Oo324 38,73918 00***

0.300 38.93782 0.00297 38.89712 0.00399 38,856*0 0.00502 38.81567 O.O0606 38.73418 00819

0.350 38.93581 0.00*38 38.89*50 0.00586 38.85317 0.00736 38.8H83 O.O0886 38.72911 01191

0«*00 38.93373 0-00577 38.89180 0.00772 38.8*985 0»00968 38.60789 0.01165 38.72395 01561

0.*50 38.93156 0.00716 38.88900 0.00957 38.8*6** 0.01198 38.80386 0.0i4*l 38.71869 01928

0.500 38.92925 0*0085* 38.88608 0.011*0 38.8*289 0.01427 38.79970 0.0i7l5 38.71330 02293

0.550 38.92679 0.00990 38.88300 0.01321 38,83920 0.01654 38.79539 0.0l987 38.70775 0265*

0.600 38.92*15 0.01125 38,87974 0.01501 38,83532 0.01878 38.79089 0.02256 38.70202 03013

0.650 38.92125 0.01259 38.87621 0.01680 38,83117 0.02101 38.78613 0.02523 38.69602 .03369 0.700 38.91791 0.01392 38.87225 0.01857 38.82659 0.02322 38.78093 0.02789 38.68958 03722

0.750 38.91382 0.01523 38.86755 0.02032 38.82127 0.02542 38.77*99 0.03051 38.68241 ,0*072 0.800 38.90850 0.0165* 38.86161 0.02206 38.81*71 0.02758 38.76781 0.03311 38.67400 0**18

0.850 38.9012* 0.01783 38.85373 0.02378 38.80622 0.02973 38.75870 0.03569 38.66366 0*761

0.900 38.891H 0.01910 38.8*299 0.025*8 38.79*87 0.03186 38.7*67* 0.0382* 38.65047 05101 0.950 38,87696 0.02036 38.82822 0.02716 38.779*9 0.03395 38.73075 0.0*075 38.63326 05*36

1.000 38,857*0 0.02161 38.80806 6.02882 38.75872 0.03603 38.7o938 0.0*32* 38.61069 05767

1.100 38,79565 0.02*0* 38.7*512 0.03206 38.69*60 0.04006 38.6**o7 0.0*810 38.54301 06415

1.200 38.69085 0.026*0 38.63918 0.03520 38.58751 0.04*01 38.5358* 0.05281 38.43250 07043

1.300 38.52313 0.02867 38.*7038 0.03822 38.*l763 0.0*778 38.36*88 0,0573* 38.259 3 8 076*6

1.400 38.26513 0.03083 38.21139 0.0*111 38.15765 0.05140 38.10391 0.06168 37.996*2 0822*

1.500 37.88303 0.03289 37.828*2 0.0*386 37.77381 0.05483 37.71921 0.06579 37.61000 ,08772

Page 121
TABLE 13 (CONTINUED)

X .oloo X .0150 X a .0200 X > .n250 X .0300

T -H ME -H HE -H HE -H HE -H HE

<K) (j/MOLf) (J/MOLE) (J/MOLE> <J/MOLE> (J/MOLE) (J/MOLE) (j/MOLf) (J/MpLE) (J/MOLE) (J/MOLE) 0.000 38.68558 -0.01618 38,*9616 -0.02206 38.30572 -0.02692 38 U**2 -0.03092 37.92236 -0.03*16

0.001 38.68558 -0.01618 38.*9616 -0.02206 38.30572 -0.02692 38 U**l -0,03091 37.92236 .0.03*16

0.002 38 685*8 -0.01618 38,*9616 -0.02206 38.30571 -0.02691 39 ,11**1 -0,03091 37.92235 .0.03416

0.003 38,68557 .0.01617 38.*96l5 -0.02205 38.30570 -0.02690 38 11*39 -0,03090 37.9223* .0.03*1*

0.00* 38,68556 -0.01616 38.*96l3 -0.0220* 38,30569 -0.02689 38 ,11*38 -0,03088 37.92232 .0.03*13

0.006 38. 68552 -0.01613 38.*9609 -0.02200 38.3056* -0.02685 38 11*33 -0,03084 37.92227 .0.03*08

o.ooa 38.685*7 -0.01608 3B.*960* -0.02195 38.30558 -0.02679 38 1)*?6 -0.03078 37.92220 .0.03*02

0.010 38.685*1 -0.01602 38.*9596 -0.02188 38.30550 -0.02672 38 ,11*17 -0.03070 37.92211 - 0-0339*

0*012 38.6853* -0.01595 38.*9588 -0.02180 38.305*0 -0.0266* 38 U407 •O.O3O6I 37.92199 -0*03385

0.01* 38.68525 -0.01587 38.*9577 -0.02171 38.30529 -0.02653 38 ,1139* -0,03050 37.92186 -0*03373

0.016 38.68515 -0.01578 3B.*9566 -0.02160 38,30516 -0.026*2 38 ,11380 -0,03038 37.92171 .0.03360

0.018 38.6850* -0.01568 38.*9553 -0.021*9 38.30501 -0.02629 38 H36* -0.03024 37.92153 .0*033*5

0.020 38.68*92 -0.01557 3«.*9538 -0.02135 38,30*8* -0.0261* 38 ,113*6 -0,03008 37,9213* .0.03329

0.025 38.68*58 -0.01526 38,*9*96 -0.02098 38.30*37 -0.02572 38 .11294 -0.02962 37.92078 .0.03280

0.030 38.68*20 -0.01*90 38,*9**8 -0.0205* 38,30380 -0.02522 39 ,11231 -0,0?9o8 37,92010 .0.03222

0.035 38.68377 -0.01*52 38.*9393 -0.02005 38,30316 -0.02*65 38 -U159 -0.0?8*5 37.91931 .0.0315*

0.0*0 38.68332 •0.01*11 38.*933* -0.01952 38.302*6 -0.02*03 38 .11079 -0.0J775 37.91843 .0.03079

0.0*5 38.68285 -0.01368 38.*9270 -0.01895 38.30169 -0.02336 38 .10992 -0.02700 37.917*6 .0.02996

0.050 38.68236 -0.0132* 38.*9203 -0.01836 38.30088 -0.0226* 38 .10898 -0.02619 37.91642 -0.02907

0.060 38.68133 -0.01233 38.49062 -0.01712 38.29912 -0.02113 38 .1069* -0.0?*4* 37.91412 -0.02713

0.070 38.68026 -0.01139 38,*89l2 -0.01582 38.29725 -0.01952 38 .10472 -0.02256 37.91161 .0.02501

0.080 38.679,6 -0.010** 38.*8755 -0.01*48 38.29527 -0.0178* 38 .10238 -0.02059 37.90892 .0.02278

0.090 38.678 3 -0.009*8 38.*8595 -0.01312 38.29322 -0.01612 39 09992 -O.O185* 37.9060* .0.020**

0.100 38.67689 -0.00852 38.*8*30 -0.01174 38.29111 -0.01*37 39 .09738 -0.0J645 37.90315 .0.0180*

0.120 38.67*57 -0.00659 38.*8093 -0,00897 38,28676 -0.01081 38 ,09211 -0,0l2l7 37.89701 .0.01308

0.1*0 38.67220 -0.00*67 38,*77*8 -0.00618 38.28228 -0.00721 38 0866* -0.0o780 37.89060 .0.00799

0.160 38.66981 -0.00J77 38.*7398 -0.003*0 38.27770 -0.00359 3« .08103 -0.06339 37.88401 .0.00283

0.180 38.667*0 -0.00087 38.*70*3 -0.000*1 38.27306 0.00004 38 >075 3 3 O.OolO* 37.87727 0.00238

0.200 38.66*98 0.00102 38.*6685 0.00216 38.26836 0.00367 38 06954 0.0n550 37.87042 0.00763

U.250 38.65885 0.00570 38.45779 0.00 9 08 38.256*3 0.01275 39 ,05481 0.0l669 37.85295 0*02086

0.300 38.652** 0,01036 38,*4860 0,01598 38.2**31 0.02185 39 03981 0,0279* 37,83512 0.03*21

0.350 38.6*636 0.01499 38,43931 0.02287 38.23205 0.03096 38 02462 0.03922 37.81703 0.0*763

0.*00 38.63998 0.01960 38.42990 0.02974 38.21965 0.04004 38 ,00925 0,050*9 37.79873 0.06106

0.*50 38.633*9 0.02*18 38.42037 0.03656 38.20710 0.04909 37 99371 0.06173 37.78023 0.07**7

0.500 38.62687 0.02873 38,41069 0.0*335 38.19*39 0.05809 37 978 0.07292 37,76153 0.08783

0.550 39.62009 0.0332* 38.40085 0.05008 38.18151 0.06703 37 96209 0.08*05 37.74262 0-10113

0.600 38.61312 0.03772 38.39082 0.05678 38.16843 0.07591 37 94597 0.09511 37.72348 0.11*35

0.650 38.60589 0.0*217 38.38052 0.063*2 38.15507 0.0847* 37 9 2 9 5 7 0.1o6lO 37.70*06 0*127*9

0.700 38.598 23 0.0*657 38.36977 0.07000 38.14127 0.093*9 37 9 1272 0.1i7 l 37.68*17 0*1*054

0.750 38.58982 0.050 1** 38.35829 0.07654 38.12672 0.10218 37 895,3 0.1278* 37.66354 0*153*9

0.800 38.58018 0.05527 38.34558 0.08301 38.11095 0.11078 37 87631 O.I3857 37.6*169 0*1663*

0.850 38.568m 0.05955 38.33095 0.089*2 38.09327 0.11931 37 85559 0.1*920 37.61793 0.17906

0.900 38.55*19 0.06379 38.313*8 0.09576 38,07276 0.1277* 37 83204 0.15972 37,59136 0.19166

0.950 38.53577 0.06798 38.29203 0.10203 38,04828 0.13609 37 80*55 0.17012 37.56085 0.20*12

1.000 38.51199 0.07211 38.2652* 0.10822 38,01849 0.1**32 37 77176 0,180*0 37.52509 0.216*3

1.100 38.**19* 0.08021 38.18928 0.1203* 37.93664 0.160*6 37 684 4 0.20053 37,*3150 0.2*055

1.200 38.329i5 0.0880* 38.07080 0.13209 37.812*7 0.17608 37 55420 0.2?003 37.29600 0*26390

1.300 38.15388 0.09559 37.89014 0.1*337 37.62644 0.19112 37 36280 0.23880 37.099 2 5 0-28639

l.*00 37.88895 0.10280 37.62027 0.15*18 37.35165 0.20550 37 08310 0.25675 36.81*6* 0.30791

1.500 37.50079 0.10965 37.22780 0.16**4 36.95487 0.21917 36 68202 0.27381 36.40927 0.32836

Page 122
TABLE 13 (CONTINUED)

X o • 0350 X = .0400 X • 0450 X > •fl500 X = • 0550

T -H ME -H HE -H HE -H HF -H HE

<K> <J/MOLF> ' J/MOLE> IJ/MOLE' Ij/MOLE) 1 J/MOLE' <J/MOLE> <j/M0LF> (J/MoLE' <J/MOLE> IJ'M01E> 0.000 37.72966 -0.03676 37.53637 -0.03877 37.34257 -0.04027 37.14830 .0.04130 36,95360 .0.0*190

0.001 37.72966 -0.03676 37.53637 -0.03877 37.3*257 -0.04027 37.14829 -0.04129 36,95360 .0 0*190

0,002 37.72965 -0.03675 37.53636 -0.03876 37.3*256 -0.04026 37,1*828 .0.04129 36.95359 .0 04189

0.003 37.72963 -0.0367* 37.53635 -0.03875 37.3*25* -0.04025 37,14827 -0,04127 36,95357 .0 04188

0.00* 37.72962 .0.03672 37.53633 -0.03874 37.3*252 -0.04023 37,14825 -0.04126 36.95355 _0 04186

0.006 37.72956 -0.03668 37.53627 -0.03869 37.34246 -0.04018 37.148)8 -0.04121 36.95348 .0 04181 0.008 37.729*8 -0.03661 37.53619 -0.03862 37.34238 -0.04011 37.148)0 -0.04114 36.95339 -0 04174

0.010 37.729 3 9 -0.03653 37.53609 -0.03854 37.34227 -0.04002 37.U798 -0.04104 36.95328 -0 04164

0.012 37.729 2 7 -0.036*3 37.53596 -0.03843 37.34214 -0.03992 37.U785 -0.04U93 36.95313 -0 04153

0.01* 37.729)3 -0.03631 37.53581 -0.03831 37.34198 -0.03979 37.147*8 -0.040*0 36.95297 .0 04140

0.016 37.72896 -0.03617 37.5356* -0.03817 37.34180 -0.03964 37.U7S0 -0.04065 36,95277 .0 04125

0.018 37.72878 -0.03602 37.535*5 -0.03801 37.34160 -0.03948 37.14729 -0.04048 36.95255 .0 04107

