Explanation

(a) $v_{rms} \propto \sqrt{T}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{v_{1}^{2}}{v_{2}^{2}} = \frac{T_{1}}{T_{2}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{v^{2}}{2v^{2}} = \frac{273}{T_{2}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T_{2} = 1092$ K
=819$℃$