Question:
$\mathrm{n}$ moles of an ideal gas with constant volume heat capacity $\mathrm{C}_{\mathrm{V}}$ undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is:
Correct Option: 1
Solution:
(1) At constant volume
Work done $(\mathrm{W})=\mathrm{n} \mathrm{R} \Delta \mathrm{T}$
and Heat given $Q=C_{v} \Delta T+n R \Delta T$
So, $\therefore \frac{\mathrm{W}}{\mathrm{Q}}=\frac{\mathrm{nR} \Delta \mathrm{T}}{\mathrm{C}_{\mathrm{v}} \Delta \mathrm{T}+\mathrm{nR} \Delta \mathrm{T}}=\frac{\mathrm{nR}}{\mathrm{C}_{\mathrm{V}}+\mathrm{nR}}$