NATL INST. OF STAND & TECH

I NBSIR 75-770

NIST

PUBLICATIONS

The Equation of State for Ammonia

Lester Haar

John Gal lagher

Equation of State Section

Heat Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

Interim Report

September 1975

Prepared for

ice of Standard Reference Data

I Bureau of Standards

/ o 0

|ton

' D c 20234

/f7S

NBSIR 75-770

THE EQUATION OF STATE FOR AMMONIA

Lester Haar

John Gallagher

Equation of State Section

Heat Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

Interim Report

September 1975

This is an interim report. The final report will appear in the Journal of

Physical and Chemical Reference Data.

This report is to be superseded by a future publication which will receive

general distribution and should be cited as a reference. Please consult

the NBS Office of Technical Information and Publications to obtain the proper citation,

U.S. DEPARTMENT OF COMMERCE, Rogers C.B. Morton, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

Prepared for The Office of Standard Reference Data

National Bureau of Standards

Washington, D C 20234

The Equation of State for Ammonia

by

Lester Haar and John Gallagher

1. Introduction.

In this report, we present an outline of the basic results of an

extensive correlation of the thermodynamic properties of ammonia^. The

purpose of this report is to present an early working version of that correlation

for the convenience of those workers with an immediate need

for such results and to which they can refer in an unambiguous manner.

This report has been prepared in answer to several urgent requests for

such a version.

We present the basic equations used for the description of the

properties of ammonia and listings of computer programs from which all the

thermodynamic properties for ammonia can be calculated for the temperature range

including the triple point temperature to about 5/3 the critical temperature and for

the pressure range including the dilute gas to about 8000 bars. The

reference state for all properties is the ideal gas at zero kelvin. The

physical constants used are consistent with those recommended by Cohen and

2 3 Taylor . The mass of a mole of ammonia was taken to be 17.03026 grams .

2. The derivation of the thermodynamic surface.

In this section, we describe the results of a fit of selected P,p,T

data schematically represented in figure 1 to an analytic equation of state in

the least squares sense. A detailed discussion of the process of data selection

and of the selection of parts of the analytic equation is contained in

reference 1. The equation so obtained contains the pressure as a 44 term double

power series function of temperature and density. This equation can then be used to
reproduce all the available P,p,T experimental data as well as to produce

limited extrapolations (based on thermodynamic arguments) of the surface into

important regions where data are sparse. The range of the equation is bounded

at low temperatures by the triple point temperature (195. 48K) and the melting

curve for the liquid, and at high temperatures by the isotherm at 750K (which

is approximately 5/3 the critical temperature). The pressure range extends

to 8,000 bar. No mathematical constraints were imposed on the equation , and

only P , p

, T data were used in the least squares f it .

Following Keenan et al. the Ilelmholtz free energy function was

represented in reference 1 as the sum of two terms: the first is the

contribution from the equation of state; the second is a function of

temperature only and refers to the properties of the ideal gas. Thus the

Helmholtz free energy was expressed,

A(p,T) « A(p,T) + A°(T), (D

where A°(T) is the contribution of the ideal gas. T is the absolute

3

temperature in Kelvin and p is the density in grams per cm . A quantity

0(p,T) was defined by

A(p,T) = RT [In p + pQ (p,T)] (2)

Since P - p

2 3A/dp,

Eqs. (l)and(2) yield,

P - pRT [1 + pQ + p

2 3Q/9p] . (3)
We note that

Q (p-0) - B

2

, (3a)

where is the second virial coefficient. The form chosen for Q was

9 6

Q " 7 7 P 1

" 1 (t-t J

5 '1

, (4)

i-1 j-1

where x = , = 1.2333498 and R is the gas constant. Equation 3 for the

pressure was fitted in the least squares sense to the experimental P,p 5 T data,

The results of this fit are values for the constants a., listed in table 1.

