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(C) For a diatomic gas,the molar heat capacity at constant pressure is $C_P = \frac{7}{2}R$ and at constant volume is $C_V = \frac{5}{2}R$.Heat suppli

Vedclass · Accepted Answer

$7:5:2$

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(C) For a diatomic gas,the molar heat capacity at constant pressure is $C_P = \frac{7}{2}R$ and at constant volume is $C_V = \frac{5}{2}R$.Heat supplied at constant pressure is given by $\Delta Q = \mu C_P \Delta T = \frac{7}{2} \mu R \Delta T$.Change in internal energy is given by $\Delta U = \mu C_V \Delta T = \frac{5}{2} \mu R \Delta T$.Using the first law of thermodynamics,work done is $\Delta W = \Delta Q - \Delta U = \frac{7}{2} \mu R \Delta T - \frac{5}{2} \mu R \Delta T = \mu R \Delta T = \frac{2}{2} \mu R \Delta T$.Therefore,the ratio $\Delta Q : \Delta U : \Delta W = \frac{7}{2} : \frac{5}{2} : \frac{2}{2} = 7 : 5 : 2$.

Column-$I$	Column-$II$
$(a)$ Adiabatic	$(i)$ $\Delta Q = \Delta U$
$(b)$ Isothermal	$(ii)$ $\Delta Q = \Delta W$
	$(iii)$ $\Delta U = -\Delta W$

Heat is supplied to a diatomic gas at constant pressure. The ratio of $\Delta Q : \Delta U : \Delta W$ is

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