Question

The ratio of the speed of sound in helium gas to that in nitrogen gas at same temperature is (γ_He = \(\frac {5}{3}\), γ_N2 = 4 , M N₂ =28)

• A. \(\frac {5}{\sqrt {3}}\)
• B. \(\sqrt{\frac {7}{5}}\)
• C. \(\sqrt{\frac {2}{7}}\)
• D. \(\sqrt{\frac {5}{3}}\)

Hint:

We know that
v = √(rRT / M)
For Helium (He) and Nitrogen (N₂), we have:
v_He / v_N2 = √(5/3RT / 4)
v_He / v_N2 = √(7/5RT / 14)
v_He / v_N2 = √(5 x 28 / 7R)
v_He / v_N2 = √(5RT / 3 x 4)
v_He / v_N2 = 5 / √3

Answer 1

The Correct Option is A

We know that
v = \(\sqrt {\frac {rRT}{M}}\)
\(\frac {v_{He}}{v_{N_2}}\) = \(\frac {\sqrt {\frac {5/3 RT}{4}}}{\sqrt {\frac {7/5 RT}{14}}}\)
\(\frac {v_{He}}{v_{N_2}}\) = \(\sqrt {\frac {5\times 28}{7R}} \sqrt {\frac {5RT}{3\times 4}}\)
\(\frac {v_{He}}{v_{N_2}}\) = \(\frac {5}{\sqrt {3}}\)
Therefore the correct option is (A) \(\frac {5}{\sqrt {3}}\)