< t <• ij

(a.. = 0 for all .. not listed in table 1). By differentiation of eq (1)

we obtain for the entropy,

S(p,T) - R[Jtn p + pQ - pt 9Q/9t] + S°(T), (5)

the internal energy,

E(p,T) -= RpTt3Q/8t + E°(T), (6)

the constant volume heat capacity,

C (p,T) - - Rpr 2

3 2 Q/8 T

2 + C °, v v

(7)
4 Table 1 i j a,. *1 1 1 2 -1j.z95oz jo/j 1

**3 -8. 121177091!) 1 A -6.9690043553 1 5 -9.73658023A9 1 6 3. A8166A2617 2 1 8.8100AA5762 2 2 -5.07895A8707 2 3 -68.261583422 2 A -74. 727156949 2 5 49.751854179 2 6 -14.487156374 3 1 -10.467902857 3 2 361.91907645 3 3 1327. 8270222 3 A 1484.2843304 3 5 -82.229122939 3 6 20.170856719 A 1 75.049574001 4 2 -2103. 9451938 A 3 -7576.1007937 A A -8334.8746422 A 5 43.998475959 A 6 -9.2773376718 5 1 -409.02964153 5 2 6212.2822515 5 3 22341.800329 5 A 23618.791735 6 1 1072.479955 6 2 -10816.10642 6 3 -38259.344112 6 A -38233.534003 7 1 -1471.4013145 7 2 11195.138723 7 3 38544.628190 " 7 A 35887.294649 8 1 1046.2341301 8 2 -6365.7466698 8 3 -21314.815310 8 A -18162.094974 9 1 -305.80081169 9 2 1532.0616045 9 3 5021.6962092 9 A 3812.3691534
the enthalpy function,

H(p,T) - RT[pQ + p

2 3Q/3p + p T 3Q/3t + 1] + E° (T) , (8)

the constant pressure heat capacity,

C

p

(p.T) - C

v

+ R. | , (8a)

where,

a - 1 + pQ + p

2 3Q/3p - p T 3Q/3 T - p

2

T 3 2 Q/3x3p ,

and

3-1+2 pQ +4 p

2 3Q/3p + p3 2 Q/3p 2

, the heat capacity for the saturated fluid ,

T (3P/3T) dPe C

S

U

P

^

(3P/3p)

T

dT * (9)

where P

g

is the vapor pressure of the liquid •

S°, E° and C^

0

are the corresponding contributions obtained from A°(T)

A°(T) - (G° - E°) - RT(1 + In A. 8180 T) , *°>> df A°<« •

E

o. Ao

(I) . T

dA°W. (10)

di

C ° - - T d

2 A°(T)/dT2

, v
where G° is an analytic representation of the results reported by Haar 5 for

the properties of the ideal gas state,

11

G - E

= a, in T a

± T

1 " 3

, (10a)

RT 1 i=2

where E is the energy for the ideal gas at 0 K. The coefficients a. are

o 1 listed in table 2.

Table 2

a

l

-3.872727

a

2

.64463724

a

3

3.2238759

*4 -.0021376925

a

5

.86890833xl0

-5

a

6

an -.24085149xl0~ 7

a

7

.36893175xl0"10

a

8a

9

-.35034664xl0"13

,2056303xl0"

16

aio

.6853420xl0

_2°

a

ll

.9939243x10"

24

The heat capacity values and the other thermodynamic functions calculated

from eq (10a) for the temperature range 100 K < T < 1000 K agree with those

tabulated in reference 5 to within the accuracy of those values.
7

Though equations (l-10a) are complete, it is necessary to introduce the

Gibbs phase conditions in order to calculate the properties for the coexisting

phases. However, it was shown by Haar and Gallagher^, that almost negligible

error results if an explicit relation is used for P^ fitted separately to the

saturated vapor pressure data of Cragoe^ for the range from the triple point

7 8

to 373K and of the mean of the data of Beattie and Lawrence and Keyes

above 373K. The equation so obtained is

loe P

= - + B + CT + DT2 + ET

•LOg

e s T

T in kelvin (IPTS68), P in atm.

- A - -3684.7798

- B = 20.428787 (10b)

- C - -.02893289

- D - 3.4798128xl0~5

- E - -9.2219845x10'

9

.

Equation (10b) and eq (3) define the coexisting phases for this report and

all properties over the temperature-pressure range of the thermodynamic

surface, subject to the low temperature boundary of the melting solid.

The thermodynamic surface is consistant with the following values for the

parameters at the triple point,

T = 195.48 K

t P = .06063 bar

tg

t = .00006382 g/c 3

, = .73374 g/c 3

P ,

and at the critical point,

T = 405.4 K

c

P = 113.04 bar

c

P c = .2350 g/c

3
7a

The relationship between the pressure and temperature of the melting

solid was calculated by means of the Clapyron equation, using the latent heat

of fusion and the specific volumes for the saturated liquid and solid.

