Exact treatment of the Joule-Thomson coefficient

As we showed in Section 2.5.4, thermal averages in isostress isostrain ensembles can be related through a Laplace transformation. Hence, for the conjugate stress r and strain A, wc may employ E i. (2.121) and change variables according to Tja — t and — A giving 

In the thermodynamic limit we may apply the maximum term method (see Appendix B.4) to write 

Taking the logarithm of this expression we have from Eqs. (2.79), (5.131), and the Legendre transform T = U — TS that 

To evaluate the partial derivative on the far right side of this expression we rewrite it more explicitly as 

putting together these last two expressions, we obtain 

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