The ratio of the speed of sound in helium gas to that in nitrogen gas at 295 K is ( Ratio of specific heats γ for helium is 5/3 and that for nitrogen is 7/5. Molecular weight for helium and nitrogen are 4 and 28 respectively.) (a) √(2/7) (b) √(3/5) (c) √(3)/5 (d) 5/√(3)

Answer: (d). vHevN₂ = √γHeγN₂·MN₂MHe = √((5/3)/(7/5)×28/4) = √(25/21× 7) = √(25/3) So the answer is (d) 5/√(3).

The ratio of the speed of sound in helium gas to that in nitrogen gas… | MHT CET 2026 (20 Apr, Shift 1)

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Speed of Waves

The ratio of the speed of sound in helium gas to that in nitrogen gas at $295$ K is ( Ratio of specific heats $\gamma$ for helium is $\frac{5}{3}$ and that for nitrogen is $\frac{7}{5}$ . Molecular weight for helium and nitrogen are $4$ and $28$ respectively.)

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Answer: (d)

$\dfrac{v_{He}}{v_{N_2}} = \sqrt{\dfrac{\gamma_{He}}{\gamma_{N_2}}\cdot\dfrac{M_{N_2}}{M_{He}}}$
$= \sqrt{\dfrac{5/3}{7/5}\times\dfrac{28}{4}} = \sqrt{\dfrac{25}{21}\times 7} = \sqrt{\dfrac{25}{3}}$
So the answer is (d) $\dfrac{5}{\sqrt{3}}$ .

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