A 15g mass of nitrogen gas is enclosed in a vessel at a...

The formula of root-mean-square speed, ${v}_{rms} = \sqrt{\dfrac{3RT}{M}}$. For doubling the ${v}_{rms},$ temperature, should be made $4$-time is, ${T}_{f} = \left(273 + 27\right)\times4K = 1200K$, the formula of, $∆ Q = ∆ U + W\left(W = 0\right)$,
$⇒ ∆ Q = ∆ U= n{C}_{V} ∆ T= \dfrac{15}{28} \times \dfrac{5}{2}$ R ∆ T$<br />$⇒ ∆ Q = $\dfrac{15}{28} \times \dfrac{5}{2} \times8.3 \times \left(1200 - 300\right)$ J\approx10KJ.$</p></blockquote>$