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First law of thermodynamics, heat capacity

Problem 2.51

An ideal gas with the adiabatic exponent γ\gamma undergoes a process in which its internal energy relates to the volume as U=aVαU=a V^{\alpha} where aa and α\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 ΔU\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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