A reversible adiabatic process is an isentropic (constant-entropy) process, (a) Let αS = V–1(∂V/∂T)S. Use the first Maxwell equation in (4.44) and Eqs. (1.32), (1.35), and (4.31) to show that αs = −Cvk/TVα. (b) Evaluate αs for a perfect gas. Integrate the result, assuming that Cv is constant, and verify that you obtain Eq. (2.76) for a reversible adiabatic process in a perfect gas. (c) The adiabatic compressibility is ks ≡ −V−1(∂V/∂P)s. Starting from (∂V/∂P)s = (∂V/∂T)s (∂T/∂P)s, prove that ks = Cvk/Cp.
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