9 For the latent heat, the value reported by Overstreet and Giauque was used; for

the specific volume for the solid at the normal melting point, the

value reported by McKelvey and Taylor"^ was used, and for the corresponding specific
8

11 volume of the liquid the value reported by Cragoe and Harper was used.

The Clapeyron equation is the relation

dp, an

where the quantities u' and u refer to the specific volumes of the liquid

and solid, respectively, and L refers to the latent heat of fusion. From

the above data, the quantity —r-—— - 4x10 ^ atm ^ ; and Eq (11) can be

integrated to yield

T = T

g exp[4xl0 5 (P - P

g )], (12)

where T and P are the triple point values. (The differences between the

s s triple point values and those of the normal melting point are negligible.)

Also, since P^ at the triple point is very small, the relationship can be

simplified to

T - 195.48 exp {AxlO-5

P (atm)}. (13)

J. Computer programs.

The properties calculated from the equations presented in this report

have been compared with the various thermodynamic measurements reported for

ammonia in the comprehensive review in reference 1. In almost all cases the

agreement is within the experimental accuracy of the data. Comparisons

of results with P,p,T data are given here in figures 2 and 3. It was

established in reference 1 that for most of the vapor phase and for the

coexisting phases, the calculated enthalpies are accurate to within 0.1%.
To facilitate the application of these results we present in Appendices

I and II computer programs with which the various properties of ammonia can

be calculated. Two such programs are included:

Computer program I in Appendix I refers only to certain

properties for the coexisting phases, including the latent

heat of vaporization, the vapor pressure of the saturated

liquid, the densities of the saturated vapor and the

saturated liquid. The dependent variable for these is

either the temperature or the corresponding pressure of

the saturated liquid.

Computer program II in Appendix II is a general program for

all the thermodynamic properties discussed in section 2 of

this report. The dependent variables are either pressure

and temperature or density and temperature.
References

10

1. L. Haar and J. Gallagher, Thermodynamic Properties for Ammonia,

Submitted for publication in the Journal of Physical ?nd Chemical Reference Data.

2. E. R. Cohen and B. N. Taylor, Fundamental Physical Constants, J. Phys

.

Chem. Ref. Data 2, No. 4, 663 (1973).

3. A. E. Cameron and E. Wickers, Report on the International Committee on

Atomic Weights (1961). J. Am. Chem. Soc. 84, 4192 (1962).

4. J. F. Keenan, F. G. Keyes, P. G. Hill, and J. G. Moore, Steam Tables ,

John Wiley and Sons, New York (1969).

5. L. Haar, Thermodynamic Properties of Ammonia as an Ideal Gas, J. Research

N.B.S. _72A, 207 (1968).

6. C.S. Cragoe, C.H. Meyers and C.S. Taylor, Vapor Pressure of Ammonia,

Sci. Pap. Bur. Stand. 16, 1 (1920).

7. J. A. Beattie and C.K. Lawrence, Some of the Thermodynamic Properties

of Ammonia, I. The Compressibility and an Equation of State for Ammonia,

J. Am. Chem. Soc. 52_, 6 (1930).

8. F.G. Keyes and D.B. Brownlee, The Vapor Pressure of Liquid Ammonia

up to the Critical Temperature. J. Am. Chem. Soc. 40_, 25 (1918).

9. R. Overstreet and W.F. Giauque , Ammonia, The Heat Capacity and Vapor

Pressure of Solid and Liquid, Heat of Vaporization, The Entropy Values

from Thermal and Spectral Data, J. Am. Chem. Soc. _59, 254, (1937).

10. E.C. McKelvey and C.S. Taylor, Composition, Purification, and Certain

Constants of Ammonia. Sci. Pap. Bur. Stands. _18, 655 (1923).

11. C.S. Cragoe and D.R. Harper, 3d, Specific Volume of Liquid Ammonia,

Sci. Pap. Bur. Stands. 17, 287 (1921).

12. C.H. Meyers and R.S. Jessup, The Specific Volume of Superheated Ammonia

Vapor, Refrig. 11, 345 (1925).
11

13. C.S. Cragoe, E.C. McKelvey, and G.F. O'Connor, Specific Volume of

Saturated Ammonia Vapor, Sci. Pap. Bur. .Stands. _18, 655 (1923).

14. J.S. Kazarnowsky , The Compressibility of Ammonia at High Temperatures

and High Pressures, Acta. Phys. Chim. U.S.S.R. 12, 513 (1940).

