Kinetic theory of ideal gases

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Question

Nitrogen gas is at 300ºC temperature. The temperature (in K) at which the rms speed of a $H_{2}$ molecule would be equal to the rms speed of a nitrogen molecule, is____.
(Molar mass of $N_{2}$ gas 28 g).

Easy

Solution

Let T is the temperature of $H_{2}$ gas
$\begin{array}{l} G i v e n : V_{H_{2}} = V_{N_{2}} \\ \Rightarrow \sqrt{\frac{3 R T}{M_{H_{2}}}} = \sqrt{\frac{3 R (273 + 300)}{M_{N_{2}}}} \\ \Rightarrow T = \frac{573}{28} \times 2 = \frac{573}{14} = 40.93 K \end{array}$

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