Question

When the temperature of a gas T is increased by 400 kelvin, the velocity of sound in the gas becomes $2^{\frac{1}{2}}$ times the velocity at initial temperature T. Find the value of T.

• A. 15 deg C
• B. 273 deg C
• C. 127 deg C
• D. 75 deg C

Answer 1

The correct option is C 127 deg C

We know,
$T\propto v^2$
$T_1=Tand{T}_2=T+400$
$\Rightarrow \frac{T_1}{V_1^2}=\frac{T_2}{V_2^2}$
$V_1=Vand{V}_2=\sqrt{2}V$
$\Rightarrow \frac{T}{V^2}=\frac{T+400}{2V^2}\Rightarrow 2T-T=400\Rightarrow T=400k\Rightarrow T={127}^{\circ }C$.