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First law of thermodynamics, heat capacity

Problem 2.60

Two thermally insulated vessels are interconnected by a tube equipped with a valve. One vessel of volume \(V_{1}=10 \) \(\mathrm{l}\) contains \(v=2.5\) moles of carbon dioxide. The other vessel of volume \(V_{2}=\) 100 \(\mathrm{l}\) is evacuated. The valve having been opened, the gas adiabatically expanded. Assuming the gas to obey the Van der Waals equation, find its temperature change accompanying the expansion.

Reveal Answer
ΔT=−vaV2(γ−1)RV1(V1+V3)=−3.0 K\Delta T=-\frac{v a V_{2}(\gamma-1)}{R V_{1}\left(V_{1}+V_{3}\right)}=-3.0 \mathrm{~K}
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