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Temperature-Entropy Diagram for

Parahydrogen Triple-Point Region

343

C. F. SINDT AND D. B. MANN

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NBS TECHNICAL NOTE 343

ISSUED JUNE 22, 1966

TEMPERATURE- ENTROPY DIAGRAM FOR

PARAHYDROGEN TRIPLE- POINT REGION

C. F. SINDT AND D. B. MANN

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 tor 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 15 cents.

TEMPERATURE -ENTROPY DIAGRAM FOR

PARAHYDROGEN TRIPLE -POINT REGION

by

C. F. Sindt and D. B. Mann

Cryogenics Division

NBS- Institute for Materials Research

Boulder, Colorado

Abstract

The three-phase region at and near the triple point of parahydrogen is presented on the graphical coordinates of temperature and entropy.

Isobars from 10 mm Hg to 340 atmospheres, temperatures from 11° to

23 °K and specific volumes covering the range of from 10. 5 cc/gm to

15, 000 cc/gm are included. The energy base of enthalpy and entropy

are consistent with previous data published by this laboratory.

Key words: Enthalpy, entropy, parahydrogen, pressure -volume,

properties, temperatures, triple -point region, T-S diagram.

in

Temperature -Entropy Diagram for Parahydrogen

Triple-Point Region*

An extension of the temperature-entropy state diagram to cover

temperatures and pressures near the triple point is required as a useful

tool in analysis of processes originating or terminating in this region.

Recent interest in this low temperature area has been supplied by the

relatively poor storage characteristics of liquid hydrogen under high heat

fluxes at the normal boiling point. The studies of liquid subcooling with

controlled mixing and, more recently, the characterization of liquid-solid

(slush) mixtures are only two of the many processes requiring coherent

thermophysical property data at temperatures below the normal boiling

point.

It is the purpose of this note to correlate the principle analytical

and experimental data already in the published literature in respect to

common energy bases and dimensional units. The result is a temperature

entropy diagram of a rather restricted scope for properties near the

triple point, but compatible with existing diagrams which extend to conditions at or above ambient.

Figure 1 shows the relative location of the phase boundaries for

parahydrogen near the triple point. Region I has been defined by the

extensive experimental and analytical work of Roder and Goodwin [ 1961] , and Roder et al. [ 1965] . Regions II and III have been' described by Mullins

et al. [ 196l] . Recent experimental work of Dwyer et al. [ 1965a] along with

1 the more dated solid -liquid phase data of Bartholome [ 193 6] define region IV.

Figure 2 shows the temperature-entropy surface generated using

the above data.

^Sponsored by NASA Marshall Space Flight Center, Huntsville, Alabama.
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Figure 1. Hydrogen T-S Diagram Phase Boundaries
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ENTROPY, Joules /g °K

Figure 2 . Parahydrogen Temperature -Entropy diagram

Construction of the diagram was complicated by differences in

entropy and enthalpy bases and temperature scales. These differences

were resolved in a number of ways.

Dimensional units and energy bases were those selected by

Roder and Goodwin [ 1961] . The reasons are based on continuity of data

for engineering calculations. The Roder data cover the temperature

range of 20 - 300°K and pressures to 100 atmospheres. Higher pressure

data below 100°K is also included. The Roder et al. [ 1965] data are of

higher accuracy but of limited scope. Therefore, figure 2 of this report

extends the data range of Roder and Goodwin [ 1961] in a continuous manner

to 11 °K.

Referring to figure 1, region I was plotted directly from Roder

and Goodwin [ 196l] above 20°K and Roder et al. [ 1965] below 20°K. The

latter data were converted to a gram basis using the molecular weight of

2. 01572 grams/mole. There is a slight shift in entropy (0. 5% at NBP),

enthalpy (0. 25%) values on matching data of Roder and Goodwin [ 1961] and

Roder et al. [1965] . Improved calculation procedures are responsible for

this small discontinuity and the change which is within the error claimed by

Roder et al. [ 1965] is not significant when graphically plotted as in figure 2.

Regions II and III are plotted from the data of Mullins et al. [ 1961] . Again methods of calculating the energy states have been improved but in

this case the base difference is of such magnitude that the data of Mullins

were changed to match the data of Roder and Goodwin [ 1961] . Entropy values

of Mullins were reduced by 0. 33 joules/gm-K° which reflects the difference

at the normal boiling point. This difference reflects the more critical

evaluation of the specific heat of the solid by Ahlers [ 1964] and a similar

reevaluation of the liquid specific heats by Younglove and Diller [ 1962] . The Roder enthalpy base was chosen to be consistent with the previous work

of Woolley et al. [ 1948] . Therefore the values of enthalpy of Mullins were

reduced by 378. 7 joules/gm.

4
The difference in temperature scales, a matter of 0. 01°K,was

neglected.

Region IV was calculated using the volume change on freezing of

i Bartholome [ 1936] and Dwyer et al.[ 1965a] . A correlation of these data

with the measured heats of fusion of Dwyer et al. [ 1965b] has yet to be

completed. In consideration of the heats of fusion an uncertainty in entropy

is possible along the saturated solid line of 0. 25 joules/gm-K° at 300

atmospheres decreasing to 0. 05 joules/gm-K° at 100 atmospheres.

The lines of constant specific volume in the liquid region were

constructed from cross plots of entropy versus specific volume with lines

of constant pressure and temperature. The specific volume along the

saturated solid line was calculated using the Clapeyron equation, the equation

for specific volume of saturated liquid for solidification from Roder, and

the heats of fusion. Enthalpies, qualities and volume lines in the two phase

regions were calculated directly from the data given by Mullins and Roder.
References

Ahlers, G. (1964). J. Chem. Phy. 41_, 89-94.

i Bartholome, E. (1936). Z. Physik. Chem. (B) 33, 387.

Dwyer, R. F. , G. A. Cook, O. A. Berwaldt and H. E. Nevins (1965a).

J. Chem. Phys., 43, 801.

Dwyer, R. F. , G. A. Cook, B. M. Shields, and D. H. Stellrecht (1965b).

J. Chem. Phys., 42, 3809.

Mullins, J. C, W. T. Ziegler and B. S. Kirk (1961). Technical Report 1,

Contract A- 593, Eng. Exp. Station, Georgia Inst. Tech.

Roder, H. M. and R. D. Goodwin (1961 ). NBS Technical Note 130,

PB 161631.

Roder, H. M. , L. A. Weber and R. D. Goodwin (1965). NBS Monograph 94.

Woolley, H. W. , R. B. Scott and F. G. Brickwedde (1948). NBS J. of

Research, 41_, 379-475.

Younglove, B. A. and D. E. Diller (1962). Cryogenics 2, No. 5, 283-287.


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