15. F.G. Keyes, The Pressure-Volume-Temperature Values for Ammonia to One

Thousand Atmospheres, J. Am. Chem. Soc. 5_3, 965 (1931).

16. K. Date, Studies on the P-V-T Relations of Fluids at High Pressures, I.

The Compressibility of Ammonia, Rev. of Phys. Chem. of Jap. 4_3, 1 (1973)

17. A. Kumagai and T. Toriumi, Pressure-Volume-Temperature Relationship of

Liquid Ammonia, J. of Chem. and Eng. Data _16, 293 (1971) .

18. D.S. Tsiklis, Compressibility of Ammonia Under Pressures to 10,000

Atmospheres, Acad, of Sci. U.S.S.R. 91_. 889 (1953).

19. A. Harlow and E.U. Frank, Private Communication from E.U. Frank.

20. K. Date, Studies of PVT Relations of Fluids at High Pressures, II.

Relations for Ammonia in the Neighborhood of the Critical Point and The

Critical Values for Ammonia, Rev. of Phys. Chem. Japan 43, 17 (1973).

USCOMMNHS [li:
Figure Caption

Fig. 1. P-T Schematic of the data included in this correlation. The

various polygons represent the range of the individual sets. The

numbers refer to references in this report for the sources of the

various data sets.

Figs. 2,3. Comparisons of calculated values with P,o,T data. The results are

presented as fractional differences in percent vs pressure in

atmospheres. The numbers to the left of the various plots refer to

data references in the text. Figure 2 refers to pressure deviations

for densities less than 1.5 times the critical density. Figure 3

refers to density deviations for values of density greater than 1.5

times the critical density.

10,000.

1000.

100.

P(bar)

10.0

1.0

406 T(K)

0 200 400 600

Temp. (K)

HG I

800
T— rr

20 —i

30 -1

~ » I * . »i t« —4 • w- * 1

*

100 ISO

* » «200 $86 —i

600

BM&<MLr4 (Critical region) —r—

100 200 300

Oi%^ul^ (Critical region)

105 HO , 115

i
Figure 3

too 1000 1—m 1

1500

• _

t

fj I 1 I 1000 * BOO

ft fa

200 400

1500

.- -i • »

* . *-r—

* ' • • •

1•

1 aX 1

V i *ar- — . . . 1

1

>

i 500 TOO 1500 s

5000

10000 -i—i 1 r

5000 1-

Appendix I

I.J

Listing of t Fortran program I:

Temperatures, Pressures and Densities along Saturation Curve.

A. The saturation pressure as a function of temperature and the

saturation temperature as a function of pressure; where T is

in degrees K, and p in atmospheres.

Function PS(T)

Function TS(P)

Function DPSDT(T)

B. The saturation liquid and vapor densities as a function of

3 Temperature-: (densities in gram/cm ) .

1. SUBROUTINE DS(T,DL,DG) to calculate approximate densities

from a simple polynomial to be used as initial guesses for

the subroutine DFIND which will improve upon these by an

iterative process.

2. SUBROUTINE DFIND (DOUT ,P ,DGUESS ,T ,DPDD) where P,T,DGUESS

are inputs, DOUT and DPDD (8P/8p) are outputs and which

also uses

3. Function PRES(D,T) which calculates the pressure in atmospheres

at any point D and T

SUBROUTINE QQ(Q,L,K,T ,D) which calculates "Q" or the

8 L+K

Q derivatives — at an^ P°int T and D.

3p 9t

C. SUBROUTINE HV(HH,T,DL,DG) which calculates the heat of vaporization

as a function of T and the previously calculated liquid and vapor

densities. The HV calculated here will be in dimensionless units,

and to obtain results in joules per gram multiply by .4882 T or in

BTU/lb. multiply by .210027 T (T in both cases in kelvins)

.
D. Units and conversion factors: a package of subroutines is included

which will convert Temp, in °F to K or K to °F, and P in PSIA to

3 3 3

atm. or atm. to PSIA, and densities in lb/ft to gm/c or gm/c

3

1

'

' to lb/ft .
1.3

FUNCTION P C (T)

PL--3684 i 7798/T + 20,+2 8787 + T*( - .n2 893 289+T*'( 3,4798l28r-5-T*9.2 2l984

1 ^cr-O ) ) PS=FXP(PL)

RETURN v END

FUNCTION TS(P)

