10 g each of $\mathrm{NH}_3, \mathrm{~N}_2, \mathrm{Cl}_2$ and $\mathrm{H}_2 \mathrm{~S}$ are expanded…
10 g each of $\mathrm{NH}_3, \mathrm{~N}_2, \mathrm{Cl}_2$ and $\mathrm{H}_2 \mathrm{~S}$ are expanded isothermally and reversibly at same temperature. Identify gas that performs maximum work.
$\mathrm{N}_2$
$\mathrm{Cl}_2$
$\mathrm{H}_2 \mathrm{~S}$
$\mathrm{NH}_3$
Solution
$W_{\max }=-2.303 n R T \log _{10} \frac{V_2}{V_1}$
Hence, $W_{\text {max }} \propto \mathrm{n}$
(Given: $\mathrm{R}, \mathrm{T}, \mathrm{V}_2, \mathrm{~V}_1=$ Constant)
$\mathrm{W}_{\max } \propto \frac{1}{\mathrm{M} \cdot \mathrm{W}}$ (Given: equal mass)
Hence, lower the molecular mass, greater is the work done. Among the given, $\mathrm{NH}_3$ has the lowest molecular mass which performs maximum work.