The RMS speed of a gas at a given temperature is given by, vrms=M3RT.
Therefore, to double the RMS speed, the temperature should be increased to four times the initial temperature. Therefore,
Tf=1200K,Ti=300K,andn=2814=21
The volume of the vessel will remain the same therefore, the process is an isochoric process. Therefore,
Q=nCvΔT=21×25R×900
⇒Q=9360J