Five moles of an ideal gas has pressure $p_0$, volume $V_0$ and temperature $T_0$. The gas is expanded to volume $3 V_0$ along a path, so that the pressure $p$ is changed as function of volume $V$ as $p=p_0\left(V / V_0\right)$. The pressure is then reduced to $p_0$ maintaining the volume constant. The gas undergoes an isobaric compression till the volume and temperature become $V_0$ and $T_0$, respectively. The total work done by the gas during the entire process is

How many rotational degrees of freedom does a rigid diatomic molecule have?

The specific heat of helium at constant volume is 12.6 J $\mathrm{mol}^{-1} \mathrm{~K}^{-1}$. The specific heat of helium at constant pressure in $\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$ is approximately (assume, the universal gas constant, $R=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

A composite slab is prepared with two different materials $A$ and $B$. The relation between their coefficient of thermal conductivity and thickness is given as $K_A=\frac{K_B}{2}$ and $X_A=2 X_B$, respectively. If the temperature of faces of $A$ and $B$ are $75^{\circ} \mathrm{C}$ and $50^{\circ} \mathrm{C}$ respectively, what will be the temperature of common surface?