A vessel contains 14g of nitrogen gas at a temperature of 27 ° C ....

The RMS speed of a gas at a given temperature is given by, ${v}_{rms} = \sqrt{\dfrac{3RT}{M}}$.

Therefore, to double the RMS speed, the temperature should be increased to four times the initial temperature. Therefore,

${T}_{f} = 1200K, {T}_{i} = 300K, \text{and}n = \dfrac{14}{28} = \dfrac{1}{2}$

The volume of the vessel will remain the same therefore, the process is an isochoric process. Therefore,

$Q = n{C}_{v}\DeltaT = \dfrac{1}{2} \times \dfrac{5R}{2} \times 900$

$⇒ Q = 9360J$