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