Nitrogen gas is at 300oC temperature. The temperature (in K) at which… | JEE Main 2020 (5 Sep, Shift 2)

Q73JEE Main 2020 · 5 SEP · SHIFT 2Medium

Molecular Speeds & Maxwell Distribution

Nitrogen gas is at 300oC temperature. The temperature (in K) at which the rms speed of a H2 molecule would be equal to the rms speed of a nitrogen molecule, is _______.

(Molar mass of N2 gas 28 g).

Numerical answer type. Work it out, then open the answer.

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Answer: 40

$v_{rms} = \sqrt{\dfrac{3RT}{M}}$ ; equal speeds need $\dfrac{T_{H_2}}{M_{H_2}} = \dfrac{T_{N_2}}{M_{N_2}}$ .
$T_{N_2} = 300 + 273 = 573$ K
$T_{H_2} = 573 \times \dfrac{2}{28} = \dfrac{573}{14} \approx 40.9$ K
So the temperature is about $41$ K (key: $40$ K).

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