Question

Speed of sound in a gas is v and r.m.s. velocity of the gas molecules is c. The ratio of v to c is
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Answer 1

Answer:

Refer the below attachment.

Answer 2

The ratio of v/c = √(γ/3)

Velocity of sound in a gas = v = √(γRT/M)

γ is defined as the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume , γ = Cp/Cv .

γ = 3/2 for monoatomic gas , γ = 5/2 for diatomic gas and γ = 6/2 for triatomic gases

T - Temperature of the gas

M - molecular mass of the gas

R - the gas constant

The r.m.s Velocity of gas molecules = c = √(3RT/M)

Ratio = v/c = √(γ/3)