Two bodies ' X ' and ' Y ' at temperatures ' $\mathrm{T}_1$ ' K and ' $T_2$ ' K respectively have the same dimensions. If their emissive powers are same, the relation between their temperatures is

A lead bullet moving with velocity ' $v$ ' strikes a wall and stops. If $50 \%$ of its energy is converted into heat, then the increase in temperature is ( $s=$ specific heat of lead)

If $C_p$ and $C_v$ are molar specific heats of an ideal gas at constant pressure and volume respectively and ' $\gamma$ ' is $\mathrm{C}_{\mathrm{p}} / \mathrm{C}_{\mathrm{v}}$ then $\mathrm{C}_{\mathrm{p}}=$ ( $\mathrm{R}=$ universal gas constant)

The change in the internal energy of the mass of gas, when the volume changes from ' $V$ ' to ' 2 V ' at constant pressure ' $P$ ' is ( $\gamma$ is the ratio of specific heat of gas at constant pressure to specific heat at constant volume)