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Q.

Initial and final state of gas are represented respectively $by (P_{1}, V_{1}, T_{1}) and (P_{2}, V_{2}, T_{2})$ . The pressure and volume of the gas during process is related by PVⁿ = constant.
Therefore net reversible work done is

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a

$\frac{(P_{2} V_{2} - P_{1} V_{1})}{(1 - n)}$

b

$\frac{(P_{2} V_{2} - P_{1} V_{1})}{(n - 1)}$

c

$- \frac{P_{2} V_{2}}{P_{1} V_{1}}$

d

$- P Δ V$

answer is B.

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Detailed Solution

$P V^{n} = c, where c is a constant$

$∴ P = c / V^{n}$

$\begin{array}{l} ∴ Work done, Δ W = - \int_{V_{1}}^{V_{2}} P d V = - c \int_{V_{1}}^{V_{2}} \frac{d V}{V^{n}} \\ \begin{array}{r} = \frac{c}{(n - 1)} [\frac{1}{V_{2}^{n - 1}} - \frac{1}{V_{1}^{n - 1}}] \\ or Δ W = \frac{1}{(n - 1)} (P_{2} V_{2} - P_{1} V_{1}) \end{array} \end{array}$

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