0.020 37.72857 -0.0358* 37.53523 -0.03783 37.34137 -0.03929 37.147 5 -0.04029 36.95231 .0 04088

0.025 37.72797 -0.03533 37.53*60 -0.03730 37,34071 -0.03875 37.14636 .0.03973 36.95159 .0 04030

0.030 37.72725 -0.03*72 37.53383 -0.03666 37.33990 -0.03808 37.14552 -0.039o5 36,95072 -0 03960 0.035 37.72641 -0.03*01 37.5329* -0.03591 37,33897 -0.03731 37.14454 -0.03826 36.94970 -0 03879

0.040 37.725*6 -0.03321 37.53193 -0.03507 37.33790 -0.03643 37.14342 -0.03735 36.94853 .0 03785

0.045 37.72**1 -0.03232 37.53080 -0.03413 37.33671 -0.03546 37.14217 -0.03633 36.94722 -0 03680

0.050 37.72326 -0.03136 37.52958 -0.03311 37.33541 -0.03439 37.14080 -0.03522 36.94579 -0 03565

0.060 37.72075 -0.02925 37.S2686 -0.03086 37.33250 -0.03200 37.13772 -0.03272 36.94256 .0 03306

0.070 37.71796 -0.02693 37.52383 -0.02836 37.32924 -0.02935 37.13426 -0.02993 36.93890 .0 .03014 0.080 37.71*96 -0.02**6 37.5206* -0.02568 37.32569 -0.02647 37.13046 -0,02688 36.93*87 -0 02693

0.090 37.71179 -0.02186 37.5170* -0.02284 37,32190 -0.02342 37.12638 .0,02363 36.93053 .0 .02350 0.100 37.70847 -0.01917 37.51338 -0.01989 37.31790 -0.02023 37.12207 -0.02021 36,92593 -0 ,01988 0.120 37.70150 -0.01359 37.50563 -0.01372 37.30941 -0.01352 37.11288 -0,0)300 36.91607 .0 01219

0.1*0 37.69*20 -0.00783 37.497*7 -0.00732 37.30043 -0.00651 37.103H .0,Oo5*3 36,90553 .0 00408

0.160 37.68665 -0.00195 37.48900 -0.00076 37.29107 0.00069 37.09290 0.00240 36.89*49 00434

0.180 37.67892 0.00*01 37.48030 0.0059) 37.281*3 0.00805 37.08235 0.0)041 36.88306 01298

0.200 37.6710* 0.01002 37.*7l*2 0.01266 37.27157 0.01552 37.07153 0.0)857 36.87131 02181 0.250 37.65089 0.0252* 37.*4863 0.02981 37.24621 0.03454 37.04365 0.039*2 36.84095 04444

0.300 37.63027 0.0*065 37.42527 0.04723 37.22015 0.05394 37.01492 0.06075 36.80959 06766

0.350 37.60932 0.05617 37.*0150 0.06482 37.19359 0.07356 36.98560 0,08238 36.77755 09125

0.400 37.588H 0.07)73 37.377*1 0.08249 37.16665 0.09330 36.95584 0.10416 36,7*500 11506

0.450 37.56667 0.08729 37.35305 0.10016 37.13940 0.11307 36.92572 0.12&00 36.71203 13895

0.500 37.5*500 0.10279 37.328** 0.1 1779 37.11186 0.13281 36.89528 0.U783 36.67871 16284

0.550 37.523U 0.1182* 37.30358 0.13537 37.08405 0.15250 36.86454 0.16962 36.64505 18671 0.600 37.50097 0.13361 37.278*6 0.15286 37.05596 0.17211 36.833s0 0.19132 36.61107 21050

0.650 37.478*3 0.1*888 37.25303 0.17027 37.02754 0.19162 36. 8o2l0 0.2)293 36.57672 23419

0.700 37.*5563 0.16406 37.22711 0.18756 36.99864 0.21102 36.77021 0.23442 36.54185 25776

0.750 37.*3197 0.17913 37.200** 0.20474 36.96896 0.23029 36.73754 0.25577 36.50620 28119

0.800 37.*07o9 0.19408 37.1725* 0.22177 36.93805 0.2*9*1 36,7o364 0.27697 36.46931 30444

0.850 37.38031 0.20889 37.1*27* 0.23866 36.90525 0.26837 36.66784 0.29798 36.43052 32751

0.900 37.35072 0.22356 37.11015 0.25539 36.86966 0.2871* 36.62926 0,3i880 36,38896 35036

0,950 37.31722 0.23807 37.07366 0.27194 36,83018 0.30572 36.58680 0.33940 36,3435* 37298

1.000 37.278*7 0.25240 37.0319* 0.28828 36.78550 0.32*08 36.53917 0.35976 36.29296 39533

1.100 37.179o3 0.280*8 36.92666 0.32033 36.67440 0.36006 36,*2225 0.39968 36.1702* 43917

1*200 37.03789 0.30769 36.77988 0.35137 36.52199 0.39494 36.26423 O.43837 36,00662 48166

1.300 36.83580 0.33389 36.572*6 0.38128 36.30925 0.*2853 36.0*6)8 0.47565 35.78326 52261

1.400 36.54629 0.35897 36.27806 0.40989 36,00997 0.46068 35.74204 0.5)132 35.47*26 56181

1.500 36.1366* 0.38279 35.86*1* 0.*3709 35.59179 0.*9l2* 35.3)960 0.54523 35.0*757 0< 59906
TABLE 13 (CONTINUED)

X • 0600 X .06*0 X • • 0650 X a • 0700 X « • 0750

T -H HE -H HE -H HE -H HF -H HF

<K> <-J/MOlP) (J/MOLE) IJ/MOLE' <J/M0LE> <J/M01E> Ij/MOLE) •j/MOLF' <J/MoLE> (J/MOLE' (j'MOLE 1 0.000 36.75852 -0.0*212 36.60221 -0.04205 36.56310 -0.04200 36.36735 -0.0*155 36.17133 .0.04083

0.001 36.75852 -0.0*212 36,60220 -0.0420* 36.56309 -0,04199 36.36735 .0,0*155 36.17132 .0.04082

0.002 36.75851 -0.0*211 36.60219 -0.0*20* 36.56308 -0.04199 36.3673* -0.0*15* 36.17131 .0.04082

0.003 36.758*9 -0.0*210 36.60218 -0.0*202 36.56306 -0.04197 36.36732 _0. 0*153 36.17129 .0.04080

0.00* 36.758*7 -0.0*208 36,60215 -0.0*201 36.56304 -0.0*195 36.36730 0.0*151 36.17127 .0.04078

0.006 36.758*0 -0.0*203 36.60208 -0.0*195 36.56297 -0.04190 36.36723 -0.0*146 36.17120 .0.04073

0.008 36.75831 -0.0*196 36.60199 -0.0*188 36.56288 -0.04183 36.36713 -0.0*138 36.17109 .0.04065

0.010 36. 758)9 -0.0*186 36.60186 -0.0*178 36.56275 -0.04173 36.36700 -0.0*129 36.17096 .0.04056

0.012 36.758 * -0.0*175 36.60171 -0.0*167 36.56260 -0.04162 36.3668* -0.0*117 36.17080 .0*04044

0.01* 36.75787 -0.0*161 36.60154 -0.0*153 36.56242 -0.041*8 36.36666 -0.0*103 36.17061 .0*04029

0.016 36.757*7 -0.0*1*5 36.60133 -0.04137 36.56222 •0.0*132 36.36645 -0.0*087 36.170*0 .0.04013

0.018 36.7574* -0.0*128 36.60110 -0.04119 36.56198 -0.0*114 36,36671 -0.0*068 36.17015 .0.03995

0.020 36.75719 -0.0*108 36,60084 -0.04099 36.56172 -0.0*09* 36,3659* -0.0*0*8 36,16988 .0.03974

0.025 36.756** -0.0*0*9 36.60008 -O.O4040 36.56095 -0.0*03* 36.36515 -0.03987 36.16906 .0.03912

0.030 36.7555* -0.03978 36.5991b -0.03967 36.56002 -0.03961 36.36*19 -0,0391* 36.16807 .0.03837

0.035 36.75**8 -0.0389* 36.59806 -0.03882 36.55892 -0.03876 36.36306 -0.03826 36,16691 .0.03749

0.0*0 36.75327 -0.03798 36.59682 -0.0378* 36.55767 -0.03778 36.36177 -0.03727 36.16558 .0.03647

0.0*5 36.75191 -0.03691 36.59542 -0.03675 36.55627 -0.03668 36.36031 -0.0361* 36.16*09 -0-03533

0.050 36.750*2 -0.03572 36.59388 -0.0355* 36.55471 -0.035*6 36.35871 -0.03*90 36.162*3 -0.03406

0.060 36.7*7o* -0.0330* 36.59039 -0.03280 36.55120 -0.03270 36.35507 -0.03207 36.15867 -0.03117

0.070 36.7*320 -0.03000 36.58641 -0.02967 36.54719 -0.02956 36.35090 -0,0288* 36.15*3* .0.02785

0.080 36.73896 -0.02666 36.56201 -0.02623 36.54274 -0.02609 36.3*626 -0.02525 36,1*953 .0.02416

0.090 36.73*37

36.729*8

-0.02306 -0.01925

36.57723

36.57214

-0.02251 -0.0185536.53792

36.53277

-0.0223* -0.01835

36.3*l 2 l -0.0?136

-0.01721 36,1*427

36,13863

.0.02014

0.100 36.33581 .0.01583

0.120 36.71899

36.70772

-0.01113

-0.00250

36.56115 36.54932

-0.01009

-0.00108

36.52166

36.5o97o

-0.00981 -0.0007036.32*12

36.311*7

_0.0n828

0.00129

36.12637

36.11307

.0.0065*

0.1*0 0.00346

0.160 36.69588 0.006*8 36.53685 0,00834 36.49707 0.00882 36.29810 0.01133 36.09896 0.01399

0.180 36.68358 0.0157* 36.52388 O.O1806 36.4839* 0.01866 36.28*15 0.02173 36.08422 0.0249*

0.200 36.67093 0.02520 36.51051 0.02803 36.*70*0 0.02875 36.26974 0.032*2 36.06896 0*03621

0.250 36.638l* 0.0*956 36.47581 0.0537* 36.*3522 0.05*79 36.23222 0.06011 36.02915 0«06549

0.300 36.60*19 0.07*6* 36.43983 0.08027 36.39873 0.08169 36.19322 0.08878 35,98766 0.09592

0.350 36.569*6 0.1001s 36.40296 0.1073* 36.36133 0.10913 36.15319 O.I18H 35.94503 0-12'09

U.*00 36.53*1* 0.12597 36.36544 0.13*71 36.32327 0.13689 36.112*0 0.1*781 35.90155 0.15B72

0,*50 36.*9835 0.15189 36.32741 0.16223 36.28*67 0.16*82 36.07103 0.17772 35.85741 0.19059

0.500 36.*62l5 0.1778* 36.28893 0.18981 36.2*563 0.19?80 36.02916 0.20771 35.81273 0.22256

0.550 36,*2560 0.20376 36.25007 0.21737 36.20619 0.22077 35.98685 0.23771 35.76758 0*25459

0.600 36.38869 0.22962 36.21083 0.2**88 36,16638 0.2*668 35.9**1* 0.26767 35.72198 0*28657

0.650 36.35139 0.25539 36.17U9 0.27229 36.12615 0.27650 35« 9 0099 0.29753 35.67593 0*318*7

0.700 36.31357 0.28102 36.13101 0.29957 36.08538 0.30*20 35.857 2

8 0.32727 35.629 2

9 0«3502*

0.750 36.27*95 0.30651 36.09002 0«3267o 36.0*379 0.33173 35* 8 1275 0.35685 35.56l8 2 0.38185

0.800 36.23508 0.33182 36.04777 0.3536* 36.00096 0.35908 35.76695 0.3862* 35.53307 0**1326

0.850 36.19331 0.35692 36.00363 0.38037 35.95622 0.38622 35.7l9 2 5 0.*l5*0 35.48242 0.*****

0,900 36.1*878 0.38180 35,95672 0,40687 35.90872 0.41312 35,66880 0.***30 35.42901 0,47535

0.950 36*.10039 0.*06*3 35,90597 0.43309 35.85738 0,*3975 35,61*51 0,*7293 35.37179 0.50595

1.000 36.0*687 0.43077 35.85010 0.*59o3 35.80092 0,*6607 35.55512 0.5 123 35,30948 0.53622

1.100 35.91837 0.*7851 35.71698 0.50988 35.66664 0.51771 35.4l5 8 0.55674 35.16369 0.59561

1.200 35.7*9!5 0.52*80 35.54330 0.55920 35.49185 0.56778 35.23472 0,6i059 34.97776 0*65322

1-300 35.52051 0.569*1 35.31042 0.6o673 35.25792 0.61604 3*. 99552 0.66249 34.73330 0*7o875

l.*00 35.20665 0.61212 34.99269 0- 6 5223 34.93922 0.66225 3*. 67198 0.7!2i9 34.40494 0*76193

1.500 3*. 77572 0.65271 34.55838 0.69549 34.50406 0.70617 3*. 23259 0.759*3 33.96133 0.81249

Page 124
TABLE 13 (CONTINUED)

0»0800 X * 0.0900 0-1000 0*1 100 X » 0«i200

T -H HE -H HE -H HE -H HE -H HE

(Kl <J/MOLF> (J/MOLE) (J/MOLE) <J/MOLE) (J/MOLE) U/MOLE) < J/MOLE) (J/MoLE) (J/MOLE) 'J/MOLE) 0.000 35.975f>4 -0.03984 35.58178 -0.03718 35,18774 -0.03374 34.79368 .0.02968 34.39792 .0.02512

0.001 0.002

0.003

0.00*

35.975()4

35.975(12 35.975nl 35.97498

-0.03984

-0.03983

-0.03981 -0.03980

35.58177 35.58176

35.58174

35.58171

-0.03717

-0.03717 -0.03715

-0.03713

35.18773

35.18772

35.18770

35.18767

-0.03374 -0.03373

-0.03371 -0.03369

34.793n7

34.79306 34,79304

34.79301

-0.02967 -0.02967 -0.029*5

.0.02963

34,39792

34,39790 34.39788 34.39785

.0

.0.

