up to 1/3 of de by use of the vapor pressure equation and the virial equation of state. We used the representation of second virial coefficients based on data of Sengers, Klein, and Gallagher, as well as the third virial coefficient, both as described in [1].

Analytical description of the vapor densities is given by our new form, constrained to qualitatively acceptable behavior near the critical point [9]. To facilitate selection of significant figures in the coefficients, we use variables u and w normalized to a maximum value of unity (at the triple point: see list of symbols). Vapor densities now are described by use of exponent B=0.36,

from eq (2), and identifies the sources. At the triple. point 90.66 K, eq (2) gives a liquid density d1 = 28.0536 mol/l resting primarily on the data of [8], as seen on the figure.

Figure 3 gives the coexisting densities of vapor and liquid methane along the abcissa, calculated by eqs (1, 2). The ordinate gives the saturation temperature. T(p). This plot provides a quick, rough estimate of the data. Conspicuously absent is the line for densi ties of freezing liquid. Some values recently have been estimated to 94.5 K (150 atm), including the volume change and heats of melting [12].

The rectilinear diameter may be derived by use of eqs (1, 2) for interpolation of d, and d, to the same temperatures. For 39 points at 112 ≤ T ≤ 188 K, our rep resentation in mol/l,

(dg+d)/2=a+bz+c exp (− €/z).

792

As

(31

The value for exponent ẞ was selected by considering the published values, B = 0.367 [10], and ß = 0.3566 [11]. The number of terms in (1) was selected to bring deviations down to the level of estimated uncertainty in data derived from the vapor pressure and virial equations. Individual relative deviations of vapor densities from eq (1) are plotted on figure 1. The rms deviation for 55 points is 0.21 percent.

Saturated liquid densities are described by our simple form [9] using argument z= (1-7),

Pipe-1=az+bz+c exp (−.72/z), (2)

=

yields an rms deviation of 0.05 percent and a critical density de 10.156+0.02 mol/l, as compared with de 10.15 adopted for present work.

=

2.44 483

i=2

A6-112.50 780

A7= 141.02 284

0.19 3073

-0.34 282

- 89.60 804

22.74 904

0.20 %

14

The signs and magnitudes of these coefficients a comparable with values found for other substances [9

Column 1 of table 1 gives the same rounded temperatures used in [14, 15]. (Experimental uncertainties do not demand conversion to the IPTS-1968.) Second and third columns of table 1 give the published data in kilo-Joules/mole. The fourth column gives our results via (5). The remaining three columns are the derived data used on the right of (5). Figure 4 gives the outline for our calculated results.

For some computations it would be convenient to use a more direct description of AH, than given by (5). For the 21 points in the fourth column of table 1 the following representation gives a maximum relative deviation A=-0.04 percent at 120 K; deviations of 0.00

Specific heats of the liquid phase, along the coexistence path, are useful for computing thermodynamic properties into compressed liquid states. Data for C, are derived from observations on the two phase, liquid-vapor system at constant volume by use of accurate PVT data for the two phases [17]. Published data for methane are quite uncertain because the authors failed to give either their experimental observations or a quantitative description of their derivations [14, 15]. The data are shown by figure 5 in

408-434 0-71-2

ccuracy exceeds that which can be attained by experimental specific heat measurements.

Data for methane first were derived in API Project 4 [21], and work to 1961 has been reviewed [22]. For present work we select the recent results of McDowell and Kruse [23], and give them an analytical repre-entation in the range 60 ≤ T≤ 400 K. With convenional notation [19], abbreviate the internal energy unction by (T) = (Eo — E%)/RT, and define the argument x = T/400 with maximum value of about unity for our range of T.

A formulation with six constants was used for nitrozen [24]. For methane [23] and for oxygen [25] it does not give a highly precise representation of the specific heats. A more precise description is obtained with the power series,

Introducing the published value of S/R at T1 = 60 K yields,

S/R=A+In (T/60) + A1 In (x) + 4·42x1/3

with constant A。= 18.852 484.

(10)

Specific heat at constant pressure, and the enthalpy function now are simply

Table 2 gives temperatures in the first column. The next three pairs of columns give data and calculated values for (7), for Co/R, and for S/R.

Independent computations of above data by Harrison et al. [27] give almost identical results at 90 ≤ T <800 K, further increasing confidence in their

accuracy.

