A vessel contains $14 \mathrm{~g} of nitrogen gas at a temperature of 27^{\circ} \mathrm{C}. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be :
Take \mathrm{R}=8.32 \mathrm{~J} \mathrm{~mol}^{-1} \,\mathrm{k}^{-1}$.