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The formula v = √(P/ρ) can be used for any gas considering isothermal process. True or False?

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The formula v = √(P/ρ) can be used for any gas considering isothermal process. True or False?

(a) True

(b) False

This question was posed to me in exam.

This question is from Speed of a Travelling Wave in chapter Waves of Physics – Class 11

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Right option is (b) False

The best I can explain: Speed of longitudinal waves is v = √(B/ρ), where B is bulk modulus.

For an isothermal process PV=const.

On differentiating, we get: PdV + VdP = 0.

∴ P = -dP/(dV/V) = B.

∴ v = √(B/ρ) = √(P/ρ).

We have used the ideal gas equation, so this is only valid for an ideal gas.

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