One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is $4 \mathrm{~cm}^2$. The gas is heated slowly to raise the temperature by $1.2^{\circ} \mathrm{C}$ during which the piston moves by 25 mm . The amount of heat supplied to the gas is $\_\_\_\_$ J.

(Atmospheric pressure $=100 \mathrm{kPa}, R=8.3 \mathrm{~J} / \mathrm{mol} . \mathrm{K}$ ) (Neglect mass of the piston)

Initial pressure and volume of a monoatomic ideal gas are $P$ and $V$. The change in internal energy of this gas in adiabatic expansion to volume $V_{\text {final }}=27 \mathrm{~V}$ is $\_\_\_\_$ J.

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same $P, V$,

T. Heating is started from left side until pressure changes to $27 \mathrm{P} / 8$. If initial volume of each compartment was 9 litres then the final volume in right-hand side compartment is $\_\_\_\_$ litres. (for this ideal gas $\mathrm{C}_{\mathrm{P}} / \mathrm{C}_{\mathrm{V}}=1.5$ )

If 2 mole of an ideal monoatomic gas at temperature $T$, is mixed with 6 mole of another ideal monoatomic gas at temperature $2 T$ then the temperature of mixture is: