Q. The rms speed of hydrogen is $\sqrt{7}$ times the rms speed of nitrogen. If $T$ is the temperature of the gas, then
A) ${T_{H}}_{2} = {T_{N}}_{2}$
B) ${T_{H}}_{2} > {T_{N}}_{2}$
C) ${T_{H}}_{2} < {T_{N}}_{2}$
D) ${T_{H}}_{2} = \sqrt{7}{T_{N}}_{2}$
Explanation
(b)
We know that
$u_{rms} = \sqrt{\frac{3RT}{M}}$
$\therefore\ u_{rms}$ of hydrogen is more than the $u_{rms}$ of nitrogen, thus its temperature is also greater than nitrogen
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.