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
  1. $- 73^\circ\text{C}$
  2. $27^\circ\text{C}$
  3. $127^\circ\text{C}$
  4. $327^\circ\text{C}$

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, $T = 300\text{ K} = 27^\circ\text{C}$

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