$($b$)$ State Carnot's theorem. Draw the PV diagram showing the Carnot's cycle for an ideal gas and

arrive at $|)/(||)Q_C|=\frac{T_H}{T_C}$

$(3$ M$)$

$($a$)$ Find the molar heat capacity of an equimolar gaseous mixture of air, ammonia, ethane and propane whose heat capacity values are $7/2$R$,4\mathrm{.}26$R$,6\mathrm{.}4$ R and $9$R respectively.$(2$ M$)$

$($b$)$ State Carnot's theorem. Draw the PV diagram showing the Carnot's cycle for an ideal gas and arrive at $|)/(||)Q_C|=\frac{T_H}{T_C}$

$(3$ M$)$