Question

When the temperature of an ideal gas is increased by $600K,$ the velocity of the sound in the gas becomes $\sqrt{3}$ times the initial velocity in it . The initial temperature of the gas is $\left(in{}^{o}C\right)$

• A. $-{73}^{0}C$
• B. ${27}^{0}C$
• C. ${127}^{0}C$
• D. ${327}^{0}C$

Answer 1

The correct option is B ${27}^{0}C$

Let, initial temperature of an ideal gas is $T$ and $v$ be the initial velocity of sound.

The speed of sound is proportional to the square root of temperature, hence as per the given condition of the problem

$v\propto \sqrt{T}$ and $\sqrt{3}v\propto \sqrt{T+600}$

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

$\therefore T=300K$

We know, $0^{\circ }C=273K$

Hence

$T=300-273={27}^{\circ }C$