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Equation of the gas state processes

Problem 2.6

A vertical cylinder closed from both ends is equipped with an easily moving piston dividing the volume into two parts, each containing one mole of air. In equilibrium at T0=300 KT_{0}=300 \mathrm{~K} the volume of the upper part is η=4.0\eta=4.0 times greater than that of the lower part. At what temperature will the ratio of these volumes be equal to n′=3.0?n^{\prime}=3.0 ?

Reveal Answer
T=T0η′(η2−1)/η(η′2−1)=0.42kKT=T_{0} \eta^{\prime}\left(\eta^{2}-1\right) / \eta\left(\eta^{\prime 2}-1\right)=0.42 \mathrm{kK}
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