A monoatomic gas of $n$ moles is heated from temperature $T_1$ to $T_2$ under two different conditions, (i) at constant volume and (ii) at constant pressure. The change in internal energy of the gas is

In a Carnot engine, when the temperatures are $T_2=0^{\circ} \mathrm{C}$ and $T_1=200^{\circ} \mathrm{C}$, its efficiency is $\eta_1$ and when the temperature are $T_1=0^{\circ} \mathrm{C}$ and $T_2=-200^{\circ} \mathrm{C}$, its efficiency is $\eta_2$. Then, the value of $\frac{\eta_1}{\eta_2}$ is

Heat energy absorbed by a system going through the cyclic process shown in the figure is

A polyatomic gas with $n$ degrees of freedom has a mean kinetic energy per molecule given by (if $N$ is Avogadro's number )