Question

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

(a) √(2/7)

(b) √(1/7)

(c) √3/5

(d) √6/5

This question was posed to me in an international level competition.

I need to ask this question from Kinetic Theory of Gases topic in chapter Kinetic Theory of Gases of Engineering Physics I

Answer 1

The correct option is (c) √3/5

Best explanation: v=\(\sqrt{\frac{γRT}{M}} \)

\(\frac{v(N_2)}{v(He)} = \sqrt{\frac{γ_{N_2}}{γ_{He}} \times \frac{M_{He}}{M_{N_2}}}=\sqrt{\frac{\frac{7}{5}}{\frac{5}{3}}×\frac{4}{28}}=\frac{\sqrt{3}}{5} \)