Q. When temperature of an ideal gas is increased from $27℃$ to $227℃,$ its $r.m.s.$ speed changed from 400 $metre/s$ to $V_{s}.$ The $V_{s}$ is
A) $516\ metre/s$
B) $450\ metre/s$
C) $310\ metre/s$
D) $746\ metre/s$
Explanation
(a) $\frac{v_{2}}{v_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} \Rightarrow \frac{v_{S}}{400} = \sqrt{\frac{(273 + 227)}{(273 + 27)}} = \sqrt{\frac{5}{3}}$
$\Rightarrow v_{s} = 400\sqrt{5/3} = 516m/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.