Question

The rms velocity of hydrogen is $\sqrt{7}$ times the rms velocity 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

Answer: (C)

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

The rms velocity of hydrogen is $\sqrt{7}$ times the rms velocity nitrogen.
$u_{H_2}=\sqrt{7}{u}_{N_2}$
The rms velocity of a gas is directly proportional to square root of temperatue.
$u\propto \sqrt{T}$
$\sqrt{T_{H_2}}=\sqrt{7}\sqrt{T_{N2}}$
$T_{H_2}=7T_{N_2}$
$T_{H_2}>T_{N_2}$