Q. By what ratio the average velocity of the molecule in a gas change when the temperature is raised from 50 to $200℃$?
A) $\frac{1.21}{1}$
B) $\frac{1.46}{1}$
C) $\frac{1.14}{1}$
D) $\frac{4}{1}$
Explanation
(c)
$\frac{\left( v_{av} \right)_{1}}{\left( v_{av} \right)_{2}} = \sqrt{\frac{T_{1}}{T_{2}}}$
Given, $T_{1} = 150 + 273 = 423\ K$
$T_{2} = 50 + 273 = 323\ K$
$\therefore\ \frac{\left( v_{av} \right)_{1}}{\left( v_{av} \right)_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} = \sqrt{\frac{423}{323}} = \frac{1.14}{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.