Consider the sound wave travelling in ideal gases of He, CH₄, and CO₂. All the gases have the same ratio P/ρ, where P is the pressure and ρ is the density. The ratio of the speed of sound through the gases VHe: VCH₄: VCO₂ is given by (a) √(7/5): √(5/3): √(4/3) (b) √(5/3): √(4/3): √(4/3) (c) √(5/3): √(4/3): √(7/5) (d) √(4/3): √(5/3): √(7/5)

Answer: (c). v = √((γ P)/(ρ)); same P/ρ, so v ∝ √γ He (monatomic) γ = 5/3; CH ₄ (non-linear polyatomic) γ = 4/3; CO ₂ (linear, taken like diatomic) γ = 7/5 So the answer is (c) √(5/3): √(4/3): √(7/5).

Consider the sound wave travelling in ideal gases of He, CH₄, and… | JEE Main 2025 (4 Apr, Shift 1)

Q21JEE Main 2025 · 4 APR · SHIFT 1Medium

Molecular Speeds & Maxwell Distribution

Consider the sound wave travelling in ideal gases of $\text{He, CH}_4$ , and $\text{CO}_2$ . All the gases have the same ratio $\frac{P}{\rho}$ , where $P$ is the pressure and $\rho$ is the density. The ratio of the speed of sound through the gases $V_{\text{He}} : V_{\text{CH}_4} : V_{\text{CO}_2}$ is given by

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Answer: (c)

$v = \sqrt{\frac{\gamma P}{\rho}}$ ; same $\frac{P}{\rho}$ , so $v \propto \sqrt\gamma$
He (monatomic) $\gamma = \frac{5}{3}$ ; CH $_4$ (non-linear polyatomic) $\gamma = \frac{4}{3}$ ; CO $_2$ (linear, taken like diatomic) $\gamma = \frac{7}{5}$
So the answer is (c) $\sqrt{\frac{5}{3}} : \sqrt{\frac{4}{3}} : \sqrt{\frac{7}{5}}$ .

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