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First law of thermodynamics, heat capacity

Problem 2.40

A certain mass of nitrogen was compressed \(\eta=5.0\) times times (in terms of volume), first adiabatically, and then isothermally. In both cases the initial state of the gas was the same. Find the ratio of the respective works expended in each compression.

Reveal Answer
 2.40. The work in the adiabatic process is n=(ηγ−1−−1)/(γ−1)ln⁡η=1.4 times greater. \begin{aligned} &\text { 2.40. The work in the adiabatic process is } n=\left(\eta^{\gamma-1}-\right.\\ &-1) /(\gamma-1) \ln \eta=1.4 \text { times greater. } \end{aligned}
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