6. Discussion

This report gives analytical descriptions of some methane properties, using existing and estimated data, as a base for preliminary computations of thermodynamic functions over the wide range from gaseous to compressed liquid states at low temperatures. It reveals deficiencies in the quantity of data available for densities of saturated vapor; in the precision of data available for saturated liquid densities; and hence uncertainty, difficult to assess, in the derived heats of vaporization. Data available for specific heats of liquid at coexistence cannot be assessed, due to a lack of published information. For thermofunctions in ideal gas states, the high quality of results derived by McDowell and Kruse suggests that they will stand for a long time.

This laboratory is undertaking an experimental program to obtain reliable and self-consistent measurements over a wide range of conditions and to compute thermodynamic properties based on their formulations.

7. References

[1] Goodwin, R. D., Thermophysical properties of methane: virial coefficients, vapor- and melting pressures, J. Res. Nat. Bur. Stand. (U.S.). 74A (Phys. and Chem.), No. 5, (Sept.-Oct. 1970).

[2] Keyes, F. G., Taylor, R. S., and Smith, L. B., The thermodynamic properties of methane, J. Math. & Phys. 1, 211 (1922). [3] Matthews, C. S., and Hurd, C. O., Thermodynamic properties

of methane, Trans. Am. Inst. Chem. Engrs. 42, 55 (1946). [4] Bloomer, O. T., and Parent, J. D., Liquid-vapor phase behavior of the methane-nitrogen system, Chem. Eng. Prog. Symposium Ser. 6, 49, 11 (1952).

[5] Vennix, Alan J., Low temperature volumetric properties and the development of an equation of state for methane, Thesis. Dept. of Chem. Engrn'g., Rice University, Houston, Texas, April, 1965.

[6] Grigor, Anthony F., The measurement and correlation of some physical properties of methane and per-deuteromethane. Thesis, Dept. of Chem., Pennsylvania State University, December, 1966.

[7] Davenport, A. J., Rowlinson, J. S., and Saville, G., Solutions of three hydrocarbons in liquid methane, Trans. Faraday Soc. 62, 322 (1966).

[8] Terry, M. J., Lynch, J. T., Bunclark, M., Mansell, K. R., and Staveley, L. A. K., The densities of liquid argon, krypton. xenon, oxygen, nitrogen, carbon monoxide, methane, and carbon tetrafluoride along the orthobaric liquid curve, J. Chem. Thermodynamics 1, No. 4, 413 (1969).

Pe from

[9] Goodwin, R. D., Estimation of critical constants Te. the p(T) and T(p) relations at coexistence, J. Res. Nat. Bur. Stand. (U.S.), 74A (Phys. and Chem.), No. 2, 221-227 (Mar. Apr. 1970).

[10] [11]

Ricci, F. P., and Scafè, E., Orthobaric density of CH, in the critical region, Physics Letters 29A, No. 11, 650 (1969). Jansoone, V., Gielen, H., DeBoelpaep, J., and Verbeke, O. B.. The pressure-temperature-volume relationship of methane near the critical point, Physica 46, 213 (1970).

[12] Sindt, C. F., Ludtke, P. R., and Roder, H. M., Slush and boiling methane characterization, private communication 9758, this laboratory, July 1, 1970.

[13] Goodwin, R. D., Formulation of a nonanalytic equation of state for parahydrogen, J. Res. Nat. Bur. Stand. (U.S.), 73A (Phys. and Chem.), No. 6, 585–591 (Nov.-Dec. 1969). [14] Wiebe, R., and Brevoort, M. J., The heat capacity of saturated liquid nitrogen and methane from the boiling point to the critical temperature, J. Am., Chem. Soc. 52, 622 (1930). [15] Hestermans, P., and White, David, The vapor pressure, heat of vaporization and heat capacity of methane from the boiling point to the critical temperature, J. Phys. Chem. 65, No. 2. 362 (1961).

[16] Clusius, Klaus, Uber die specifische Warme einiger konden sierter Gase zwischen 10 Grad abs, und ihrem triple Punkt. Z. Physik. Chem. (Leipzig) B3, 41–79 (1929). [17] Goodwin, R. D., and Weber, L. A., Specific heats of oxygen at coexistence, J. Res. Nat. Bur. Stand. (U.S.), 73A (Phys and Chem.), No. 1, 1-13 (Jan.-Feb. 1969).

[18] Goodwin, R. D., and Prydz, Rolf, Specific heats of fluorine at coexistence, J. Res. Nat. Bur. Stand. (U.S.), 74A (Phys. and Chem.). No. 4, 499 505 (July-Aug. 1970). Rossini, Frederick D., Chemical Thermodynamics (John Wiley & Sons, Inc., New York, 1950).

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