Explanation

(d) Root mean square velocity
$v_{rms} = \sqrt{\frac{3RT}{M}}$
where $R$ is gas constant, $T$ the temperature and $M$ molecular weight.
Given, ${M_{N}}_{2} = 28,\ \ \ \ {M_{O}}_{2} = 32,\ \ \ {T_{O}}_{2} = 127℃ = 127 + 273 = 400$ K
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{{v_{O}}_{2}}{{v_{N}}_{2}} = \sqrt{\frac{{T_{O}}_{2}}{{M_{O}}_{2}} \times \frac{{M_{N}}_{2}}{{T_{N}}_{2}}} = \sqrt{\frac{400}{32} \times \frac{28}{{T_{N}}_{2}}} = 1$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {T_{N}}_{2} = 350\ K = 77℃$.