0=1 . VP

T = 252. 10703 +. P* ( 5 ,66586 36+P* ( -. 12457077+P*( .OOl3 5987-P*,OOnoo5319

142))) + Q*(-i ^.37P67R+Q*( 1 .^2^1 5-Q*. 04906) ) nTr>p = i . /nPSPT ( T ) 5 PX = P ^ ( T

)

TF( ARS( l.-P/PX) .LT.l m *-5) TO ]. 0

PT= ( P-Dy ) tfnTDP

T=T+PT

00 TO * to TS=T

Q c T

11 R N

F M 0

FUNCTION OPSDT(T)

DF=-.0 289 3 28 9+3684.779 8/T/T+6.9 596256r-5*T-2.766 5 9535F.-8*T*T

r>PSOT = nF'*P s (,T)

RETURN

FNO

SURROUTTNF 0S(T>PL,D0)

OOUPLF PRECISION T,OL»nr-,

n c = . ?

0:

5

TF( T-4 n ^.4) i n ,fln,on

10 nTri ,-T/4 nt; .4

T c ( T , L T

.

1

n

^ . ) GO TO iOO

T V=DT**.^5

T2=DT**.541

T-5 = T2*T2

T4-nT^2.o^ c,^

nL = T4 + Tl^(', .i i ^ — 1 ,Ano7«T?-,Roflo?*T^)

nr. = T4-T V* ( 2 . 11 7 + 1 . ] ?«>0*T? + . ^7?5**T** ) DI_ = 0C* ( DL+1 .

)

0 g = n r * ( P

r-. + i . ) RFTURN

po 0L-nr

D^=.DC

P

r T

1 J P M no DL=0.

on = 0

.

R F T' IRN

1 On n = OT

nL=. 387 13 1 -.00096947 /Q+Q* ( 1 .15 138 7 5+Q*< -1.494 3 106+U*1.1 18 3325)

)

DG=. 08 28 86 7+. 0009 5867/Q+Q* ( -.6 0039 5 34+0* ( 1 .443 459 4

1 -0*1 . 16 7 *60R ) ) RETURN

END
1.4

SURROUT iNr DFT Nn ( ^OUT »P »n , T , nPn

)

COMMON / UQQQ / 00 »Q 1 »Q2 » 01 0 »Q20 »Q1

]

D 0 = D

I F ( T .LT.223 . 1 • A N H . n.r-T.,01 . ANO. D. LT..7) ^0=.7 3

1 = n o L=L+1

I F ( no.LF.O. ) nO=l . F-R

I F ( f) D . 0 T . . o ) p n = . o TALL QQ(QO»0»OtT»r>P)

CALL QO ( Ql. , 0» 1 9 T »0D ) CALL 00 (0? »n ,? , T ,DD)

npn=np^p (nn,Ti

T F ( npnx . LT . «; 0. ) PP^X = r^.

PP=PPFS ( OD , T

)

TF( ARS( ] ,-PP/P) .LT.l.F-^) r.O TO ?Q

X= ( P-PP ) /PPPX

OD=OD+X

I F ( L ,

L

F « ?0 ) GO TO o °0 CONTINUE'

R F T U f? N

FUNOT I ON T K ( TF

)

R ^ T I ! P N

FMn

F U N C T T 0 M P A T M ( P S I A ) P A T m = p $ I A / 1 4 . * ^ * P F T 1 1 R N

FMD

FUNCTION P r r ( n L P r r , nrn r r = n l

d r r / a ? . 4 ? R RETURN

FNH

FUNCTION DLBCF ( DCCr ) n |_ p, r f - p r, r r * a ? . 4 ? R PFTURN

FMD

FUNCTION PSTA(PATM)

P $ T A - P A T M * 1 4 . A o 6

PFTI IRN

r MD

FUNCTION T r ( T K ) TF=l . P * T K - 4 r^ . ^> 7

PFTURN

F ,M P
SURROUT!N c 00 { 0 , L , K , T

,

l ) n T M^NS t ON P ( 5 » 5 ) » 1 0 ) > TT ( 7 ) A ( 44 ) » T T ( 44 ) JJ ( 44 ) ? Al f 22 ) » A2 ( 22 ) foutVal-N^ 1" ( &1 ( 1 ) * a ( 1 ) ) , ( a? ( i

) , a ( ?i ) )