.0! .0

02512

02511 02510 02508

0.006 35.97490 -0.03974 35.58164 -0.03708 35.18759 -0.03364 34.79292 -0.0?957 34.39777 .0 02502

0.008

0.010 0.012

0.01*

35.97480 35.974*7

35.97450

35.97431

-0.03966 -0.03957

-0.03944

-0.03930

35.58153

35.58139

35.58121

35.58101

-0.03700 -0.03690

-0.03677

-0.03663

35.18748 35.18733

35.18715 35.18694

-0.03356

-0.03346

-0.03333

-0.03318

34.79281 34.792*5 34.79247

34.792?5

-0.02949

-0.02939

-0.0?926 -0.029H

34.39764

34.39749

34.39729

34.397o7

.0-0

-0-0

02494 02483

02471 02456

0.016 35.974n9 -0.03914 35,58078 -0.03646 35.18670 -0.03301 34.79200 -0,02894 34.39681 .0 02439

0.018

0.020 0.025

0.030

35.97383 35.97355 35.97272

35.97170

-0.03895

-0.03874 -0.03812

-0.03736

35.58051 35.58022

35.57934

35.57828

-0.03627 -0.03605

-0.03542

-0.03464

35,18642

35.18611 35.18520

35.18410

-0.03282 -0.03260

-0.03195

-0.03116

34,79171 34.79139

34.79045

34.789J9

-0.0?874

-0.0?852

.0,02787

-0.027o7

34.39651 34.39618

34.39520

34,39401

.0

.0.0

.0

02418 023V6

02330 02249

0.035 35.97051 -0.03646 35.57703 -0.03372 35.18279 -0.03023 34.78794 -0.02612 34.39260 -0 02152

0.0*0 0.045

0.050

0.060

35.969H

35.96760

35.96590 35.96202

-0.03543 -0.03426

-0.03297

-0.03003

35.57559

35.57398

35.57218 35.56809

-0.03267 -0.03147

-0.03014

-0.02709

35.18129

35.17960 35.17772

35.17343

-0.02915 -0.02793

-0.02656

-0.02344

34.78638

34.784*?

34.782*6 34.778iB

-0.02502

-0.0?378

-0.02239 -0.0l9i9

34.39098

34.3891b

34.38713 34.38248

-0

-0

.0

.0

02041 01915

01774

01449

0.070 35.95756 -0.02663 35.56336 -0.02357 35,16845 -0.01980 34.77298 -0.0l546 34.377 6 .0 01067

0.0&0

0.090

0.100 0.120

35.95256 35.947H

35.94123 35.928*4

-0.02284

-0.01870 -0.01425

-0.00462

35.55804

35.55221 35.54590 35.53209

-0.01960 -9.01525 -0.01055

-0.00030

35.16284

35,15666

35.14995

35,13519

-0.01568 -0.01115

-0.00623

0.00458

34.767 9 34,76059

34.75351 34.73787

-0.01122

_O.Oo 6 52 -O.OoUl

0.00988

34.37092 34.364H

34.35669

34,34021

.0

.0. 00633

00150 00378

01552

0.1*0 35.91451 0.00579 35.51696 0.01088 3b. 11893 0.01644 34.72054 0,02237 34.32188 02857

0.160

0.180

0.200

0.250

35.899*9

35.884)7

35.868 8 35.82602

35.78208

0.01680 0.02826

0.04010

0.07094 0.10308

35.50078

35.48376

35.4661JT 35.41961 35.37088

0.02277

0» 03523 0.04814 0.08198

0.11745

35.10147 35.08303

35.06380 35.01309

34,95969

0.02914

0.04252 0.05644

0.09313

0.13181

34.70186

34.682 6 34.66135

34.60653

0.03582

0.05004

0.0*492

0.10432 O.U608

34.30203

34.28093

34.25880

34.20001 34.13762

04270 05772

07349

11547

0.300 34.54858 16021 0.350 0.400

0.450

0.500

35.73687 35.69072

35.64385

35.59637

0.13608

0.16960

0.20341 0.23738

35.32060

35.26918

35.21688

35.16387

0.15401 0.19125

0.22889

0.26676

34,90444

34,84784

34.79020 34.73172

0.17182

0.21269

0.25409 0.29578

34.48846

34.42677 34.36386

34.29997

0.18946

0.23387

0,27894

0.32441

34.07273

34.00602

33.93791 33.86869

20685 25472

30339 35257

0.550 35.54838 0.27139 35.11025 0.30472 34.67254 0.33764 34.23529 0.37010 33.79855 40204

0.600

0.650 0.700

0.750

35.49992 35.45097

35.40142

35.35101

0.30538

0.33930 0.37309 0.40672

35.05609 35.00140

34.94605

34.88981

0.34270

0.3806?

0.41843 0.45607

34.61274

34.55233

34.49123

34,42920

0.37955

0.42143

0.46320

0.50482

34.16989

34.10383

34.037ol 33.96923

0.4i589

0.4*167

0.5 738 0.55293

33.72762

33.65594

33.58345

33.50995

45165

50131 55090

.60035 0.800 35.29933 0.44015 34.83227 0.49350 34,36584 0.54622 33.9000? 0.59827 33,43505 ,64959 0.850

0.900

0.950

1.000

35.24573

35.18938 35.12922

35.06400

0.47333 0.50624

0.53883

0.57106

34.77281 34.71060

34.64460 34.57357

0.53067

0.56754 0.60407

0.64020

34.30055

34,23250

34,16068

34.08387

0.58735

0.62816

0.66859

0.70861

33.82899

33.75514

33.67753 33.59496

0.64332

0.68804

0.73236 0,77622

33.35819

33.27857

33.19520 33.10689

.69854

.74713

.79531 .84300 1.100 34.91247 0.63430 34.41059 0.71113 33.90950 0.78717 33.*0924 0.86237 32.90986 93670

1.200 1.300

1.400

1.500

34.72100

34.47128

34.13810

33.69028

0.69566

0.75482 0.8H47

0.86534

34.20805 33.94785

33.60506

33.14884

0.77996 O.84634

0.90992

0.97038

33.69593 33.42529

33,07291 32.60833

0.86343 0.93699

1.00747

1.07449

33.18468

32.90363

3?. 54171 32.06878

0,94603

1.0?674

1.10*08 1,17764

32.6743b

32.38292

32.01148 31.53024

1

1

11

.02771 -11554 19971 .27977

Page 125
TABLE 13 (CONTINUED)

X 1300 X o 1400 X 1500 X >l6oO X 0< l800

T -H HE -H HE -H HE -H HE -H HE

<K> <J/MOLE> (J/MOLE* ( J/MOLE' <J/MOLE) < J/MOLE) < J/MOLE) t J/MOLE

>

(J/MoLE) 'J/MOLE' (J/MOLE) 0.300 33.72687 0.17413 33.31638 0.18779 32.90622 0.20111 32.496*2 0,21408 31.67814 0.23869

0.350 33.65730 0.22394 33.24222 0.24067 32.82756 0.25698 32.J1334 0.27286 31.58645 0.30307

0.400 33.58565 0.27519 33.16572 0.29524 32.74627 0.31479 32.32734 0,33382 31.49124 0.37014

0.450 33.512*2 0.32740 33.08743 0.35091 32.66299 0.37386 32.23912 0.39&24 31.39332 0.43905

0.500 33.43792 0.38021 33.00771 0.*073l 32.57811 0.43378 32.14914 0.45963 31.29330 0.50923

0.550 33.36238 0.43341 32.92683 0.*6417 32.49193 0.49427 32.05772 0.53368 31.19154 0*58027

0.600 33.28596 0.48681 32.84495 0.52130 32.40466 0.55509 31.96509 0.58815 31.08833 0.65190

0.650 33.20871 0.54026 32.76218 0.57856 32.31640 0.61608 31. 871 3 8 0.65284 30.98385 0.72386

0.700 33.13058 0.59373 32.67846 0.63581 32.22712 0.67711 31.776*9 0.7i760 30.87812 0.79599

0.750 33.05140 0.64704 32.59363 0.69295 32.13668 0.73804 31.68057 0.78230 30.77104 0.86810

0.800 32.97079 0.70014 32.50733 0.74989 32.04473 0.79879 31.58299 0.84681 30.66231 0.94008

0.850 32.88818 0.75296 32.41902 0.80654 31.95073 0.85924 31.48334 0.9U04 30.55144 1.01178

0.900 32.8028? 0.80540 32.32793 0.86281 31.85395 0.91931 31.38090 0,97488 30.43773 1.08308

0.950 32.71371 0.85741 32.23311 0.91863 31.75344 0.97890 31.27473 1.03823 30.32031 1.15388

1.000 32.61969 0.90891 32.13340 0.97391 31.64807 1.03794 31.16372 1.10101 30.19808 1.22406

1.100 32.41139 1.01011 31.91388 1.08256 31.41738 1.15402 30.92188 1.2?446 29.93408 1.36214

1*200 32.16498 1.10843 31.65660 1.18816 31.14925 1.26686 30*64296 1.34451 29.63367 1.49650

1.300 31.86321 1.20334 31.34452 1.29012 30.82690 1.37583 30.31036 1.46047 39.28067 1.62633

1«*00 31.48228 1.29431 30.95413 1.38787 30.42708 1.48032 29.9 li4 1.57166 28.85274 1.75087

1.500 30.99275 1.38086 30.45634 1.48086 29.92106 1.57974 29.38691 1.67749 28.32218 1.86942

TABLE 13 (CONTINUED)

X • 2000 X .2250 X 2500 X '?750 X .3OOO

T -H HE -H HE -H HE -H HE -H HE

IK) <J/MOLE> (J/MOLE) (J/MOLE) <J/MOLE> (J/MOLE) (J/MOLE) <J/M0LE> (J/MoLE) (J/MOLE* (J/MOLE) 0.300 30.86192 0.26125 29.84509 0.28600 28.83270 0.30630 27.825*0 0.32152 26.82380 0.33103

0.350 30.76190 0.33094 29.73502 0.36195 28.71296 0.38815 27.69633 0,*o893 26.68572 0*42368

0.400 30.65773 0.40385 29.62000 0.*4185 28,587*2 0.47469 27.56056 0.5ol60 26.54004 0.52260

0.450 30.55037 0.47903 29.50113 0.52455 28,*5736 0.56461 27.419*0 0,5986* 26.388*2 0.62610

0.500 30.44049 0.55579 29.37921 0.60926 28,32369 0.65698 27.274*6 0.698*1 26.2320* 0.73302

0.550 30.32858 0.63364 29.25485 0.69539 28.18712 0.75113 27.12592 0,8o03* 26.07178 0.64249

0.600 30.21496 0.71225 29.12844 0.78251 28.0*815 0.84653 26.97460 0.9 382 25.90829 0.95385

0.650 30.09986 0.7913S 29.00025 0.87031 27.90710 0.94283 26. fl 2088 1.0o6*0 25.7*210 1.06655

0.700 29.98333 0.87069 28.87042 0.95851 27.76*15 1.03968 26.66500 1.11,372 25.573*6 1M8017

0.750 29.86531 0.95011 28.73890 1.04688 27.61931 1.13682 26.5o7ol 1.2l9*7 25.402*7 1.29436

0.800 29.74554 1.02942 28.60548 1.13521 27.*72*1 1.23401 26.34678 1.32537 25.22906 1.40881

