Two ideal gases at the same absolute temperature have adiabatic indices γ₁ and γ₂ and molar masses M₁ and M₂. Their sound speeds are v₁ and v₂. Which relation is correct?
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Question

Two ideal gases at the same absolute temperature have adiabatic indices γ₁ and γ₂ and molar masses M₁ and M₂. Their sound speeds are v₁ and v₂. Which relation is correct?

G1 Physics · Accepted Answer

For an ideal gas, v = √(γRT/M). At the same temperature, v₁/v₂ = √[(γ₁/M₁)/(γ₂/M₂)]. Therefore, v₁/v₂ = √(γ₁M₂/(γ₂M₁)). Correct option: B.