All Problems

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 V1=10V_{1}=10 l\mathrm{l} contains v=2.5v=2.5 moles of carbon dioxide. The other vessel of volume V2=V_{2}= 100 l\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(γ1)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}