Consider sound waves travelling through ideal gases He, CH₄ and CO₂. All gases have the same value of P/ρ. The ratio VHe : VCH₄ : VCO₂ is:
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Question

Consider sound waves travelling through ideal gases He, CH₄ and CO₂. All gases have the same value of P/ρ. The ratio VHe : VCH₄ : VCO₂ is:

G1 Physics · Accepted Answer

Speed of sound in an ideal gas is v = √(γP/ρ). Since P/ρ is the same for all three gases, v ∝ √γ. For He, a monatomic gas: γ = 5/3. For CH₄, treated as a non-linear polyatomic gas in this question: γ = 4/3. For CO₂, a linear molecule: γ = 7/5. Therefore, VHe : VCH₄ : VCO₂ = √(5/3) : √(4/3) : √(7/5). Correct option: A.