0.014 kg of nitrogen is enclosed in a vessel at a temperature of 27 °C. Find the amount of heat energy to be supplied to the gas to double the rms speed of its molecules.

The root mean square speed is related to absolute temperature T ascrms=3kTmFor a given gas, m is fixed. Therefore, crms∝T. Hence in order to double the root mean square speed, the absolute temperature must be increased to four times the initial value. Initial temperature T1=273+27=300K. Therefore, final temperature T2=4T1=1200K.Since the volume of the vessel is fixed, ∆V = 0. Hence the heat energy supplied to the gas does no work on the gas; it only increases the internal energy of the molecules.ΔU=nCvdT =mM×5R2×T2-T1 =0.014×10328×5×8.3142×1200-300 =9353J