Physics - Heat & Thermo Question with Solution | TestHub

Given,

Temperature of Nitrogen gas is 

$T_1=300 °\mathrm{C}=300+273=573 \mathrm{K}$

Molar mass of ${\mathrm{H}}_2$ gas is $M_{H_2}=2 \mathrm{g}$

Molar mass of ${\mathrm{N}}_2$ gas is $M_{N_2}=28 \mathrm{g}$

The rms speed of gas is given by

 $V_{\mathrm{rms}}=\sqrt{\frac{3\mathrm{RT}}{\mathrm{M}}}$

Now rms speed of hydrogen gas is equal to rms speed of nitrogen gas, i.e.; ${\left(V_{rms}\right)}_{H_2}={\left(V_{rms}\right)}_{N_2}$
$\Rightarrow \frac{T_{H_2}}{T_{N_2}}=\frac{M_{H_2}}{M_{N_2}}$

Substitute the given values i above equation, we get,

$T_{H_2}=\frac{2}{28}\times 573$

$T_{H_2}=41 \mathrm{K}$