1 nATfl f t/6*1 ,6*2 » 6*3 » 6*4 *4*5 ,4*6 ,4*7 ,4*8 ,4*9/ »N/44/

^/\Ta JJ/i»2, 3 ,4,5, 6»1»2»3»4, 5 ,6,1, 2,3,4, 3,6»l»^>2» ,:+,i,6>l»2»3» /-+»l»

1 2 , 3 , 4 » 1 » 2 » 3 * 4 » 1 » 2 , 3 * 4 , 1 , 2 , 3 » 4 /

DATA P/2.>2.»3.»4.,5.»2.,4.,6.»12.,20.»3.»6.,12.»24.,6o..,4,,l2.,

1 24. ,48. » 120. ,5. ,20.*, 60. , l2o. ,240./

DATA Al /-6. 469043-56 ,-13.29562588 ,-8.121177092 ,-6.969004355 ,

] -9.736580235 . ,3.481664262 ,8.81 0044576 , -5 . 0789 56.87 1 ,-68.2615834

22 ,-74. /271569b ,49. 75165418 , -14.^6 71 5637 ,- 1 o . u 6 7 ^ri 2 86 ,361, f>19^

3765 ,1327.827022 , 1484.264330 , -d 2. 22 9 12 2 94 ,20.17085672 , 4 75.04957400 ,-2103*945194 , -7b 76 . 1 00794 ,-8334.874642 /

DATA A.2/43. 99847596 ,-9.2 7 733 7672 ,-409.0296415 ,6212.282252 , 122341.80033 ,23618.79174 ,1072.479955 ,-10816.10642 ,-38259. 3441

1

2,-38233.53 40 0 ,-1471.40.1315 ,11195.13872 ,38544.62819 ,35887.29465

3 ,1046.234130 ,-6365.756670 ,-2131^.81^31 , - 1 8 1 62 . o 949 7 ,~30 5.3008

41 17 ,1 532.061605 ,502 T.6'96209 ,^812.^6^15? /

0^0.

T P

(

L + K ) 1 ? , 1 4 , 1 p

1 ? SATURN

1A U=SO0./T

r-u— 1 .?^^ ?-4o 7 7P r;0 fF(DARS(r).LT.l.n-q.) r = l , n - 8

TT ( 1 ) = 1 . 00 IS 1=7,7

lis TT ( I ) =TT ( T-i )*C

T r ( n . |_T . 1 . F-8 ) 0=1.^-3

DD( 1

) =1

.

.no 16 T =2 » i

0

i 6 nn

(

t ) =dd ( t -i ) *r>

i fl DO 200 M=i ,N

t = T I ( M ) J=JJ

(

M )

T F ( J-L-1 ) ?oo, ?0

? ° I F ( L ) ?00 , ?4 , ?8

?4 QT = l . oo to so

? p 0 T = P ( L , L ) / ? . r-n TO 50

on jr(D -7 00,"* ?,40

^? OT=TT (

J

) <^0 TO ^ O

6.0 0T = P ( L , J-i } *TT ( J-L)

so IF(K) 2 0 "~ , A o , 7 p

6^ QT=QT*on

(

]

)

on TO 1 0 0

70 P=i

.

no 7? vsm = 1 , k' -79 D _!}-«- ( J -MM ) O T = 0 T * P * 0 D ( t - y )

1 n O Q-O+ft ( V. )*QJ

?nnroNTT MI,F

R r TU r?N

FNO
r i 0 r-J '-'V ( T , r,| , nr. )

C a LL 00 ir«': , Q,Q, T ,nL ) r ALL 00 ( 01 » ^ » l T *>!.. l TALL 00 ( 0? » i ?.n , T » 0L ) r A LL 0 0 ( S

r » ^ » n .» T » n r-

) r ALL 00 ( Si , r, , i , T » ^

)

CALL OQ ( S ? » 1 »0 » T » DO

)

HV = U* ( ^r,*5 ?-nL i; C? ) + ( SO + nr,'Sl ) ~ nL* ( UO + ^L*vj ] )

A SAtfPL^ PROGRAM To r A l r U L A T » c oR r-NSTAtVrc, Tn r b ATURa T I OiNi TF/.P^R a T.UR

IN D

c 0 p » DENSITIES iN L 5 / CU F T ANp HP AT OF VAPOR t Z aT I ON rN pTU/L? aT a r,yV="N PRrSSUR r T N PSta rO'jLn AS FOLLOWS - P'FA? i , £ S !

i f 0 p m a T ( * P t C . ^ ) D_D £ TU { P5 I } T = T S ( P ) r A l L D S ( T » X 0 L » X ^^ ) CALL nPTMO(nL,P,XPL»T.nX)

'"ALL I Nn ( nr, , p , xnr. , T , nY ) uu = wv_( T» » fS'G )*.•'*> i 30? 7* T nL = OL a ^F(n[_)

TrTF(T)

PRINT T» P5I »TT ,DL ,D^,HH

c tod

F N ^
Appendix II

Listing of Fortran Program II:

Routines for calculating at any point on the thermodynamic surface.

