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Second law of thermodynamics, entropy

Problem 2.141

One mole of a Van der Waals gas which had initially the volume V1V_{1} and the temperature T1T_{1} was transferred to the state with the volume V2V_{2} and the temperature T2T_{2}. Find the corresponding entropy increment of the gas, assuming its molar heat capacity CVC_{V} to be known.

Reveal Answer
ΔS=CVln⁡(T22/T1)+Rln⁡[(V2−b)/(V1−b)]\Delta S=C_{V} \ln \left(T_{2}^{2} / T_{1}\right)+R \ln \left[\left(V_{2}-b\right) /\left(V_{1}-b\right)\right]
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