Nitrogen gas is at $300^{\circ}$C temperature. The temperature (in K) at which the rms speed of a $\mathrm{H}_{2}$ molecule would be equal to the rms speed of a nitrogen molecule, is ____. (Molar mass of $\mathrm{N}_{2}$ gas 28 g).

JEE Main · 2020 · 05 Sep 2020 · Shift 2 · Heat & Thermodynamics

Nitrogen gas is at

30 0^{\circ}

C 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).

Answer: 40.93

Solution

Equal rms speeds require

\frac{3 R T _{N_{2}}}{M _{N_{2}}} = \frac{3 R T _{H_{2}}}{M _{H_{2}}}

, which reduces to

\frac{T _{N_{2}}}{M _{N_{2}}} = \frac{T _{H_{2}}}{M _{H_{2}}}

. The nitrogen is at

30 0^{\circ}

= 573

K with

M_{N_{2}} = 28

g/mol, and hydrogen has

M_{H_{2}} = 2

g/mol, so

T_{H_{2}} = 573 \times \frac{2}{28} = 40.93

JEE Main · 2020 · 05 Sep 2020 · Shift 2 · Numerical answer

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