Q. When the temperature of an ideal gas is increased by $600\ K,$ the velocity of sound in the gas becomes $\sqrt{3}$ times the initial velocity in it. The initial temperature of the gas is
A) $- 73℃$
B) $27℃$
C) $127℃$
D) $327℃$
Explanation
(b) By using $v = \sqrt{\frac{\gamma RT}{M}} \Rightarrow v \propto \sqrt{T}$
$\frac{v_{2}}{v_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} = \sqrt{\frac{T + 600}{T}} = \sqrt{3} \Rightarrow T = 300\ K = 27℃$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.