Question

If the volume of gas is changed from $ V_{1} $ to $ V_{2} $ isothermally, then work done is:

• A. $ RT\,\ln \frac{V_{1}}{V_{2}} $
• B. $ RT\,\ln \frac{V_{2}}{V_{1}} $
• C. $ R(T_{2}-T_{1})\ln\frac{V_{2}}{V_{1}} $
• D. $ R(V_{2}-V_{1})\ln\frac{T_{2}}{T_{1}} $

Answer 1

Answer: (B)

Ideal gas equation is $ PV=RT $
Work done in isothermal process is
$ W=\int\limits_{V_{1}}^{V_{2}}{p\,dV} $
From ideal gas law $ PV=RT $
$ \therefore $ $ W=\int\limits_{V_{1}}^{V_{2}}{\left( \frac{RT}{V} \right)}\,dV=RT\int\limits_{V_{1}}^{V_{2}}{\frac{dV}{V}} $
$ \Rightarrow W=RT\,\ln \,\left( \frac{V_{2}}{V_{1}} \right) $