A vessel contains $14 \mathrm{~g}$ of nitrogen gas at a temperature of $27^{\circ} \mathrm{C}$. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be :

Take $\mathrm{R}=8.32 \mathrm{~J} \mathrm{~mol}^{-1} \,\mathrm{k}^{-1}$.