The ratio of the velocity of sound in hydrogen gas (γ = 7/5) to that in helium gas (γ = 5/3) at the same temperature is (a) 1: 1 (b) 7: 3 (c) 21: 25 (d) √(42): 5

Answer: (d). v = √((γ RT)/(M)); MH₂ = 2, MHe = 4 vHvHe = √(7/5/2·4/5/3) = √(7/10·12/5) = √(42/25) So the answer is (d) √(42): 5.

The ratio of the velocity of sound in hydrogen gas (γ = 7/5) to that… | MHT CET 2024 (11 May, Shift 2)

Q29MHT CET 2024 · 11 MAY · SHIFT 2Medium

Molecular Speeds & Maxwell Distribution

The ratio of the velocity of sound in hydrogen gas $\left(\gamma = \frac{7}{5}\right)$ to that in helium gas $\left(\gamma = \frac{5}{3}\right)$ at the same temperature is

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Answer: (d)

$v = \sqrt{\frac{\gamma RT}{M}}$ ; $M_{H_2} = 2$ , $M_{He} = 4$
$\frac{v_H}{v_{He}} = \sqrt{\frac{7/5}{2}\cdot\frac{4}{5/3}} = \sqrt{\frac{7}{10}\cdot\frac{12}{5}} = \sqrt{\frac{42}{25}}$
So the answer is (d) $\sqrt{42} : 5$ .

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