Q. At which temperature the velocity of $O_{2}$ molecules will be equal to the velocity of $N_{2}$ molecules at $0℃$
A) $40℃$
B) $93℃$
C) $39℃$
D) Cannot be calculated
Explanation
(c) $v_{rms} = \sqrt{\frac{3RT}{M}} \Rightarrow T \propto M\ \ \ \lbrack\because v_{rms},R \rightarrow constant\rbrack$
$\Rightarrow \frac{T_{O_{2}}}{T_{N_{2}}} = \frac{M_{O_{2}}}{M_{N_{2}}} \Rightarrow \frac{T_{O_{2}}}{(273 + 0)} = \frac{32}{28} \Rightarrow T_{O_{2}} = 312K = 39℃$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.