It may be noted that the intersection point is the mid6 uc line, and that at this point the point on the 0 pressure has its maximum value ( P = d&T5/4). This is the highest pressure a t which 2 us. P isotherms cross the 2 = 1 axis, and the pressure a t which the envelope of these isotherms, which represents the IC (Bursik, 1971), CrOSseS this axis. The isotherm which at this point is the one for T = T5/2.
Bursik, J. W., Ind. Eng. Chem., Fundam., 12, 256 (1973). Hirschfelder. J. O., Curtiss, C. F., Bird, R. B., "Molecular Theory of Gases and Liquids," pp 173-175, Wiley, New York, N. Y., 1964. Holleran, E. M., J. Chem. Phys., 47, 5318 (1967).
~~~~~~~~;E: ;: ~ ~ ~ ~ C ~ 72, ; '3559P(1968), ;."~~~~~
Holleran. E. M., Jacobs, R . s.. hd. Eng. Chem., Fundam., 11, 272 (1972). Holleran. E. M.3 Sinka, J. v.9 J. Chem. PhYS., 55,4260 (1971). Morsy, T. E.,Dissertation, Technische Hochschule, Karlsruhe, West &rmany, 1963.
Chemistry Department S t . John's University Jamaica, New York-11439
Literature Cited Bursik, J . W., Ind. Eng. Chem., Fundam., 10, 644 (1971).
Eugene Holleran
Boyle Points, U C and Compressibility Curves
In the graph that follows (Figure l),a study is made of the prediction of the linear t us. d UC theory which requires the temperature a t the maximum pressure point of the UC curve to have the value Tl(max P = %TB, where TB is the Boyle temperature. The substance is helium-4 and the data are from McCarty (1972). The curve labeled I in this 2 us. P (atm) plot is a segment of the inversion curve. Curves A and B are respectively 12.58 and 165°K isothermal segments. The A isotherm corresponds to the temperature at which the 2 us. T K plot of the inversion curve data of McCarty crosses 2 = 1. The B isotherm corresponds to Tl(max P ) = VZTBwhere the Boyle temperature is taken from Glasstone (1946) as 33°K. It is obvious that the isotherm labeled B does not pass through the point of maximum pressure as required by the linear UC theory. If, however, the Boyle temperature is taken as 24.06"K (Keyes, 1941), one-half of this value is 12.03"K and this is close to the isothermal A value of 12.58"K. Obviously, the second choice of Boyle temperature gives a much better agreement with the linear t us. d UC theory. The scatter in reported Boyle temperatures is not confined io helium. Nitrogen has a t least two values, 324 (Steiner, 1948) and 335 (Guggenheim, 1957); methane, 508 (Douslin, et al., 1964) and 491 (Guggenheim, 1957); and carbon dioxide, 721.7 (Holleran, 1967) and 710.7 (Vukalovich and Altunin, 1968). There are additional problems in mixing theoretical and experimental values. For argon, various Boyle temperatures are: 396.4 (Sze and Hsu, 1966), 410 (Steiner, 1948), 411.5 (Guggenheim, 1957), and 408.2 (Sze and Hsu, 1966). The two by Sze and Hsu are obtained theoretically for Lennard-Jones (6, m ) gases with m respectively taken as 16 and 12. All of the above temperatures are Kelvin. As with the helium example, 2-P plots of isothermal and inversion curve segments for any of these substances
I
/
16
20
24
28
32
p-
Figure 1.
may lead to ambiguity in attempting to interpret whether or not the YzT5 isotherm passes through the maximum pressure point of the unit compressibility curve, depending on which value of TB is used for a particular substance. Literature Cited Douslin, D. R . , et ai., J. Chem. Eng. Data, 9, 358 (1964). Glasstone, S.. "Textbook of Physical Chemistry," 2nd ed, p 247, Van Nostrand, Princeton. N. J., 1946. Guggenheim, E. A,, "Thermodynamics," 3rd ed, pp 116, 167, North-Holland Publishing Co., Amsterdam, 1957. Holleran, E. M., J. Chem. Phys., 47, 5318 (1967) Keyes, F. G.. "Temperature, Its Measurement and Control in Science and Industry," p 59, Reinhold. New York, N. Y., 1941. McCarty, R. D., "Thermophysical Properties of Helium-4 from 2 to 1500 K with Pressures to 1000 Atmospheres," National Bureau of Standards. Technical Note 631, 1972. Steiner. L. E.. Introduction to Chemical Thermodynamics," 2nd ed, p 75, McGraw-Hill. New York. N.Y., 1948. Sze, M. M., Hsu, H. W., J. Chem. Eng. Dara, 11, 77 (1966). Vukalovich, M. P.. Altunin, V. V., "Thermophysical Properties of Carbon Dioxide," p 185, Collet's, LTD., London, 1968.
School of Engineering Rensselaer Polytechnic Institute Troy, New York 12i81
Joseph W. Bursik
CORRECTION T H E CRITICAL PROPERTIES OF BINARY HYDROCARBON SYSTEMS In this article by Sung C. Pak and Webster B. Kay [Ind. Eng. Chem., Fundam., 11, 255 (1972)J there is a typographical error in eq 1, which appears on p 260. The
298
I n d . Eng. Chem., Fundam., Vol. 13,
No. 3, 1974
equation should read: log P H = ~ 5.92822 - 3037.6/T, where T = "K and P H =~partial pressure of mercury in poundspersquareinchabsolute.
