Question

The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 K is

[IIT 1999]

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

. .

The speed of sound in a gas is given by,

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

We know that,

${\gamma }_{He}=\frac{5}{3}$

${\gamma }_{N_2}=\frac{7}{5}$

$M_{He}=4$

$M_{N_2}=28$

$\therefore \frac{V_{N_2}}{V_{He}}=\sqrt{\frac{{\gamma }_{N_2}}{{\gamma }_{He}}\times \frac{M_{He}}{M_{N_2}}}=\frac{\sqrt{3}}{5}$