Question

The RMS velocity of hydrogen is $\sqrt{7}$ times the RMS velocity of nitrogen. If $T$ is the temperature of 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

Answer: (C)

$T_{\left(H_2\right)}<T_{\left(N_2\right)}$

The expression for the root mean square velocity is $U_{rms}=\sqrt{\frac{3RT}{M}}$.

For hydrogen and nitrogen, the ratio of their root mean velocities is $\Rightarrow \frac{u_{rms}\left(H_2\right)}{u_{rms}\left(N_2\right)}=\sqrt{7}=\sqrt{\frac{T\left(H_2\right)}{2}\times \frac{28}{T\left(N_2\right)}}$.

Hence, $7=\frac{14T\left(H_2\right)}{T\left(N_2\right)}$.

Thus, $\Rightarrow T\left(N_2\right)=2T\left(H_2\right),i.e.,T\left(H_2\right)<T\left(N_2\right)$.