Question

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

• A. $T_{N_2} =T_{H_2}$
• B. $T_{H_2} =\sqrt {7} T_{N_2}$
• C. $T \left( H _{2}\right)< T \left( N _{2}\right)$
• D. $T_{N_2} =\sqrt {7} T_{H_2}$

Answer 1

The Correct Option is C

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. $u \propto \sqrt{ T }$
$
\begin{array}{l}
\sqrt{ T _{ H _{2}}}=\sqrt{7} \sqrt{ T _{ N 2}} \\
T _{ H _{2}}=7 T _{ N _{2}} \\
T _{ H _{2}}> T _{ N _{2}}
\end{array}
$