The thermodynamics of critical phenomena in gases

✍ Scribed by J.F. Lee

• Publisher: Elsevier Science
• Year: 1953
• Tongue: English
• Weight: 176 KB
• Volume: 256
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(53)90653-x

✦ Synopsis

Sonic velocity measurements have been used for some time to determine the specific heats of gases at low frequencies following the suggestion of Einstein (1) 2 that the reaction rates of reactive gas mixtures could be found from similar measurements. However, the equation for sonic velocity expressed in terms of the ratio of the specific heats and the isothermal bulk modulus becomes indeterminate when applied to the critical point. In this paper a determinate expression for the sonic velocity at the critical point is derived which permits a direct solution for the constant volume specific heat as a function of the critical values of temperature, specific volume, sonic velocity and Joule-Thomson coefficient. The calculated values obtained from this expression are examined in comparison with existing data. Finally the approach to the problem from the standpoint of classical thermodynamics is appraised in the light of some findings from statistical thermodynamics.

DERIVATION OF C~ AT CRITICAL POINT

The sonic velocity at zero frequency is expressed as follows : Cv, mC, C* where a = sonic velocity, m = molecular weight, v = molar volume, and -v (Op/Ov), and -v(Op/Ov)r are the isentropic and isothermal bulk moduli, respectively. It can be shown that for any pure substance, Cp = C,-T(Op/OT)~2/(op/Ov)T.

If this expression is substituted in Eq. 1, the following equation is obtained for the sonic velocity.

C~ 2 Tv2 ( OP )2, V2 ( Op )