0.850 29.62356 1.10849 28.46974 1.22334 27.32307 1.33105 26.18399 1.+3H7 25.05295 1.52324

0.900 29.49870 1.18716 28.33107 1.31109 27.17072 1.42773 26. 0l6]0 1.53665 2*. 87366 1.63740 0.950 29.37011 1.26531 28.18865 1.39830 27.01460 1.52388 25.648*1 1.6*161 24.69051 1.75105

1.000 29,23675 1.34281 28.04149 1.48484 26.85377 1.61933 25.674o? 1.7*585 24.50267 1.86397

1.100 28.95075 1.49537 27.72820 1.65529 26.51340 1.80745 25.30679 1.95143 24.10878 2.08680

1.200 28,62897 1.64390 27.37991 1.82134 26.13880 1.99083 24.9o6o6 2.15195 23.68210 2.30428

1*300 28.25571 1.78747 2 6. 98i47 1.9819* 25.7i5 3 6 2.16828 2*. 45778 2.346o8 ?3.209 l6 2*5l493 1.400 27.8o9i7 1.92525 26.51182 2.13611 25.22276 2.33868 23.9*238 2.5 3 257 22.67110 2.71736

1.500 27.26237 2.05643 25.9*485 2.2829* 24.63577 2.SQ102 23.33551 2.7i027 22.04447 2*91030

Page 126
TABLE 14 THE VAPOR PRESSURE OF HE3

P (TORR)

HE* SOLUTION*

T \

(K) 0.300 0.320

0.340

0.360

0.360

0.400

0.420 0.440

0.460

0.460 0.500

0.520

0.540 0.560

0.560

0.600

0.620 0.640

0.660

0.680

0.700 0.720

0.740

0.760

0.780

0.800 0.820

0.8*0

0.860

.880 0.900

0.920

0.940

0.960

0.980

1.000

1.050

1.100 1.150

1.200 1.300

1.400

1.500

0.0001

2.102-006

3.962-006

6,961.006

1,153-005

1.817-005 2.7*6-005

*. 067-005 5.680-005

7.865-005

1.070-00*

l.*37-00* 1.916-00* 2.550-00*

3.*o3-00* .569-00*

6.182-00*

8.*3*-00*

1.159-003

1.599-003 2«211-003

3.05*-003 .205-003

5.759-003

7.832-003

1.057-002 I.*l3-O02

1.873-002 2.*59-oo2

3.199-002

*• 125-002 5.271-002

6.677-002

8.390-002

1.0*6-001

1.29*-00l

1.589-001 2.579-001

*• 028-001 6.081-001

8.9o7-001

1.768*000 3.220*000

5.468.000

0.0002

204-006 923-006

3«2.005

304-005 630-005

482-005 968-005

129-00* 555-00*

098-00* 783-00* 6*5.00*

73*.00*

120.00* 903.00*

022-003 328-003

733-003 27*-003

998-003

96*-003

250.003 951-003

183-003 209-002

58*-002

063-002

671-002

*3*-002

383-002

554-002 988-002

729-002

083-001 33*-001

632-001

631-001

089-001

153-001 990-001 779*000

234*000 485*000

0.0005

1.051-005 1.980-005 3,478.005

5,756-005

9,068-005

1.369-004

1.992-004 2.810-004

3.860-004 5.180-004

6.818-004

8,829.004

1,128.003 1.426.003

1,789.003 2.233-003

2.779-003 3.454-003

4,297-003

5. 356-003

6,691-003

8.381.003

1.052-002 1,323-002

1,665-002 2.096-002

2.635-002 3.306-002

4.136-002

5.157-002

6.404-002

7.917-002 9.742-002

1.193.001

1.453.001

1.761-001 2.786-001

4.273-001

6.367-001

9.238-001

1.811*000 3.274*000 5.534*000

0*0010

2.101-005

3.9S9-005 6,952.005

1.151-004

1,812-004 2.734-004

3.978-004 5.608-004

7.69*-00*

1.031-003

1.353-003

1.745-003 2.217.003 2.781.003

3.45l-oo3

4.247-003

5.192-003

6.317-003

7.662-003

9.277-003

1.123-002

1.359-002

1.646-002

1.997-002 2.425-002 2.9*7-002 3.585-002 .361-002

5.304-002

6.+43-002 7,816-002

9.462-002

1.143-001 1.376-001

1,652-001

1.976-001 3.044-001

4.578-001

6.724-001 9.650-001

1.865*000 3.341*000

5,616*000

0.0020

4,200-005

7.910-005

1.389.004 2,298-004 3.617.004

5.457-004

7.937-004

1.119-003 1.534-003 2.053-003

2.691-003

3,463.003

4,386.003

5.479.003

6.761-003 8.258-003

9,998-003

1.202-002 1.436-002

1.709-002 2.026-002

2.396.002 2.829.002

3.337.002 3.936.002

4.6*2-002

5.*77-002

6.*63-002

7.629-002 9.005-002

1.063-001

1.254-001 l.*78-001

1.7*1-001 2.0*7.001

2,403-001 3.557-001 5.186-001

7.435-001

1.047*000 1.971*000 3,475*000

5,779*000

0.0030

6.295.005

1.185-004 2.080.004

3.442-004 5.417-004

8.170-004

1.188-003

1.67*-003 2.29*-003

3.070-003

*. 022-003 5.173-003

6.5*5-003

8.163.003

1.005.002 1.225-002

l.*78-002 1.769-002 2.103-002

2.485-002 2.924-002 3.*27-002

*. 005-002

*. 671-002 5,*39-002

6.328-002

7.358-002

8.553-002

9.9*1-002

1.155-001

1.3*3-001

1.560-001

1.812-001 2.103-001

2.440-001 2.828-001 4.067-001

5.79 -001 8.142-001

1.129*000 2.077*000

3.608*000 5.942*000

0.00*0

8.366-005

1.579.004 2.770.004

4, 582.004 7.209-004

1.087-003

1. 581-003 2.227-003

3.052-003

4.082-003

5.347-003 6.874-003

8.*92.0o3

1.083. Oo2 1.333-002

1.622-0Q2

1.953-002 2.333-002

2.76S-002

3.256-002

3.817-002 4,*52-0p2

5.l74-o 2 5.996.002 6.934.002

8.004-002

9.228-002

1.063-001

1.224-001

1.409-001 1.621-001

1.864-001 2.144.001

2,*6*-00l

2.831-001

3.251-001 .575-001

6.392-001

8.846-001

1.210*000 2.183*000

3.741*000

6,104*000

0.0050

047-004 97j-004

457-004 717-004 995-004

356-003 972-003

777-003

805-003

o9o-003 665-003

566-003

083-002 349-002

659-002

016-002 26-002

894-002 25-002

026-002 705-002 72-002

337-002

315-002 20-002

671-002

109-001 270*001 53-001

66J-001

897-001

I67-OOI 74-001

823-001

220-001 671-001

O80-OOI

99„- 01 545-001

2 9 1*000 288*000

873*000

265*000

0.0060

1.255-004

2.362-00* 4,143-004 6.849.00^

1.077-003

1.62^-003 2.361-003

3.325-003 .555-003

6.092-003

7.976-003

1.025.002

1.295-002

1,613-002 1.983-002 2.409-002

2.897-002

3.451-002 4.080-002 .789-002

5.588-002

6.466-002

7.494-002 8.626.002 9.898-002

1.133-001

1.294-001

1.475-001 1.680-001 1.911-001 2.172-001

2.468-001 2.802-001

3.180-001

3.607-001 4.089-001

5.583-001

7.585-001

1.024*000

1.372*000 2.393*000

4.005*000 6.426*000

0,0080

,670-004 140-004

,505-004

,099-004 ,431-003 156-003

134-003 413-003

044-003

082-003

,056-002 ,359-002 717-002

137-002

,626-002 188-002 830-002

558-002 380-002

305-00?

340-002 497-002

res-002

123-001 283-001

,462-001

,661-001 .883-001 131-001

,408-001

,718-001 ,065-001

,453-001

,887-001

,374-001 ,919-001 579-001

766-001 162*000 532*000

,601*000

,266*000 M7*000

Page 127
TABLE 1* (CONTINUED)

P (TORB)

