In an isobaric process of an ideal gas, the ratio of work done by the system to the heat supplied \(\left(\frac{W}{Q}\right)\) is

For an isobaric process,
\(\begin{aligned}
& \Delta \mathrm{Q}=\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{~T} \text { and } \Delta \mathrm{U}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{~T} \\
& \mathrm{~W}=\Delta \mathrm{Q}-\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{~T}-\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{~T}
\end{aligned}\)
\(\therefore \quad \frac{W}{\Delta Q}=\frac{\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{T}-\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}}{\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{T}}=\frac{\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}}{\mathrm{C}_{\mathrm{p}}}\)
\(=\frac{\frac{C_p}{C_v}-1}{\frac{C_p}{C_v}}\)
\(\therefore \quad \frac{W}{\Delta Q}=\frac{\gamma-1}{\gamma} \quad \ldots\left(\because \frac{C_p}{C_v}=\gamma\right)\)