In an isobaric process of an ideal gas,the ra | vedclass

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(C) For an isobaric process,the pressure $P$ remains constant.Heat supplied to the system is given by $Q = n C_{P} \Delta T$.Work done by the system i

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$\frac{\gamma}{\gamma-1}$

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(C) For an isobaric process,the pressure $P$ remains constant.Heat supplied to the system is given by $Q = n C_{P} \Delta T$.Work done by the system is given by $W = P \Delta V$.Using the ideal gas equation $PV = nRT$,for a constant pressure process,$P \Delta V = nR \Delta T$.Therefore,$W = nR \Delta T$.The ratio of heat supplied to work done is $\frac{Q}{W} = \frac{n C_{P} \Delta T}{n R \Delta T} = \frac{C_{P}}{R}$.We know that $C_{P} - C_{V} = R$,so $R = C_{P} - C_{V}$.Substituting $R$ in the ratio: $\frac{Q}{W} = \frac{C_{P}}{C_{P} - C_{V}}$.Dividing the numerator and denominator by $C_{V}$: $\frac{Q}{W} = \frac{C_{P}/C_{V}}{(C_{P}/C_{V}) - 1}$.Since $\frac{C_{P}}{C_{V}} = \gamma$,we get $\frac{Q}{W} = \frac{\gamma}{\gamma - 1}$.

In an isobaric process of an ideal gas,the ratio of heat supplied and work done by the system $\left(\frac{Q}{W}\right)$ is given by $\left[\frac{C_{P}}{C_{V}}=\gamma\right]$.

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