Subroutine FZ (T , F,DF , DDF , DTF) which calculates for a given temperature

T in deg K, the ideal gas functions for the free energy F, entropy DF,

C DDF, and internal energy DTF, all in dimensionless units.

P Functions for calculating internal energy, enthalpy, entropy,

CL and C as functions of D,T and ideal gas functions, all in

P v

'

dimensionless units.

Phase finder: SUBROUTINE PHASE (P , T , DL ,DG ,K) which will, for any

point P and T supplied, return a value of K as follows:

K=0 point is on sat. curve, guesses for DL and DG returned

K=l T<T , vapor phase, guess for DG returned, DL set = DG

K=2 T<T

c

, liquid phase, guess for DL returned, DG set = DL

K=3 T>T DG=DL , guess returned.

c K=-l error return for T < or P < 0. or for either P missing

and T > T . c for T<T , and P missing or = 0. , P will be calculated, and the

C S 3

1

appropriate densities found. Similarly, for P<P

c and T missing or = 0.,

T will be calculated,

sat
II.

2

SUPROUTl NF FZ( T F » OF , DHF > DT F

)

OOUPLF PRECISION T D

I

M FNS I ON A(

1

?)

DATA A/-3. 872727, .64463/ 24, J. ^3871; 9, -,nn21 3 76925, .ob89nbJ3F-I>.

1 - . 2 4 0 8 f> I 4 9 F - 7 , . 3 6 8 9 3 1 7 5 F - 1 0 » - • 3 !>0 3 4 6 6 4 F - 1

3"

» . 2 0 5 6 3 0 2 7 F - 16,

2 -.68 5 342E-2 0,.?9 3 9242 7E-24,0./

U = T

I F ( T.LF.l 0. ) U=10.

F = a ( 1 ) * A LOr, ( U ) + A ( ? ) /U+A ( ~

) + A ( a ) *U:+ A (

<=> ) *U*U4-A f 6 ) *U* *^ + A ( 7 ) *U*#4

1 +A ( 8 ) *U,#*'5 + A < 0 ) *U v *6+A MO) *U**7.+ A (11) *U**P

HF = A ( 1 ) * ( ALOG ( U ) +1 . ) + AO) + 2.*A(4)*U + 3 . * A ( 5 ) *'U *'U + 4.*A(6)*U

+ 5*^A,( 7 )*il**4 + 6 • *A ( ° ) *U* * r- + 7 . * a ( o ) + p

. -""A ( 1 ^ ) *M ;; --'7

? + Q ,*A ( 1 1 ) *U**8

DnF = A ( 1 ) /U + 2 .* A ( A ) +6 . * A ( 5 ) * U+ 1 2 . * A ( 6 ) *U*U4 2 0. *a f 7 j lf U**? + 3 0 ,*A ( fl ) *

1 U**4 + 42 . *.A C 9 ) *U**5 + 56.*A ( 1 0 ) *U**6 4 7 ? . * A ( 1 1 ) *U**7

DDf=-ODF^U

D F = - D F DTF = nF + F-l . RETURN

END

subROuti nf Phase ( p * t ».d.l , dg » ^

)

i F ( P ) 10,10,20

iO if(T-i°-. ) on,io,T9

17 T F ( T - A 0

r

. 5 ) 1 A , o 0 , o 0

1 4 P = P 5 ( T ) 16 CALL P 5 ( T » n L » n O ) K = 0

RETURN

20 I F ( T ) 7.2* 22 » 3,0

22 I F ( P-l 1 1 . 5^ ) 24* ?4 »"o0

? 4 I F ( P - • 0 A } 9 0 > ? 6 » ? 6

? 6 T = T S ( P ) GO TO 16

30 TF(T-4 0

r> ^?»<0>^6

3? PX-PS ( T

)

34 CALL D S ( T D L » D G

)

IF(P-PX) 36 »• 14»40

?6 DG=DG*P/PX

DL = DG

K = l RETURN

4 0 DG=DL

K = 2 RETURN

50 D = P*(..0002107-5.19F-8*P-2.289F-7^T ) -1 .2823 F-6*T

D = D + P / T/4 • 8 1

8

I E ( D • LT • 1 »F-5 ) D= .00001

PL = D

DG = DL

K = 3

RETURN

QO DL=P.

