Q. At temperature $T,$ the $r.m.s.$ speed of helium molecules is the same as $r.m.s.$ speed of hydrogen molecules at normal temperature and pressure. The value of $T$ is
A) $273℃$
B) $546℃$
C) $0℃$
D) $136.5℃$
Explanation
(a) $v_{rms} = \sqrt{\frac{3RT}{M}} \Rightarrow T \propto M \Rightarrow \frac{T_{He}}{T_{H}} = \frac{M_{He}}{M_{H}}$
$\Rightarrow \frac{(273 + 0)}{T_{He}} = \frac{2}{4} \Rightarrow T_{He} = 546K = 273℃$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.