d
Workdone by $n$ moles of a gas when its volume changes from $\mathrm{V}_{1}$ to $\mathrm{V}_{2}$ is,
$\mathrm{W}=\mathrm{n} \mathrm{RT} \log _{\mathrm{e}} \frac{\mathrm{V}_{2}}{\mathrm{V}_{1}}$
For, $n=1$
$\mathrm{W}=\mathrm{RT} \ln \frac{\mathrm{V}_{2}}{\mathrm{V}_{1}}$
For an isothermal process, $\Delta \mathrm{U}=0$ $\Delta \mathrm{Q}=\Delta \mathrm{U}+\mathrm{W}=0+\mathrm{RT} \ln \frac{\mathrm{V}_{2}}{\mathrm{V}_{1}}$
$\therefore$ Entropy $=\frac{\Delta Q}{T}=R \ln \frac{V_{2}}{V_{1}}$