Question

For a diatomic gas change in internal energy for unit change in temperature for constant pressure and constant volume is $\Delta U_{1}$ and $\Delta U_{2}$ respectively. The ratio of $\Delta U_{1}: \Delta U_{2}$ is

• A. 5 : 3
• B. 3 : 5
• C. 1 : 1
• D. 5 : 7

Answer 1

Answer: (C)

According to first law of thermodynamics,
$\Delta Q=\Delta U+\Delta W$
At constant pressure,
$\Delta Q=n C_{P} \Delta T, \Delta U=\Delta U_{1}$,
$ \Delta W=P \Delta V=n R \Delta T$
$\therefore n C_{P} \Delta T=\Delta U+n R \Delta T$ or
$n\left(C_{P}-R\right) \Delta T=\Delta U_{1}$
At constant volume, $\Delta Q=n C_{V} \Delta T, \Delta W=0$
$ \therefore n C_{V} \Delta T=\Delta U_{2}$
Thus, $\frac{\Delta U_{1}}{\Delta U_{2}}=\frac{C_{P}-R}{C_{V}}=\frac{C_{V}}{C_{V}}=1: 1$