A vessel contains hydrogen and nitrogen gases in the ratio $2: 3$ by mass. If the temperature of the mixture of the gases is $30^{\circ} \mathrm{C}$, then the ratio of the average kinetic energies per molecule of hydrogen and nitrogen gases is (Molecular mass of hydrogen $=2$ and molecular mass of nitrogen $=28$ )

When 54 g of ice at $-20^{\circ} \mathrm{C}$ is mixed with 25 g of steam at $100^{\circ} \mathrm{C}$, then the final mixture at thermal equilibrium contains

A solid sphere at a temperature $T \mathrm{~K}$ is cut in to two hemisphere. The ratio of energies radiated by one hemisphere to the whole sphere per second is

If $d Q, d U$ and $d W$ are heat energy absorbed, change in internal energy and external work done respectively by a diatomic gas at constant pressure, then $d W: d U: d Q$ is