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First law of thermodynamics, heat capacity

Problem 2.42

Find the rate vv with which helium flows out of a thermally insulated vessel into vacuum through a small hole. The flow rate of the gas inside the vessel is assumed to be negligible under these conditions. The temperature of helium in the vessel is T=1,000 KT=1,000 \mathrm{~K}.

Reveal Answer
v=2γRT/(γ−1)M=3.3 km/sv=\sqrt{2 \gamma R T /(\gamma-1) M}=3.3 \mathrm{~km} / \mathrm{s}
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