0 . 056kg of Nitrogen is enclosed in a vessel at a temperature of...

The RMS speed of the molecule is given by ${v}_{RMS} = \sqrt{\dfrac{3RT}{M}}$. Therefore, to double the speed the temperature must become $4$ times.

Therefore, the change in the temperature is $∆ T = 3{T}_{0}$.

Now the process is isochoric (enclosed vessel) therefore, the heat required will be,

$H = n{C}_{v} ∆ T ⇒ H = \dfrac{56}{28} \times \dfrac{5}{2}R \times 3 \times \left(273 + 127\right) = 12000cal = 12kcal$