An ideal gas expands adiabatically, $(\gamma=1.5)$. To reduce the r.m.s. velocity of the molecules 4 times, the gas has to be expanded

The temperature at which oxygen molecules will have same r.m.s. speed as helium molecules at $57^{\circ} \mathrm{C}$ is (molecular masses of oxygen and helium are 32 and 4 respectively.)

Two black spheres $\mathrm{P} \& \mathrm{Q}$ have radii in the ratio $4: 3$. The wavelength of maximum intensity of radiation are in the ratio $4: 5$ respectively. The ratio of radiated power by P to Q is

The heat energy that must be supplied to 14 gram of nitrogen at room temperature to raise its temperature by $48^{\circ} \mathrm{C}$ at constant pressure is (Molecular weight of nitrogen $=28, R=$ gas constant, $\mathrm{C}_{\mathrm{p}}=\frac{7}{2} \mathrm{R}$ for diatomic gas)