T \

(K) 0.300 0.320

0.3*0

0.360

0.380

o.*oo

0.420 0.**0

0.460

0.480 0,300

0.520

0.540

0.560

0.58o

0.600

0.620

0.640

0.660 0.680

0.700

0.720

0.740 0.760

0.780

0.800

0.820

0.840 0.860

0.880

0.900

0.920 0.940

0.960

0.980

1.000

1.050

1.100

1.150

1.200

1.300 1.400

1.500

0.0100

2.082-00*

3.913-00*

6. 858.Q0*

1.133-003

1.781.003 2.684-003 3.900-003 5.490-003

7.518-003

1.005-002 1.315-002

1.690-002 2.13*-002

2.656-002

3.261-002

3.958-002 .752-002

5*653-002

6.666-002

7.803-002 9.073-002

1.0*9-001

1.206.001

1.380-001

1.573-001 1.787-001 2.02*-001 2.286-001

2.577-001

2.900-001

3.258-001

3.656-001 .097-001

.588-001

5.133-001 5.739-001

7.566-001 9.935-001

1.299*000 1.690*000

0.0150

3.100-004 5.819.00*

1.019.003

1.682.003 2.6*3.003

3.98o-003 5.780-003

8.135-003

l.ll*-002

1. 89-002

1.9+8-002 2.501-002

3.158-002

3.928-002 .821-002

5.8*7-002

7.016-002 8-337-002

9.821-002

1.1*8-001 1.332-001

1.537-001

1.762.001 2.011-001

2. 28*. 001 2.585-001

2.91*-001

3.276-001

3*672-001 4.107-001

*. 583-001 5.105-001

5.679.001

A. 308. 001 6.998.001

7.755-001

9.990-001 1.281*000

1.635*000 2.079*000

2.8o7*000 3.31**OO0

*. 526*000 5.165*000

7.06**000 7.8*8*000

0.0200

*. 096-00* 7.682-00*

1.3**-003 2.218-003

3.483-003 5,2*3-003

7.612-003

1.071-002

1. 466-002

1.959-002 2.562-002

3.289.002

*, 153-002 5,165-002

6,338-002

7.685-002

9.217-002

1.095-001

1.289-001

1.505-001

1.7*6-001 2.011-001

2,30*-001 2.625-001

2.977-001

3.362-001 3.782-001

*. 2*0-001 .739-001

5.282-001

5. 87^-001 6.519-001

7.220-001

7.98^-00l

8,816-001

9.721-001

1.235*000

1.561*000

1.96**000 2.460*000 3.810*000 5.791*000

8.618*000

0.0250

5.069-00*

9.*99-00*

1.661.003 2,739-003

*. 2*9-003 6,*7l-oo3

9.392-003

1.321-002

1.808-002 2.*l6-002

3,l6o-002

*. 0*6-002 5.120-002

6.367-002 7,812-002

9,*7l-002

1.136-001

1.3*9-001

1.587-001

1.853-001 2.1*8-001

2,*73-001

2.831-001

3.223-001

3.65l-ool

*. 118-001

*. 626-001 5.l78-ool

5.778-001

6. 28-001

7.133-001 7.896-001

8.723-001

9.619-001

1.059*000 1.16**000

1.466*000 1.835*000 2.285*000

2.832*000 .295*000

6. 04*000

9.373*000

0.0300

6.015-00*

1.126-003 1,969.003

3,245-003

5,093.003

7.662-003

1.112-002

1.564-002 2.140-002

2.839-002

3.739-002 4.800-002

6,059-002

7.535-002

9.245-002

1.121-001

1.344-001

1.595-001

1.877-001 2.191-001

2.539-001

2.923-001

3.344-001

3.805-001 .307-001

.855-001

5. 9-001

6.093-001

6.790-001

7,5^5-001

8.360-001

9. 2^0-001 1.019*000

1.121*000

1.232*000 1.351*000

1.692*000 2.103*000

2.599*000

3,196*000

.771*000

7.006*000

1.011*001

0.0350

6.933-004

1.298.003 2,267.003

3.736.003 5,861.003

8.817-003

1.279-002

1.799-002 2.462-002

3.289-002

*. 302-002 5.522-002 6.970.002

8,668-002

1.063-001

1.289-001 1.5*6-001

1.835-001 2*159-001

2.520-001

2.920-001 3.360-001

3.8*3-001 .371-001

,9^6-001

5.572-001

6.250-001

6.984-001

7.777-001

8.633-001

9.556-001

1.055*000

1.162*000

1.277*000

1. 01*000

1.53+*000

1.912*000 2.365*000

2.906*000

3.552*000

0.0400

7.822-004

1.463-003 2.366.003 .211-003

6,605-003

9.935-003

1.442-002

2.02 7 -002 2.774-002

3.706-002 .8*7-002

6.222-002

7. 85*. 2 9.767.002

1.198.001

1.453-001

1.742-001 2-068-001

2.433-001

2.8*0-001

3.290-001

3.785.001

*. 328-001

*. 922-001

5. 568-00I 6.270-001

7.030-001

7.852-001 8.739-001 9.69*-001

1.072*000

1. 183,000 1.302*000

1. 429*000

1.366*000

1.712*000 2.127*000

2.620*000

3.206*000 3.900*000

0.0*50

682-00*

624-003

835-003

669-003

324-003

102-002 598-002

2*7-002

075-002

109-002 374-002 899-002

710-002

083-001

329-001 611-001

932-001

294-001 699-001

l5o-001 6*9-001

198-001 8O0-OOI

*58-001

173-001 950-001

79 -001 698-001

676-001 073*000

186*000 307*000

*3fl*000 577*000

727*000

887*000

337*000 870*000

500*000

2*2*000 5.237*000 5.693*000 6 7.596*000 8.175*000 8

1 .084*001 1.156*001 1

0.0500

9.5l0-00^

1.778-003 3,104-003 5.112-003

8,017-003

1.206-002

1.750-002 2.^60-002

3.367-002 .99-002

5.885-002

7.555-002 9,538-002

1,186-001

1. 56-001

1.765-001 2.117-001

2.513-001

2.957-001

3. 51-001

3.998-001 .600-001

3.259.001

5.979-001

6.762-001

7.612-001 8.530-001

9.521-001

1.059*000 i.m*ooo

1.297*000

1,^29*000

1.570*000

1.722*000

1 .884*000 2.057*000

2.543*000 3.115*000

3.787*000 .576*000

1*0*000 6.578*000 7 7*3*000 9.300*000 9 226*001 1.295*001 1

0.0530

031-003 927-003

363-003 538-003

685-003

306-002 895-002

666-002

6*8-002

875-002 378-002

189-002

03*-001 286-001

579-001 9l*-001 296-001

726-001 208-001

?**-001 337-001

990-001

'05-001 86-001

335-001 255-001

250-001

032*000

148*000 272*000 05*000

5*7*000

700*000 863*000

037*000

223*000

7*3*000 354*000

068*000 902*000

008*000 846*000

362*001

Page 128
TABLE 14 (CONTINUED)

P (TORB)

T \

(K) 0.300 0.320

0.3*0

0,360

0,380

0.400 0.420

0.440 0.460

0.480

0.S00

0.S20

0.540

0.560

0.580

0.600

0.620

0.640

0.660

0.680 0.700

0.720 0.740

0.760

0.780 0.800

0.820 0.840

0.860

0.880

0.900 0.920

0.940

0.960

0.980

1.000

1.050

1.100 1.150

1.200

1.300

1.400 1.500

0.0600

107-003 069.003

611-003 9*8.003

328-003 03-002

036-002

864-002 920-002

238-002

854-002

802-002

112-001

383-001 697-001

058-001 469-001

932-001 51-001

028-001

666-001

369-001

139-001 979-001

892-001 882-001

951-001

110*000 234*000

367*000 510*000

663*000

826*000

001*000

187*000 385*000

939*000

587*000

343*000 222*000 29*000

038*001 29*001

0.06*0

1.166-003 2.179.003

3.803.003

6.264=003

9.824-003

1. 78-002

2.145-002

3.017-002 .130-002

5.520-002

7.223-002

9.277-002

1.172-001

1. SB.001 1.790-001 2.170-001

2.604-001

3.092-001

3.640-001 4.249-001 4.923-001

5.664-001

6. 76.001

7.363.001

8.326.001

9.370-001 1.050*000

1.171*000 1.302*000

1.442*000 1.593*000

1 .753*000 1.925*000 2.108*000 2.304*000 2.512*000

3.093*000

3.771*000

4.559*000 5.474*000

7.760*000

1.080*001

1.481.001

0.0650

1.181-003 2,206-003

3,850-003

6,341.003

9,946-003

1,496-002 2.171-002

3.054-002

4.181-002

5.589-002 7.314-002

9.393-002

1,186-001

1.476.001

1.812-001 2.198-001

2.637-001

3.132-001

3.686-001 4.303-001 4.986-001

5.737-001

6,560-001

7,457.001

8,433.001 9.491-001

1.063*000 1.186*000

1.319*000

1.461*000 1.613*000

1.776*000

1.949*000 2.135*000

2.333*000 2.543*000

3.131*000 3.816*000

4.612*000 5.536*000

7.842*000

1.091*001

1.494.001

0.0700

1.251-003 2.337-003 4,0*9-003

6,718-003

1,054-002

1.586-002 2.301-002 3.238-002

4.433-002 5.926-002

7.757-002

9,964-002

1.259-001

1.566-001

1.923-001 2.333-001

2.799-001

3.325-001

3.914-001 4.570-001

5.295-001 6.094-001

6.968-001

7.922-001 8,959-001

1.008*000

1.130*000 1.260*000

1.401*000 1.551*000

1.713*000

1.885*000 2.069*000 2.266*000

2.475*000 2.698*000

3.318*000

4.039*000

4.875*000

5.842*000

8.246*000

1.142*001

1,558*001

0.0750

1.318-003 2.462-003

4.298.003

7,080-003

1.111-002 1.671-002 2.426-002

3.414-002

4.675-002

6.251-002

8,183-002

1.051-001

1.328-001

1.654.001 2.031-001

2.464-001

2.956-001

3.512-001 4.135-001

4.829-001

5.596-001

6.440-001

7,365-001

8,374.001

9,471.001

1.066*000

1.194*000

1.332*000

1.481*000

1.640*000 1.810*000

1.992*000 2.187*000

2.394*000

2.614*000 2.848*000

3.501*000 4.257*000

5.133*000

6.142*000

8,642*000

1.193*001

1.621*001

0.0800

1.382-003 2.582-003 4.507.003

7.425.003

1.165-002

1.753-002 2.546-002

3.583-002 4.908-002

6.564-002

8.594-002

1.104-001

1.396-001

1.738-001 2.134-001

2.590-001

3.108-001

3.693-001

4.349-001 5.079-001

5. 887-001 6.776-001

7.750-001 8,812.001

9.967.001

1.122*000

1.257*000

1.402*000

1.558*000 1.726*000

1.905*000 2.096*000

2.301*000

2.518*000

2.749*000

2.995*000

3.679*000 4.471*000

5.384*000

6.436*000 9.031*000

1.243*001

1.683*001

0.0900

1.500.003 2.804.003

4,896.003

8,069.003

1.267.002

1.907-002 2.770-002

3.901-002

5.346-002

7 M52-002 9.369.002

1.205-001

1.523-001 1.897.001 2.331-001

2.829-001 3.397-001

4.038-001

4.756-001

5.556-001 6.442-001

7.417.001 8.485-001 9.650-001

1.092.000

1.229*000 1.377*000

1.536*000

1.708*000

1.891*000 2.087*000

2.297*000

2.520*000

2.758*000

3.010*000 3.279*000

4,023*000

4.882*000 5.871*000

7.005*000 9.784*000

1.339*001

1.804*001

O.lOOO

606-003

003-003 247-003

652.003

359-002

047-002 975-002

l«2-002 747-002

693-002

008-001 297-001

64o-001

044-001 513-001

052-001 666-001

359-001

137-001 003-001 962-001

018-001

175-001 044*000

l8i*000 33o*000 90*000

663*000

849*000

047*000 260*000

487*000

728*000 9B5*000

258*000 548*000

35i*000 275*000

336*000 549*000

051*001 432*001

92o*001

0.1100

1.700-003 3.182-003 5,561.003

9.176.003

1.442.002 2.174-002

3.161-002 .57-002

6.114-002

8.189-002

1.074-001

1.382.001

1.749-001 2.180-001

2.682-001

3.258-001 3.915-001

4.658-001

5.491-001

6.419-001 7.448-001

8.581-001

9.822-001 1.118*000

1.265*000

1.425*000

1.597*000

1.782*000

1.982*000 2.195*000

2.423*000

2.666*000 2.925*000

3.201*000

3.494*000 3.804*000

4.663*000 5.650*000

6.780*000 8.069*000

1.120*001

1.521*001 2.031*001

0.1200

,783-003

,339-003 ,841-003

,644-003 ,517-002

,288-002

,329-002

,696-002

,447-002 .640*002 134-001

,460-001

,848-001

,306-001

,837-001 4*9-001

147-001 935-001

821-001

807-001

,901-001 106-001 043*000

187*000 344*000

,514*000

,697*000

,895*000 107*000

,334*000

,577*000

,836*000 112*000

,405*000 717*000

,047*000

,959*000 ,007*000

,204*000 ,566*000

,186*001 ,607*001

,139*001

Page 129
TABLE 14 (CONTINUED)

P (TORR)