DG = 0.

K = -l

R FTURN

END
II. 3

SUPROUT T N^ THERMF ( D » T » rP , C V « F , H » S

)

COMMON //'JQQQ/ Q 0 0 » 0 Q 1 » Q 0 2 » Q 1 0 » 0 2 0 » Q 1

1

U = «500 ./T

CALL QQO(QOQ,n»0»T»D)

CALL QQQ(QO] >0»1 »T,D)

CALL QQQ(QO?»0»2»T,D)

CALL QOQ ( Q 1 0 » 1 » 0 » T » D

)

CALL QOU (Q?0»2*0,T,D)

CALL QQQ (Ql 1 » 1

1

9 T ,D

)

CALL FZ(T,FT»SIG»CPIG»FIG)

ENFR = D*U »- Q 1 0 + FIG

FNITH='FNER + 1. + D#OC)r> + D*D*QOl

FNTR = S T G + D*U*Ql 0-0*0 0 0- A LOG (4,81 R*D*T)

CV=CPIG-1 .-D*U*U*Q?0

rP= ( i , + n* ( ooo-u*ui o+n* ( ^o i-'J*oi i ) ) j **2/ ( i , + n* ( 2 . *ubo+r>* ( 4 ,*uo i + d*

1 Q02 ) ) ) +CV

RETURN

END

thp following samplf program will calculate the density and fivf thermodynamic FUNCTIONS AT A POINT (P,T) 5UPPLIFD. P SUPP^-IFD I N PAR, T I N DFG C

h F N S I T Y IN GM/CC* rP»CV»S IN JUIJL FS / Giv

i DFG r* AND iNIfRNaL ENERGY* ENTHALPY

IN JOULE S/GM.

1 READ 2 » PB AR » T

C

2 FORMAT ( 2F10.3 ,F10..6 »2F10.3 ,3F10.5 ) P'=P.RAR/] .0] ^2^

IFtP.Lr.C.) STOP

T = Tr + ?7% 1 S CALL PHASF(P»T»DL»DG»K)

I F ( K.FQ.-l ) GO TO 1 CALL DF TND ( D »P » DL , T » DX

)

GALL THFRMF( D»T »CP »CV,F»H»S

)

tP=CP*«48R?

CV=CV*. 4RR2

S = S * • 4 R R ? H=H*.4RR?*T

E=F*.4RR?*T

PRINT ?>PBAR>TC»DvH>F»S»cP»CV

GO TO ] END
NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OK REPORT NO.

NBSIR 75-770

2, Oov't Accession

No.

_**•i '»t Kpr*L mtpnf IpiLIll c Arriiccirtn M r\ -> ' 'L Lt lull 1\U,

4. TITLE AND SUBTITLE

TE) p Fnnafi nn nf St"^t"P f nr AmmnniP

5. Publication Date September 1975

6. Performing Organization Code

7. AUTHOR(S)

Lester Haar and John Gallagher

8. Performing Organ. Report No.

0 D F W R r>R MIWC OR C A M 1 7 A T IOIM MAMF AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2210147

11. Contract/Grant No.

12. Sponsoring Organization Name* and Complete Address (Street, Gity, State, ZIP) 13. Type of Report & Period

Covered

Interlum

14. Sponsoring Agency ("ode

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

An outline is presented of the basic results of the extensive correlation for the

thermodynamic properties of ammonia recently completed at this laboratory. Computer

programs are presented for the calculation of thermodynamic properties in the range

including the triple point temperature to 5/3 the critical temperature and

pressures from the dilute gas to 8000 bar.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Ammonia; correlation; gas ; liquid; thermodynamic

properties; thermodynamic surface.

18. AVAILABILITY [^] Unlimited

_H For Official Distribution. Do Not Release to NT IS

1 3 Order From Sup. of Doc, U.S. Government Printing Office Washington. D.C. 20402. SD Cat. No. CI

{jfc} Order Ercim National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCL ASS1FIED

21. NO. OF PAGES

27

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

22. Price

$ 3-75

USCOMM-DC 29042-P74