First slide

Kinetic theory of ideal gases

Question

If V_S is velocity of sound in air, and V_R is RMS velocity of gas molecules

Moderate

A

$v_{S} > v_{R}$
B

$v_{S} = v_{R}$
C

$v_{S} = v_{R} {(\frac{γ}{3})}^{\frac{1}{2}}$
D

$v_{R} = v_{S} {(\frac{γ}{3})}^{\frac{1}{2}}$

Solution

$v_{R} = \sqrt{\frac{3 RT}{M}} v_{S} = \sqrt{\frac{γ RT}{M}}$
Hence, $v_{S} = v_{R} {(\frac{γ}{3})}^{\frac{1}{2}} < v_{R}$ .

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