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Second law of thermodynamics, entropy

Problem 2.137

The expansion process of v=2.0v=2.0 moles of argon proceeds so that the gas pressure increases in direct proportion to its volume. Find the entropy increment of the gas in this process provided its volume increases α=2.0\alpha=2.0 times.

Reveal Answer
ΔS=v(γ+1)Rγ1lnα=46 J/K\Delta S=\frac{v(\gamma+1) R}{\gamma-1} \ln \alpha=46 \mathrm{~J} / \mathrm{K}