Q. At what temperature is the root mean square velocity of gaseous hydrogen molecules equal to that of oxygen molecules at $47℃$
A) $20\ K$
B) $80\ K$
C) $- 73\ K$
D) $3\ K$
Explanation
(a) $v_{rms} = \sqrt{\frac{3RT}{M}} \Rightarrow T \propto M\ \ \ \lbrack\because v_{rms},R \rightarrow constant\rbrack$
$\frac{T_{H_{2}}}{T_{O_{2}}} = \frac{M_{H_{2}}}{M_{o_{2}}} = \frac{T_{H_{2}}}{(273 + 47)} = \frac{2}{32} \Rightarrow T_{H_{2}} = 20K$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.