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First law of thermodynamics, heat capacity

Problem 2.51

An ideal gas with the adiabatic exponent \(\gamma\) undergoes a process in which its internal energy relates to the volume as \(U=a V^{\alpha}\) where \(a\) and \(\alpha\) are constants. Find: (a) the work performed by the gas and the amount of heat to be transferred to this gas to increase its internal energy by \(\Delta U\) (b) the molar heat capacity of the gas in this process.

Reveal Answer
 2.51. (a) A=ΔU(γ−1)/α;Q=ΔU[1+(γ−1)/α]; (b) C==R/(γ−1)+R/α.\begin{aligned} & \text { 2.51. (a) } A=\Delta U(\gamma-1) / \alpha ; Q=\Delta U[1+(\gamma-1) / \alpha] ; \text { (b) } C=\\ =& R /(\gamma-1)+R / \alpha . \end{aligned}
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