Question

When the temperature of an ideal gas is increased by $600\text{K}$, the speed of sound in it become $\sqrt{3}$ times the initial speed. The initial temperature of the gas is

• A. $200\text{K}$
• B. $300\text{K}$
• C. $400\text{K}$
• D. $500\text{K}$

Answer 1

The correct option is B $300\text{K}$

We know the speed of sound in a gas is given by,

$v=\sqrt{\frac{\gamma RT}{M}}$

where $\gamma$ is the adiabatic index, $R$ is universal gas constant, $T$ is absolute temperature and $M$ is molecular mass of the gas.

As the medium and the gas remain same, the only parameter that changes here is the temperature.

$\Rightarrow v\propto \sqrt{T}$

So,

$\frac{v_1}{v_2}=\sqrt{\frac{T_1}{T_2}}$

$\Rightarrow \frac{v}{\sqrt{3}v}=\sqrt{\frac{T}{T+600}}$

On solving this, we get

$T=300\text{K}$