Question

The rms velocity of hydrogen is $\sqrt{7}$ times the rms velocity of nitrogen. If $T$ is the temperature of the gas, then

• 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 C $T\left(H_2\right)<T\left(N_2\right)$

$U_{\text{rms}}=\sqrt{\frac{3RT}{M}}\Rightarrow \sqrt{7}\sqrt{\frac{3R{T}_{N_2}}{28}}=\sqrt{\frac{3R{T}_{H_2}}{2}}$
(given in the question)

$\therefore T_{N_2}=\sqrt{2}{T}_{H_2}$
$\Rightarrow T_{N_2}>T_{H_2}$