Question

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

• A. $\sqrt{2/7}$
• B. $\sqrt{1/7}$
• C. $\sqrt{3}/5$
• D. $\sqrt{6}/5$

Answer 1

The correct option is C $\sqrt{3}/5$

Given,

$M_{He}=4g/mol$

$M_{N_2}=28g/mol$

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

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

$T=300K$

The speed of sound in a ideal gas,

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

The ratio of speed of sound in nitrogen to speed of sound in helium is

$\frac{v_{N_2}}{v_{He}}=\sqrt{\frac{{\gamma }_{N_2}}{{\gamma }_{He}}.\frac{M_{He}}{M_{N_2}}}$

$\frac{v_{N_2}}{v_{He}}=\sqrt{\frac{7/5}{5/3}.\frac{4}{28}}$

$\frac{v_{N_2}}{v_{He}}=\frac{\sqrt{3}}{5}$

The correct option is C.