0.1300 0.1400 0.1500 0.1600 o.ieoo 0.2000 ft.225n

(K)T \

0.300 1.855-003 1.917-003 1.969-003 2.0H-003 2.072-003 2.102-003 2.103.003

0.320 3.477-003 3.596-003 3,697-003 3.781-003 3.904-003 3.972-003 3.990-003

0.340 6.087-003 6.301-003 6.484-003 6.640-003 6.871-003 7,008-003 7.067-003

0.360 1.006-002 1 .042-002 1.073-002 1. 100-002 1.141-002 1.167-002 1.180-002

0.380 1.583-002 1.642-002 1.693-002 1.736-002 1.805-002 1.850-002 1.877-002

0.400 2.390-002 2.480-002 2.559-002 2.628-002 2.737-002 2.811-002 2.860-002

0.420 3.480-002 1.615-002 3.733-002 3.837-002 4.003-002 4.120-002 4.204-002

0.440 4.913-002 5.106-002 5.278-002 5.429-002 5.674-002 5.850-002 5.985-002

0.460 6.748-002 7.0l 9 -002 7.260-002 7.475-002 7.825-002 8.082-002 8.288-002

0.480 9.050-002 9.419-002 9.751-002 1.005-001 1.053-001 1.090-001 1.120-001

0.500 1.1B8-001 1.237-001 1.282-001 1.322-001 1.388-001 1,438-001 1,481-001

0.520 1.531-001 1 .595-001 1,654-001 1.706-001 1.794-001 1.862-001 1.922-001

0.540 1.940-001 2.023-001 2.098.001 2.166-001 2.281.001 2.371.001 2,451.001

0.560 2.421-001 2.526-001 2.621-001 2,708-001 2.856-001 2.972-001 3.078.001

0.580 2.980-001 3.112-001 3.231-001 3.340-001 3.527-001 3.675-001 3.813.001

0.600 3.625-001 3.786-001 3.934-001 4.069-001 4.301-001 4.488-001 4.«64_ool

0.620 4.3*0-001 4.557-001 4.737-001 4.902-001 5.188-001 5.420-001 5.641-001

0.640 5«l92-00l 5.429-001 5.647-001 5.846-001 6.194-001 6.478-001 6.753-001

0.660 6.126-001 6.409-001 6.669-001 6.908-001 7.327-001 7.671-001 8. 008-001

0.680 7.168-001 7.502-001 7.810-001 8.094-001 8.593-001 9.007-001 9.414-001

0.700 8.323-001 8.714-001 9,077-001 9.411-001 1.000*000 1.049.000 1.098.000

0.720 9.596-001 1 .005*000 1,047.000 1.0 8 6*000 1.156*000 1.214*000 1.272.000

0.740 1.099.000 ] .152*000 1.201.000 1.246.000 1.326.000 1.394.000 1.463.000

0.760 1.252*000 1.312*000 1,368.000 1.421*000 1.513.000 1.592.000 1.672.000

0.780 1.418*000 1 .487.000 1.551*000 1.610*000 1.717.000 1.808.000 1.901.000

0.800 1.597*000 1.676*000 1.749*000 1.817*000 1.938*000 2.042*000 2.150*000

0.820 1.791*000 1 .880*000 1.962*000 2.039*000 2.177*000 2.296*000 2.419*000

0.840 2.000*000 2.100*000 2.192*000 2.279*000 2.435*000 2.570*000 2.710*000

0.860 2.225*000 2.336.000 2.440*000 2.537*000 2.712*000 2.864*000 3.023*000

0.880 2.4*5*000 2.589*000 2.704*000 2.813*000 3.009*000 3.179*000 3.358*000

0.900 2.722*000 2.859*000 2.968*000 3.108*000 3.327*000 3.517*000 3.718*000

0.920 2.996*000 3.147*000 3.290*000 3,423*000 3.666*000 3.878*000 4.102*000

0.940 3.288.000 3,455.000 3,611*000 3,759.000 4,027*000 4.262.000 4.512.000

0.960 3.598*000 3.781.000 3.953*000 4.115*000 4.411.000 4.670*000 4.947.000

0.980 3.928*000 4.127.000 4,316*000 4.494*000 4,818.000 5.104*000 5.409.000

1.000 4.277*000 4.494*000 4.700*000 4,894*000 5,249*000 5.563*000 5.899.000

1.050 5.241*000 5.508*000 5.761*000 6.000*000 6.440*000 6.830*000 7.252*000

1.100 6.346*000 6.669*000 6.975*000 7.266*000 7.801*000 8.278*000 8.798.000

1.150 7.608*000 7.992*000 8.358*000 8.705*000 9.347*000 9.923*000 1.055*001

1.200 9.040*000 9.493*000 9.924*000 1.033*001 1.110*001 1.178*001 1.253*001

1.300 1.250*001 1.311*001 1,369*001 1.424*001 1.528*001 1.621*001 1,725*001

1 .400 1 .689*001 1 .768*001 1.844*001 1.916*001 2.051*001 2.175*001 2.313*001

1.500 2.242*001 2.342.001 2.437*001 2.529.001 2.701*001 2.858*001 3.035.001

0.2500

072-003 949-003

020-003

177-002 877-002

87 -002 ?30-002

038-002

3«2-002

136-001 505-001

957-001

501.001

1*6-001 904-001

784-0OI

795-001 948-001

25i-o01 7U-001

135*000 315*000 515*000

734*000

973*000 234*000

516*000

821*000

150*000 503*000

882*000

286*000 717*000

176*000 664*000

l8o*000 60r*00O

246*000

109*001 318*001

816*001 434*001

192*001

0.2750

2.016-003

3.859-003 6.889-003

1.159-002 1.856-002 2.846-002

4.208-002

6.024-002

8.384-002

1.139-001

1.513-001 1.971-001 2,524.001

3.182-001 3.955.001 4.855-001

5.891-001

7.073-001

8.412-001

9.918-001

1.160*000

1.347*000

1,553*000 1.780*000 2.027*000

2.298*000 2.591*000

2.908*000

3.250*000

3.617*000 4.011*000

4.433*000 4,882*000

5,361*000

5,870*000

6,410*000

7.902*000

9.609*000

1.155*001 1.374*001

1.894*001 2.539*001

3.329.001

0.3000

941-003

733-003 693-003

131-002 817-002

796-002

146-002 953-002

309-002

131-001 506-001

967-001

524.001

189.001 971-001

883-001

936-001

138-001 503-001 004*000

176*000 367*000 578*000

811*000

065*000 343*000

645*000

972*000

324*000

703*000 111*000 546*000

011*000 507*000

034*000 594*000

141*000 913*000

193*001 420*001

960*001

630*001 448*001
TABLE 15 THE H£3 CONCENTRATION IN THE VAPOR ABOVE HE3 - HE* SOLUTIONS

XV

O.OOOl 0.0002 0.0005 0.0010 0.0020 0.0030 0.0040 0.005o 0.0060 0.0080

T(K) 0.3Q0

0.320

0.340 0.360

0.380

1 0000 9999 9998

9995

9987

1 .0000

1 .0000 0.9999 0.9997

0.9993

1.0000

1.0000 1.0000 0,9999

0,9997

1.0000

1.0000 1.0000 0,9999

0.9999

1

11

1

0000

0000 0000

0000 9999

1.0000

1.0000

1.0000 1.0000

1.0000

1.0000

1 .0000

1 .0000 1.0000

1.0000

1.0000

1,0000 1.0O00

1.0000

1.0O00

1

1T

1

1

0000

0000 0000

0000 0000

1.0000

1.0000

1.0000

1,0000

1.0000

0.400

0.420

0.440 0.460

0-480

9970 9938

9879 9779

9620

0.9985 0.9969 0.9939

0.9888 0.98o6

0.9994 0.9988 0.9976

0.9955

0. Q9 21

0.9997 0.9994

0.9988 0.9977

U.9960

9998

9997 9994

9989

9980

0,9999

0.9998 0.9996

0.9992

0.9987

0.9999

0.9998

0.9997

0.9994

0.999

0.9999

0.9999

0.9997

0.9995

0.9995

9999

9999

9998

9996

9993

1.0000 0.9999

0.9998

0.9997

0.9995

0.500

0.520

0.540 0.560

0.580

9377

9032

8570 7988

7300

0.9678

0.9491 0.9230

O.8881 0.8439

0.9869

0.9790 0.9677

0.9520

0.9310

0.9934

0.9894

0.9835 0.9753

0.9642

9967

9946

,9917 9875

,9817

0.9978

0,9964

0,9944

0.9916

0.9877

0.9983

0.9973

0.9958 0.9936

0.9907

0.9986

0.9978

0.9966 0.9949

0,992*

9989

9982

9972

9957

.9937

0.9991 0,9986 0.9979

0,9968

0.9953

0.600

0.620

0.640

0«660

0«680

6538 5744

4961 4225

3561

0.7906

0.7296

0.6631 0.5940

0.5251

0.9041 0.8708

0-8310

0.7851 0.7342

0.9496

U.9308

0.9 75 0.8795

0.8465

,9740

.9641 9514

.9357 -9167

0.9825

0.9757 0.9669

0.9560

0.9427

0.9868 0.9816

0.9749

0.9666

0.9563

0.9893 0.96s 2 0.9798

0.9730

0.9646

.9911 9876

98 3 .9773

.9702

0.9932

0.9906

0.9871 0.9828 0.9774

0.70O

0.720

0.740

0.760

0.780

2981 2486

2071

1727

1443

0.4593

0.3982

0.3431 0.2944 0.2522

0.6796

0.6230

0.5661 0.5104

0.4572

0.8090 0.7675

0.7227

0.6755

0.6272

.8942

.8681 .8386

.8060

.7705

0.9267 0.9078

0.8860

0.8614

0.8340

0.9438

0.9290 0.9118

0.8921 0.8698

0.«544

0.9423

0.928o 0.9115

0.8928

.9616 .9513

.9391 .9250 .9088

0.9708 0.9628

0.9534

0.9424

0.9297

0.800

0.820 0.840

0.860

0.880

1210

,1019 0863

0?34

0&27

0.2159

0.1850 0.158B

0.1367 O.H80

0.4075

0.3618 0.3205

0.2834

0.2566

0.5787

0.5311

0.4851 0.4414

0.4005

.7327 .6933

,6528

.6120 ,5714

0.8040 0.7718

0.7378

0.7024 0.6662

0.8*51 0.8181 0.7892

0.7585

0.7264

0.87lg

0,84«7

0.8236

0.7966

0.7681

.8906 ,8704

,8482

.8243

,7986

0.9153

0,8991 0.8812

0.8616

0.8404

0.900 0.920

0.9*0

0-960

0.980

0539

0466 0404

0353

0309

0.1023

0.089 0.0777

O.O681 0.0600

0.2216

0.1962

0.17 3

9 0«l545 0.1375

0.3626

0.3278

0.2961 0.2675

0.2416

,5317

.4932 .4564

•4216

,3888

0.6295

0.5930

0.5570

0.5218 0.4878

0.6934

0.6597

0.6259

0.59 2? 0.5590

0.7383

0.7075

0.676i 0.6444

0.6127

.7716

.7434

.7143

.6846 .6546

0.8177

0.7937 0.7686

0.7425

0.7157

1.000 1.050

1.100

1.150 1.200

.0272 0202

.0154

.0119 .0095

0.0530 0.0396

0.0303

0.0236 0.0188

0.1227

0.0934 0.0723

0.0570 0.0456

0.21B5

0.1708

0.1348 0.1077

0.0871

.3582 .2914

.2373

.1943

.1601

0.4553

0.3811 0.3179

0.2653 0.2222

0.5266 0.4505

0.3829

0,3247 0.2756

0.5813

0.5057 0,4365

0.3751 0.322

,6245

.5507 .4813

,4184

,3627

0.6864

0.6196

0.5523

0.4889 0.4308

1.300

1.400

l'5oO

.0063 >0044 0032

0.0124

0.0087

0.0064

0.03o5

0.0215

0.01S9

0.0592

0.0421 0.0312

.1117

• 0808

• 0606

0.1586

0.1164

0.0881

0.2006

0.1493

0.1140

0.2386 0.1798

O.1385

,2730

• 2081

• 161&

0.3332

0.2591 0.2042

Page 131
TABLE 15 (CONTINUED)

XV

O.OlOO

T \

(K)

.3oO

,320

,340

,360

,380

.400 420 440

.460 480 500

520

540

560

580

.600

'620 640

6*0

680

,7pO

720

,740

,760

,780

,8oO

.820

.840 860

.880 900

920

940

960

980

000

050

100

150 200

300

400

500

0.0150 0.0200 0.0250 0t0300 0.0350 0.0*00 0.045o 0.05oO 0.0550

0000

0000

0000 oooo

0000 oooo 9999

9999

9998

9996

9993

9989

9983

9974

9962

9945

9924

9896

9861

9817

9763

9699

9622

9531

9427

9308

9173

9023

8857

8676

8481

8273

8053

7822

7582

7335

6699

6059

5438

4855

3840

3038

2425

1.0000

1,0000

1.0000

1.0000

1,0000

1.0000

1.0000

0.9999

0.9998

0.9997

0.9995

0.9992

0.9988

0,9982

0.9974

0.9963

0.9948

0.9929

0.9905

0.9875

0.9839

0.9794

0.9741

0.9679

0,9606

0.9522

0.9427

0.9319

0.9200

0.9068

0.8924

0.8768

0.8600

0.8422

0,8234

0,8o37

0.7513

0.6960

0.6398

0.5845

0.4818

0.3944

0.3236

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9999

0.9998

0.9996

0.9994

0,9991

0.9986

0.9980

0.9972

0.9961

0.9946

0.9928

0.9905

0.9877

0.9843

0.98o2

0.9754

0.9698

0.9633

0.9559

0.9475

0.9381

0.9277

0.9163

0.9038

0,89o3

0,8758

0,86o3

0.8440

0.7998

0.7519

0.70l7

0.6508

0.5522

0.4636

0.3884

1,0000

1.0000

1.0000

1,0000

1,0000

1.0000

1.0000

0.9999

0.9999

0.9998

0.9997

0,9995

0,9993

0,9989

0,9984

0.9977

0.9968

0.9956

0.9941

0.9923

0.9900

0.9872

0.9839

0,9800

0,9754

0.9701

0.9640

0.9571

0.9494

0.9408

0.9312

0.9208

0.9095

0.8973

0.8842

0.8702

O.8321

0.7899

0.7449

0.6983

0.6052

0.5182

0,4416

OOOO

OOOO

OOOO

OOOO

OOOO

OOOO

OOOO

OOOO 9999

9998

9997

9996

9994

9991

9986

9980

9973

9963

9950

9934

9915

9892

9864

9830

9791

9746

9695

9636

9570

9496

9415

9325

9227

9122

9008

8886

8550

8175

7768

7341

6466

5623

4859

1.0000

1.0000

1.0000

1,0000

1,0000

1.0000

1.0000

1.0000

0.9999

0.9999

0.9998

0.9996

0.9995

0.9992

0.9988

0.9983

0.9976

0.9968

0.9957.

0.9943

0,9926

0.9906

0.9881

0.9852

0.9819

0,9779

0.9734

0.9683

0.9625

0.9561

0.9489

0.9411

0,9325

0.9231

0.9130

0.9022

0.8722

0.8384

0.8013

0.7619

0,6798

0.5987

0.5234

1.0000

1,0000

1,0000

1,0000

1,0000

1.0000

1.0000

1.0000

0.9999

0.9999

0.9998

0.9997

0.9995

0.9993

0.9989

0.9985

0.9979

0.9971

0.9961

0.9949

0.9934

0.9916

0.9895

0.9869

0.9839

0.9804

0.9764

0.9719

0.9667

0.9610

0.9546

0.9476

0,9399

0.9315

0.9224

0.9127

0.8856

0.8548

0.8207

0.7843

0.7070

0.6292

0.5556

l.OOOo

1,0000

l.OOOo

l.ooOo

1.0000

1.0000

1.0000

I.OOqO

0.9999

0.9999

0.999 8 0.9997

0.9996

0,9993

0,9990

0.9986

0.998!

