Question

A gas is expanded to double its volume by two different processes. One is isobaric and the other is isothermal. Let W₁ and W₂ be the respective work done, then –

• A. W₂ = W₁ln (2)
• B. W₂ =\frac{W_{1}}{\ln(2)}
• C. W₂ =\frac{W_{1}}{2}
• D. Data is insufficient

Answer 1

Answer: (A)

W₂ = W₁ln (2)

Answer 2

W₁ = P_i (V_f – V_i) = P_iV_i$\left( \frac{V_{f}}{V_{i}} - 1 \right)$

= nRT (2 – 1) = nRT

W₂ = nRT ln$\left( \frac{V_{f}}{V_{i}} \right)$= nRT ln (2) = W₁ ln (2)