Question

When the temperature of an ideal gas increased by 300 K the velocity of sound in the gas becomes $\sqrt{2}$ times its initial velocity in it. The initial temperature is:

• A. 73${}^o$c
• B. 27${}^o$C
• C. 127${}^o$C
• D. 327${}^o$C

Answer 1

Answer: (B)

27${}^o$C

Since $\nu \propto \sqrt{T}$

By problem:

$\frac{\sqrt{2}\nu }{\nu }=\sqrt{\frac{t+300}{t}}$

$\sqrt{2}=\sqrt{\frac{t+300}{t}}$

$2t=t+300$

$t=300k$

$t=(300-273{)}^{\circ }C$ $(\because 273+tk=t^{\circ }C)$

$={27}^{\circ }C$