0.9974

0.9965

0.9954

0.994]

0.9924

0,9905

0,988 2 0.9855

0.9823

0.9787

0.9746

0.970

0.964 8 0.959

0.952,

0,9457

0.9^81

0.9299 0.9210

0.896 3 0.8680

0.8365

0.8025 0,7298

0.6552

0.5835

OOOO

OOOO OOOO

OOOO

OOOO

OOOO

oooo

oooo 9999

9999

9998

9997

9996

9994

9991

9987

9982

9976

9968

9958

9946

9931

9913

9892

9868

9839

9806

9769

9726

9679

9626

9568

950*

9435

9359

9278

9050

8788

8496

8178

7491

6776

6080

1.0000

1.0000

1.0000

1.0000

1,0000

1.0000

1.0000

1.0000

0.9999

0.9999

0.9998

0.9998

0,9996

0.9994

0.9992

0.9988

0.9984

0.9978

0.9971

0.9961

0.9950

0.9936

0.9920

0,9901

0,9878

0.9852

0.9821

0.9787

0.9748

0.9704

0.9656

0.9602

0,9543

0,9479

0.9409

0.9334

0.9123

0.8879

0.8605

0.8307

0.7656

0.6971

0.6295

Page 132
TABLE 15 (CONTINUED)

XV

T \

<K)

.300

,320

,340

,360

,380

400

420

440

460

480

500

520

540

560

580

600

620

640

660 680

700

720

740

760

780

,800

820

840

>860

.880 900

920

940

960

980

000

050

100

150 200

,300

,400

,500

0.0600 0.0640 0.0650 0.0700 0.0750 0,0800 0.0900 0.1000 O.lloO 0.1200

0000

0000

0000 oooo

0000

0000

0000 oooo 9999

9999

9999

9998

9996

9995

9992

9989

9985

9979

9973

9964

9954

9941

9926

9908

9887

9862

9834

9802

9766

9726

9681

9631

9576

9516

9451

9381

9184

8956

8699

84i»

7800

7143

6487

1.0000

1.0000

1.0000

1.0000

1,0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9999

0,9998

0.9997

0.9995

0.9993

0.9990

0.9986

0.998i

0.9974

0.9966

0.9956

0.9944

0,9930

0.9913

0.9893

0.9870

0.9843

0.9813

0.9779

0.9740

0.9698

0.9650

0.9599

0.9542

0.9481

0.9414

0.9227

0.9ol0

0.8765

0.8496

0.7901

0.7266

0.6626

1.0000

1,0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9999

0.9998

0.9997

0.9995

0.9993

0.9990

0.9986

0«9981

0.9974

0.9966

0.9957

0.9945

0.9930

0.9914

0.9894

0,9871

0.9845

0.98i5

0.9781

0.9744

0.9702

0.9655

0.9604

0.9548

0,9487

0.9422

0.9237

0*9022

0.8780

0«85i4

0.7925

0.7295

0.6659

1.0000

1,0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9999

0.9998

0.9997

0.9995

0.9993

0.9990

0.9987

0.9982

0.9976

0.9968

0.9959

0.9948

0.9935

0,9919

0,9900

0,9879

0.9854

0.9826

0.9795

0.9759

0.9720

0.9676

0.9628

0.9575

0.9518

0.9457

0.9282

0.9o80

0.8851

0.8598

0.8036

0.7430

0.6813

OOOO

OOOO

OOOO

OOOO

OOOO OOOO

OOOO

OOOO OOOO 9999

9999

9998

9997

9996

9994

9991

9987

9983

9977

9970

9961

9951

9938

9923

9906

9886

9862

9836

9806

9773

9735

9694

9649

9599

9545

9487

9322

9130

8913

8672

8135

7551

6953

1.0000

1.0000

1.0000

1.0000

1,0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9999

0.9998

0.9997

0,9996

0,9994

0.9991

0.9988

0.9984

0.9978

0.9971

0,9963

0.9953

0.9941

0,9927

0.9911

0.9891

0.9869

0.9844

0.9816

0.9784

0.9749

0.9710

0.9667

0.9620

0.9569

0.9514

0.9357

0.9175

0.8968

0»8738

0.8224

0.7661

0.7081

1.0000

1.0000

1.0000

1.0000

1,0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9999

0,9998

0.9997

0.9996

0.9994

0.9992

0.9989

0.9985

0.9980

0.9974

0.9966

0.9957

0.994ft 0.9933

0.9918

0.9901

0.9881

0.9858

0.9833

0.9804

0.9772

0.9737

0,9698

0.9655

0.9609

0.9558

0.9416

0.9250

0.9061

0.8850

0.8375

0.7851

0.7304

l.OOOo

1,0000

l.OOOo

1,0000

l.OOOo

1.0000

1.0000

l.OOOo

1.0000

0.9999

0.9999

0.9998

0.9998

0.999*

0.99^5

0.9992

0.9990

0.9986

0.9981

0.9976

0.9969

0.9960

0.9950

0.9939

0,992 5 0,9909

0.98*0

0.9870

0.9fl4 6 0.9820

0.979

0.9758

0.9722

O.9683

0.9641

0.9594

0.9464

0.931i

0.9137

0.894g

0.850}

0.8 l0 0.7492

OOOO OOOO

OOOO

OOOO 0000

oooo oooo

oooo oooo 9999

9999

9998

9998

9997

9995

9993

9990

9987

9983

9977

9971

9963

995*

9943

9930

9915

9898

9879

985?

9833

9805

9775

9742

9706

9667

9624

9503

9362

9200

9 l9 8607

8144

7655

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.9999

0.9999

0.9999

0.9998

0.9997

0.9995

0.9993

0.9991

0.9988

0.9984

0.9979

0.9972

0.9965

0.9956

0.9946

0.9934

0.9920

0.9904

0.9886

0.9866

0.9843

0.9818

0.9790

0.9759

0.9725

0.9689

0.9649

0.9536

0.9404

0.9253

0.9083

0.8697

0.8261

0.7795

Page 133
TABLE 15 (CONTINUED)

XV

0.1300 0.1400 0.1500 0.1600 0.1600 0.2000 0.2250 0.2500 Q.2750 0.3000

T \

(K)

0.3o0 1 .0000 1.0000

1 ,0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1,0000

1,0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1,0000

1,0000

l.OOOp

1,0000

1,0000

l.OOoo

1,0000

1.0000

1.0000

1 .0000

1 .0000

1.0000

1.0000

0.370

0.340

0.3*0

0.3AO

1 .0000

1 .0000

1 .0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.400 1 .0000 1.0000 1.0000 1,0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.4?0

0.440

0.4*0

i.oooo

1 .0000

1 .0000

0.9999

1.0000

1.0000

1.0000

0.9999

1.0000

1.0000

1.0000

0.9999

1.0000

1.0000

1.0000

0.9999

l.QOOO

1.0000

1.0000

0.9999

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0O00

1.0000

i.ooo

l»OOQ0

1.0000

1.0000

0.9999

1.0000

1.0000

1.0000

0.4P0 1.0000 0.9999

0.500

0.5?0

0.540

0,560 o.sno

0.9999

0.9999

0.9998

0.9997

0,9995

0*9994

0.9999

0.9999

0.999ft 0.9997

0,9996

0.9994

0.9999

0,9999

0,9998

0,9997

0,9996

0,9994

0.9999

0.9999

0.9998

0.9997

0.9996

0,9994

0.9999

0.9999

0.9998

0.9997

0.9996

0.9995

0.9999

0,9999

0,9998

0.9997

0.9996

0.9995

0.9999

0.9999

0.999ft 0.9997

0,9996

0.999s

0,9999

0.9999

0.9998

o!9vy 7 0.9996

0.9995

0.9999

0.9999

0.9998

0.9997

0.9996

0.9999

0.9999

0,9998

0,9997

0,9996

0.600 0*9995 0.9995

0*6?0

0«640

0*660

0.6*0

0.9991

0-9988

0.9984

0.9980

0.999?

0.9989

0.9985

0.998]

0.9992

0.9989

0.99fi6 0.9981

0.9992

0.9989

0.9986

0.9982

0.9993

0«9990

0.9987

0.9983

0.999?

0.9990

0.9987

0.9984

0.9993

0.9991

0.998ft 0.998s

0.9993

0.999j

0.9988

0.998 5

0*9993

0«999l

.9989

0.9986

0.9993

0.999J

0.9989

0.9986

0.700 0.9974 0.9975 0.9976 0.9977 0.9978 0.9979 0.9980 0,9981 0.9982 0.9982

0.720

0.740

0.760

0.7A0

0*9967

0.9959

0.9949

0.9938

0.9968

0.9961

0.9951

0.9941

0.9970

0.9962

0.9954

0.9943

0.9971

0,9964

0.9955

0.9946

0.9973

0.9966

0.9958

0.9949

0.9974

0.9968

0.9961

0.9952

0.9976

0.9970

0.9963

0.9955

0.9977

0.9971

0.9965

0.9957

0*9977

0.9972

0.9966

0.9959

0.9978

0.9973

0.9967

0.9960

O.SQO 0.9925 0.992ft 0.9932 0.9934 0.9939 0,9943 0.9946 0.9949 0.9951 0.9953

0.8?0

0.840

0.860

0.880

C9910

0«9893

0.9874

0.9852

0.9914

0.989A

0.9880

0.9860

0.9918

0.99 3 0.9886

0.9867

0.9922

0.9907

0.9891

0.9873

0.9927

0.9914

0.9899

0*9882

0.9932

0.9919

0.9905

0.9890

0.9936

0.992*,

0.9912

0.9897

0.9939

0.9929

0.991 7 0.9903

0.9942

0*9932

0.9921

0«9908

0.9944

0.9935

0.9924

0.9912

0.900 0.9829 0.9838 0.9845 0.9852 0.9864 0.9873 0.9882 0,9889 0.9894 0.9899

0.920

0.940

0.960

0,980

0.98o2

0.9773

0.9742

0.9707

0.9813

0.9786

0.9756

0.9723

0.9822

0.9796

0.9768

0.9737

0.9830

0.9805

0.9778

0,9749

0.9843

0.9821

0.9796

0.9769

0.9854

0,9833

0.9810

0,9786

0.9864

0.984S

0.9824

0,9802

0.987 2 0.9855

0.9«3 5 0,9814

0.9879

0.9862

0.9844

0.9825

0.9885

0,9869

0.9852

0,9834

1.000 0.9670 0.9688 0.9704 0,9718 0.9741 0.9759 0.9777 0.979 2 0.9804 0.9814

i*o=.o I'lOO

1*150

1-200

0«9564

0«9440

0«9298

0*9139

0.9588

0.9*72

0.9338

0.9187

0.96o9

0.9499

0.9372

0.9229

0.9628

0.9523

0.9402

0.9267

0.9659

0.9563

0*9453

0*9329

0.9684

0.9595

0.9494

0.9380

0.9708

0.9628

0.9536

0.943 ?

0.9728

0.96&4

0.9569

0.9474

0.9745

0.9676

0*9597

0-9509

0.9758

0.9694

0.9620

0.9538

1.300 0.8774 0.8842 0.89o2 0.8955 0.9044 0.9118 0.9193 0.9254 0.9305 0.9349

1.400

1.500

0.8361

0.7918

0.8450

0.8027

0.8528

0.8124

0.8598

0.8211

0.8718

0.8361

0.8816

0.8485

0.8917

0.8614

0.900o

0.8721

0.9070

0.8811

0.9130

0.8889

Page 134
Table 16. The Enthalpy and Entropy of He Along the Solubility

Curve and the Heat Absorption Rate of the Dilution Refrigerator

T X

l H„ (X,

3

v I T) S

3 (Xr

T) H

3 (Xv

T) - H3 °(T) (T /T.) m i Q=0

(°K) (j/mole He 3

) (J/°K mole He ) (J/mole He

3

) T = Tm

0.000 0. 064000 0.0 0. 0. 0.001 0.064000 9.451 x 10" 5

0. 10716

-5

8. 188 x 10 0.365

0.002 0. 064002 3.781 x 10" 40. 2143 3. 277 x 10" 4 0.364

0.004 0.064007 1. 513 x 10" 3 0.4286 1. 312 x 10" 3

0. 361

0.006 0. 064016 3.404 x 10" 3

0. 6427 2.954x 10" 3

0. 359

0.008 0. 064029 6. 050 x 10" 30. 8567 5.254x 10" 0. 357

0.010 0. 064045 9.452 x 10" 31. 0705 8.214x 10" 3

0. 355

0.015 0. 06410 0.02125 1. 604 0.01850 0. 349

0.020 0. 06418 0. 03772 2. 134 0. 03288 0. 345

0. 025 0. 06429 0.05881 2. 660 0. 05132 0. 339

0.030 0. 06443 0. 08443 3. 182 0. 07377 0. 334

0.03 5 0. 06459 0.11448 3.697 0. 10012 0. 329

0.040 0. 06480 0. 14884 4.206 0. 13028 0. 325

0.045 0.06503 0. 1873 4.705 0. 1641 0. 320

0.050 0. 06530 0.2298 5. 195 0. 2014 0.316

0.060 0. 06596 0.3257 6. 141 0. 2857 0. 306

0.070 0. 06680 0.4347 7. 032 0.3813 0. 298

0.080 0. 06784 0. 5549 7.867 0.4865 0. 289

0.090 0. 06906 0. 6844 8. 643 0. 5995 0. 281

0. 10 0. 07042 0.8213 9.362 0.7186 0.274

0. 12 0. 07361 1. 1122 10. 643 0.9699 0. 262

0. 14 0. 07731 1.4190 11. 739 1.2328 0. 255

0. 16 0. 08157 1.736 12. 670 1.502 0. 250

0. 18 0. 08628 2. 058 13.468 1.774 0. 247

0. 20 0. 09144 2.383 14. 154 2. 046 0. 245

0.25 0. 10618 3.195 15.49 2.718 0. 245

0.30 0. 12363 3.988 16.43 3. 364 0. 252

0.35 0. 14373 4.749 17. 10 3.975 0. 260

0.40 0. 1665 5.471 17. 59 4. 541 0. 271 0.45 0. 1918 6. 150 17. 96 5. 061 0.283

0. 50 0. 2201 6.732 18.22 5.478 0. 297

0. 55 0. 2527 7.338 18. 39 5.916 0. 311

0.60 0.2908 7.810 18.46 6. 216 0. 326

Page 135
TABLE 17 THE HE3 CONCENTRATION. SPECIFIC HEAT. AND ENTROPY AT CONSTANT u

T = 0.000 DEGREES

T X c,

4 S

3 (K) U/MOIE-K) (J/MOLE-K) 0.000 0.06400 0.0000 0.0000

0.001 0*06400 0.1072 0.1072

0.002 0.06399 0.2144 0.2143

0.003 0.06398 0.3217 0.3215 0.00* 0.06396 0.4290 0.4288 0.006 0.06391 0.6443 0*6434

