When the temperature of an ideal gas is increased by $600\text{ K}$, the velocity of sound in the gas become…
When the temperature of an ideal gas is increased by $600\text{ K}$, the velocity of sound in the gas become $\sqrt{3}$ times the initial velocity in it. The initial temperature of the gas is
$- 73^\circ\text{C}$
$27^\circ\text{C}$
$127^\circ\text{C}$
$327^\circ\text{C}$
Solution
Velocity of sound in gas, $v = \sqrt{\frac{\gamma RT}{M}} \Rightarrow v \propto \sqrt{T}$
$\because \frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{T + 600}{T}} = \sqrt{3}$
The initial temperature of the gas, $T = 300\text{ K} = 27^\circ\text{C}$