Q. The temperature of an ideal gas is increased from $27℃$ to $927℃.$ The root mean square speed of its molecules becomes
A) Twice
B) Half
C) Four times
D) One-fourth
Explanation
(a) $v_{rms} \propto \sqrt{T},\frac{v_{2}}{v_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} \Rightarrow v_{2} = \sqrt{\frac{(273 + 927)}{(273 + 27)}}v_{1} \Rightarrow v_{2} = 2v_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.