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First law of thermodynamics, heat capacity

Problem 2.52

An ideal gas has a molar heat capacity CVC_{V} at constant volume. Find the molar heat capacity of this gas as a function of its volume V,V, if the gas undergoes the following process: (a) T=T0eαVT=T_{0} \mathrm{e}^{\alpha \mathrm{V}} (b) p=p0eαVp=p_{0} \mathrm{e}^{\alpha V}, where T0,p0,T_{0}, p_{0}, and α\alpha are constants.

Reveal Answer
2.52. (a) C=CV+R/αVC=C_{V}+R / \alpha V (b) C=CV+R/(1+αV)C=C_{V}+R /(1+\alpha V)
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