Question

Initial and final state of gas are represented respectively by (P₁ ,V₁ ,T₁) and (P₂,V₂ ,T₂). The pressure and volume of the gas during process is related by PVⁿ = constant. Therefore net reversible work done is

• 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. – PDV

Answer 1

Answer: (B)

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

Answer 2

PVⁿ = c where c is a constant

\ P = c/Vⁿ

\ Work done, DW = – $\int_{V_{1}}^{V_{2}}{PdV} = –c\int_{V_{1}}^{V_{2}}\frac{dV}{V^{n}}$

= $\frac{c}{(n - 1)}\left\lbrack \frac{1}{V_{2}^{n - 1}} - \frac{1}{V_{1}^{n - 1}} \right\rbrack$

or DW = $\frac{1}{(n - 1)}$ (P₂V₂ – P₁ V₁)