Question

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

• A. $T(H_2) = T(N_2)$
• B. $T(H_3) > T(N_2)$
• C. $T(H_2)< T (N_2)$
• D. $T(H_2) = \sqrt{7}T(N_2)$

Answer 1

Answer: (C)

$T(H_2)< T (N_2)$

Answer 2

Root mean square speed $U_{rms}=\sqrt{\frac{3RT}{M}}$
$\Rightarrow \, \, \, \, \, \, \, \, \, \frac{u_{rms}(H_2)}{u_{rms}(N_2)}=\sqrt{7}=\sqrt{\frac{T(H_2)}{2}times\frac{28}{T(N_2)}}$
$\Rightarrow \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, 7=\frac{14 T(H_2)}{T(N_2)}$
$\Rightarrow \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, T (N_2) = 2T (H_2)$
$i.e. \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, T(H_2) < T (N_2)$