Question

Heat is supplied to a diatomic gas at constant pressure. The ratio between heat energy supplied and work done is:

( $\gamma$ for diatomic gas $=\frac{7}{5}$)

• A. $3:4$
• B. $2:1$
• C. $7:2$
• D. $2:5$

Answer 1

The correct option is C $7:2$

Let the change in temperature of diatomic gas be $\Delta T$

$\therefore$ Heat supplied at constant pressure $Q=n{C}_p\Delta T$

Using first law of thermodynamics : $Q=\Delta U+W$

$\therefore$ $W=Q-\Delta U=n{C}_p\Delta T-n{C}_v\Delta T$

$⟹$ $W=n(C_p-C_v)\Delta T$

$⟹$ $\frac{Q}{W}=\frac{C_p}{C_p-C_v}$

But $C_p=\gamma C_v$, thus $\frac{Q}{W}=\frac{\gamma C_v}{\gamma C_v-C_v}=\frac{\gamma }{\gamma -1}$

$\therefore$ $\frac{Q}{W}=\frac{\left(7/5\right)}{\left(7/5\right)-1}=\frac{7}{2}$