Question

A piston can freely move inside a horizontal cylinder closed from both ends. Initially, the piston separates the inside space of the cylinder into two equal parts each of volume V₀, in which an ideal gas is contained under the same pressure P₀ and at the same temperature. What work has to be performed in order to increase isothermally the volume of one part of gas 2 times compared to that of the other by slowly moving the position –

• A. P₀V₀
• B. 2 P₀V₀
• C. P₀V₀ ln$\frac{9}{8}$
• D. P₀V₀ $\mathcal{l}n2$

Answer 1

Answer: (C)

P₀V₀ ln$\frac{9}{8}$

Answer 2

External work = work done on both gases

= – (work done by the gases)

= –$\left\lbrack P_{0}V_{0}\mathcal{l}n\frac{4/3V_{0}}{V_{0}} + P_{0}V_{0}\mathcal{l}n\frac{2/3V_{0}}{V_{0}} \right\rbrack$ = – P₀V₀ ln $\frac{9}{8}$