Question

For an isobaric process involving an ideal gas, the ratio of heat supplied and work done by the system (gas) is

• A. $\frac{\gamma -1}{\gamma }$
• B. $\gamma$
• C. $\frac{\gamma }{\gamma -1}$
• D. $1$

Answer 1

The correct option is C $\frac{\gamma }{\gamma -1}$

For isobaric process heat supplied to the system is given as,
$Q=n{C}_P\Delta T$, where $n=$number of moles of gas
$W=P\Delta V$, represents work done by the gas
$\Rightarrow \frac{Q}{W}=\frac{\eta C_P\Delta T}{P\Delta V}...\left(i\right)$
For an ideal gas, $PV=nRT$
$\Rightarrow P\Delta V=P{V}_f-P{V}_i$
$\Rightarrow P\Delta V=nR{T}_f-nR{T}_i=nR(T_f-T_i)$
$\therefore P\Delta V=nR\Delta T...\left(ii\right)$
From Eq.$\left(i\right)\&\left(ii\right)$,
$\frac{Q}{W}=\frac{n{C}_P\Delta T}{nR\Delta T}=\frac{C_P}{R}$
Substituting $C_P=\frac{R\gamma }{\gamma -1}$ we get,
$\frac{Q}{W}=\frac{\left(\frac{R\gamma }{\gamma -1}\right)}{R}$

$\therefore \frac{Q}{W}=\frac{\gamma }{\gamma -1}$