0.008 0.06383 0.8604 0.8583

0.010 0.06374 1.0777 1.0737

0.012 0.06362 1.2964 1.2894 0.014 0.06349 1.5168 1.5058

0.016 0.06333 1.7391 1.7228 0.018 0.06316 1.9637 1.9406

0.020 0.06296 2.1907 2.1592

0.025 0.06238 2.7704 2.7100

0.030 0.06169 3.3693 3.2677

0.035 0.06088 3.9888 3.8333

0.0*0 0.05997 4.6282 4.4074

0.045 0.05896 5.2846 4.9903

0.050 0.05786 5.9564 5.5816

0.060 0.05547 7.3202 6.7879

0.070 0.05289 8.6727 8.0182

0.080 0.05022 9.9790 9.2623

0.090 0.04755 11.2077 10.5096

0.100 0.04494 12.3295 11.7500

0.120 0.04009 14.1442 14.1746

0.140 0.03585 15.6269 16.4861 0.160 0.03182 16.4656 18.7486

0.180 0.02908 17.5207 20.7065

0.200 0.02654 18.1627 22.5819

0.250 0.02155 19.2703 26.7752

0.300 0*01806 19.7727 30.3369

0.350 0.01551 20.1378 33.4078

0.400 0.01356 20.3670 36.1131

0.450 0.01203 20.5341 38.5205

0.500 0.01079 20.7311 40.6925

0.550 0.00977 20.9525 42.6780

0.600 0.00890 21.1960 44.5111

0.650 0.00815 21.4933 46.2188

0.700 0.00749 21.8847 47.8254

0.750 0.00690 22.4606 49.3538

0*800 0.00635 23.3202 50.8299

0.850 0.00583 24.7028 52.2826

0.900 0.00531 26.8309 53.7531

0.950 0.00478 29.7390 55.2922

1.000 0.00421 33.7787 56.9838

1.100 0.00283 70.4503 61.4275

1.200 0.00098 173.8501 71.4579

1.300 0.00000

1.400 0.00000

1.500 0,00000

0.010 DE6REES 0.020 DEGREES

M» 4 (J/MOLE-K) (J/MOLE-K)

^4

(J/MOLE-K) (J/MOLE-K)

0.06404 1.0745 1.0705 0.06393 1.2925 1.2856 0.06379 1.5122 1.5013 0.06364 1.7339 1.7177 0.06346 1.9578 1.9348 0.06326 2.1842 2.1528 0.06269 2.7621 2.7019 0.06199 3.3593 3.2580 0.06118 3.9770 3.8219 0.06026 4.6146 4.3943 0.05925 5.2693 4.9755 0.05815 5.9395 5.5651 0.05575 7.3009 6.7681 0.05316 8.6518 7.9953 0.05048 9.9571 9.2365

0.04780 11.1858 10.4812 0.04518 12.3082 11.7193

0.04031 14.1265 14.1403 0.03605 16.2838 16.4491 0.03200 16.5749 18.7085 0.02924 17.2729 20.6659

0.02669 18.1539 22.5403

0.02167 19.2629 26.7319

0.01817 19.7703 30.2925 0.01560 20.1326 33.3632 0.01364 20.3647 36.0677 0.01210 20.5319 38.4749

0.01085 20.7267 40.6466

0.00982 20,9480 42.6317

0.00895 21.1917 44.4643

0.00819 21.4842 46.1716

0.00753 21.8781 47.7774

0.00694 22.4507 49.3054

0.00639 23.3033 50.7806

0.00587 24.677B 52.2321 0.00535 26.7920 53.7007

0.00481 30.1574 55.2370 0.00424 33.3057 56.9242

0.00286 69.3165 61.3469

o.ooioo 167.7101 71.0943

0.00000

0.00000 0.00000

0.06418 2 .1645 2.1337

0.06360 2 .7375 2.6779 0.06290 3 • 3294 3.2290 0.06208 3 .9418 3.7880 0.06116 4 .5742 4.3553 0.06014 5 .2240 4.9314

0.05903 5 8895 5.5161 0.05660 7 .2435 6.7092

0.05399 8 .5892 7.9272

0.05128 9 .8921 9.1598

J. 04856 11 .1205 10.3968

0.04591 12 .2446 11.6281 0.04098 14 .0840 14.0380 0.03665 16 -1448 16.3389 0.03259 16 .5830 18,5794 0.02974 17 .2843 20.54*9

0.02714 18 -1273 22.4163

0.02204 19 • 2403 26.6030

0.01848 19 7634 30.1600

0.01586 20 1166 33.2303

0.01387 20 3580 35.9322

0.01231 20 5265 38.3393

0.01104 20 7124 40.5100

0.00999 20 9355 42.4935

0.00910 21 1778 44.3252

0.00834 21. 4654 46.0311 0.00766 21. 8554 47.6354

0.00706 22. 4094 49.1613

0.00650 23. 2577 50.6334

0.00597 24. 6067 52.0817

0.00545 26. 6765 53.5449

0.00491 29. 9752 55.0730

0.00433 33. 1382 56.7474

0.00294 67. 6812 61.1063

0.00108 161. 3305 70.5365

0.00000 0.00000 0.00000

Page 136
TABLE 17 (CONTINUED)

a 0.050 DEGREES - 0.100 DEGREES 0.200 DEGREES

T X C^4

a

3 X C^4 °3 X H*4

°3

<K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) (J/MOLE-K) 0.050 0.06530 5.5557 5.1950 0.00000 0.0000 0.0000 0.00000 0.0000 0.0000

0.060 0.06270 6.8655 6.3235 0.00000 0.0000 0.0000 0.00000 0.0000 0.0000

0.070 0.05989 8.1771 7.4805 0.00000 0.0000 0.0000 0.00000 0.0000 0.0000

0.080 0.05696 9.4606 8.6566 0.00000 0.0000 0.0000 0.00000 0*0000 0.0000

0.090 0.05401 10.68*7 9.8424 0.00000 0.0000 0.0000 0.00000 0*0000 0.0000

0.100 0.05113 11.8185 11.0281 0.07042 10.7161 9.3624 0. 00000 0*0000 0.0000

0.120 0-04571 13.7293 13.3640 0.06307 12.6129 11.4848 0.00000 0*0000 0.0000

0.140 0.04092 15.6793 15.6114 0.05656 1*.6070 13.5676 0.00000 0*0000 0.0000

0.160 0.03653 16.3652 17.7909 0.05061 15.5667 15.6134 0.00000 0*0000 0.0000

o.iflo 0.03327 17.1204 19.7439 0.04604 16.*952 17.*878 0.00000 0*0000 0.0000

0.200 0.03037 17.9369 21.59*1 0.04201 17.3821 19.276* 0.09144 16.4768 14.1542

0.250 0.02*67 19.096* 25.74*2 0.03412 18.705* 23.3201 0. 07228 17.9647 18.0039

0.300 0.02068 19.7137 29.2804 0.02858 19.*075 26.7968 0. 05973 18*8660 21.3658

0.350 0.01776 20.023* 32.3*61 0.02453 19.8*30 29.8213 0.05086 19.4110 24.3173

0.400 0.01553 20.299* 35.0331 0.02145 20.1291 32.*896 0.04*25 19.7611 26.9326

0.450 0.01378 20.5010 37.4367 0.01903 20.3481 3*. 8720 0.03914 20*0048 29.2741

0.500 0.01236 20.6535 39.6039 0.01708 20.4712 37.0237 0.03507 20*1931 31.3911

0.550 0.01119 20.8399 41.5799 0.01548 20.6821 38.9813 (J. 03175 20*3386 33.3225

0.600 0.01020 21.0771 43.4025 0.01*12 20.8861 *0.7902 0.02898 20*4920 35.0978

O.650 0.00935 21 .3497 45.1000 0.01297 21.0600 *2.*690 0.02664 20*6195 36.7435

(1.700 0.00861 21.6978 46.69** 0.01196 21.3002 *4.0377 0.02461 20*7636 38.2765

0.750 0.00794 22.1987 *S.2076 0.01106 21.6663 45.5190 0.02285 21*0191 39.7161

0.800 0.00733 22.9486 *9.6632 0.01025 22.2308 46.9343 0.02128 21*2345 41.0815

0.850 0.00675 24.1307 51.0879 0.00950 23.0723 48.3062 0.01985 21*7372 42.3801

0.900 0.00618 25.9657 52.5170 0.00878 24.3589 49.6597 0.01854 22*3342 43.6408

0.950 0.00560 28.8207 53.9953 0.00806 26.3229 51.0274 0.01729 23*1609 44.8695

1.000 0.00498 32.1825 55.5896 0.00731 28.9821 52.4529 0.01607 24.4603 46.0892

1.100 0.00354 58.0966 59.596* 0.00565 30.5216 55.7487 0.01358 28.8125 48.6278

1.200 0.00162 123.0201 67.1211 0.00355 100.1625 60.6*64 0.01079 36.3583 51.5631

1.300 0.00000 0.00078 284.0930 75.0865 0.00742 71.5849 55.6015

1.400 0.00000 0.00000 0.00317 15Q.1686 63.4901

1.500 0.00000 0,00000 0.00000

TABLE 17 (CONTINUED)

T = 0.300 DEGREES T = 0.400 DEGREES T = 0.500 DEGREES

TIK)

X c,

4 (J/MOLE-K)

b

3 (J/MOLE-K)

X C^4

(J/MOLE-K)

S

3 (J/MOLE-K)

0.300 0*12363 19.7721 16.4293

0.350

0.400

0.450 0.500

0.10046 0.08543

0*07*56

0.06625

19.8066

19.8861 20.0199 20.1422

19.4823 22.1262

2*.*7*5

26.5893

0.16650 0.13616

0.11739

23.1794

21.6682

20.9547

17.5895 20.2286 22.4585

0.550 0.0596* 20.2486 28.5136 0.10385 20.7183 24.**o5

0.600

0.650

0.700

0*750

0.05*23

0.0*973

0.04589

0.04258

20.3453

20.4394 20.5386

20.6601

30*2792

31*9111 33.4292

34.8500

0.09340

0.08499

0.07803

0.07214

20.6270 20.5979

20.6054

20.6428

26.2377

27.8867 29.4129

30.8354

0.800 0.03968 20*8229 36.1883 0.06707 20.7156 32.1697

0.850 0.900

0.950

1.000

0.03710

0.03477

0.03261 0.03058

21.0496

21.3783

21.8696 22.5569

37.*572

38.6691 39.8373

40.9762

0.06263

0.05868

0.05512

0.0518*

20.8357

21.0216

21.3016

21.7007

33.4289

34.6247 35.7683

36.8707

1*100 0.02670 24.8215 43.2273 0.04583 23.0394 38.9969

1.200

1.300

1.400

1.500

0.02275

0.01839 0.01329

0*00707

29.2769

37.0332

48.3665

146.6084

45.5737

48.2695

51.8038

57.7753

0.04014

0.03432 0.02796

0.02064

25.5243

29.9765

38.4167 57.3025

41.1031 43.3198

45.8542

49.12*2

(J/MOLE-K) (J/MOLE-K)

0.22010 28.4688 18.2210 0.17706

0.15343 0.13675

0.12391 0.11354

0.10490 0.09753

0.09111 0.085*4

0.08032

0.07127

0.06314

0.05531 0.04725

0.038*6

24.1038

22.1874

21.5281 21.2093 21.0*32

20.9682

20*9631 21*0241 21*1636

21*3912 22*2135

23.7633

26.5004 31.3845

4Q.5955

20.7168 22.6966

24.4396

26.0209

27.4773

28.8323 30.1028

31.3024 32.4424

33.5333

35.6068

37.6018

39.6073

41.7432

44.2029

Page 137


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WASHINGTON, D.C. 20230

POSTAGE AND FEES PAID

U.S. DEPARTMENT OF COMMERCE

OFFICIAL BUSINESS