Question

The $r.m.s.$ velocity of hydrogen is $\sqrt{7}$ times the $r.m.s.$ velocity of nitrogen. If $T$ is the temperature of the gas :

• A. $T\left(H_2\right)=T\left(N_2\right)$
• B. $T\left(H_2\right)>T\left(N_2\right)$
• C. $T\left(H_2\right)<T\left(N_2\right)$
• D. $T\left(H_2\right)=\sqrt{7}T\left(N_2\right)$

Answer 1

The correct option is A $T\left(H_2\right)=T\left(N_2\right)$

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

Given, $V_{rm{s}_{H_2}}=\sqrt{7}\times V_{rm{s}_{N_2}}$

$\sqrt{\frac{3RT\left(H_2\right)}{2}}=\sqrt{7}\times \sqrt{\frac{3RT\left(N_2\right)}{14}}$

$\Rightarrow T\left(H_2\right)=T\left(N_2\right)$