By Rowland S. Benson and W. A. Woods (Auth.)
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There are two inversion temperatures for each pressure. The Joule-Thomson "cooling" effect cannot take place above the maximum inversion temperature nor below the minimum inversion temperature. These values are 2a/bR mol and 2a/9bRmoi respectively for a "Van der Waals1 gas". It will be recalled that the critical temperature is 8a/2 7bR mol . The ratios of the inversion temperatures to the critical temperature are ADVANCED 54 T. 75. 1. 2. 1500 723 621 603 202 25 Critical temperature OK T 304 134 126 117 33 4.
Using the state equation u = u(T,v) 42 hence ADVANCED ENGINEERING THERMODYNAMICS du = ®r dT *($ du = ££ dT = dv CydT u(T) for an ideal gas. u If we consider the identity du] 3PJT 3v = 0. The term (3p/9v)T for an ideal gas is equal to -p/v and since [ P f 0 l 9 PJ T Thus the internal energy is independent of the pressure or as before u = u(T) for an ideal gas. tin some texts the formal definition of an ideal gas is pv = Rmol r mnlT and (a) (b) In other texts the second equation is replaced by u = u(T) (c) Sometimes u = u(T) is defined as a linear function.
C) dmi + dm2 = 0 (d) = dmigi + dm 2 g 2 = 0. (e) = g2· Now from (a) and from (b) and (c) dG Comparing (d) and (e) we have gi Gibbs function is the same in each phase. 48 ADVANCED or ENGINEERING THERMODYNAMICS s2-si HT V2-VI* The phase change is a reversible process. ) 1 Therefore, S2-S1 dT v2-V! 72) This is called the Clausius-Clapeyron equation and is used to calculate either the pressure p, the specific volume v or the latent heat 1 from experimental data. Liquefaction of Gases There is a large number of industrial processes using extremely low temperatures.
Advanced Engineering Thermodynamics by Rowland S. Benson and W. A. Woods (Auth.)