What is the ratio of the velocity of sound in hydrogen (γ = 7/5) to that in helium (γ = 5/3) at the same temperature? (Molecular weight of hydrogen and helium is 2 and 4 respectively.) (a) (√(42))/(5) (b) (5)/(√(42)) (c) (√(21))/(5) (d) (5)/(√(21))

Answer: (a). v = √((γ RT)/(M)) at the same T vHvHe = √((7/5)/(5/3)·4/2) = √(21/25· 2) = (√(42))/(5) So the answer is (a) (√(42))/(5).

What is the ratio of the velocity of sound in hydrogen (γ = 7/5) to… | MHT CET 2021 (21 Sep, Shift 2)

Q68MHT CET 2021 · 21 SEP · SHIFT 2Medium

Molecular Speeds & Maxwell Distribution

What is the ratio of the velocity of sound in hydrogen $\left(\gamma = \frac{7}{5}\right)$ to that in helium $\left(\gamma = \frac{5}{3}\right)$ at the same temperature? (Molecular weight of hydrogen and helium is 2 and 4 respectively.)

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Answer: (a)

$v = \sqrt{\frac{\gamma RT}{M}}$ at the same $T$
$\frac{v_H}{v_{He}} = \sqrt{\frac{7/5}{5/3}\cdot\frac{4}{2}} = \sqrt{\frac{21}{25}\cdot 2} = \frac{\sqrt{42}}{5}$
So the answer is (a) $\frac{\sqrt{42}}{5}$ .

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Molecular Speeds & Maxwell Distribution question from MHT CET 2021 (21 Sep, Shift 2)

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