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Q.

In a mixture of gases, the average number of freedom per molecule is 6. The r.m.s. speed of the molecules of the gas is C. The velocity of sound in the gas is

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a

$2 C / 3$

b

$C / \sqrt{2}$

c

$C / \sqrt{3}$

d

$3 C / 4$

answer is C.

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Detailed Solution

we know that $γ = 1 + (2 / f)$ where f =degrees of freedom

$∴ γ = 1 + \frac{2}{6} = \frac{8}{6} = \frac{4}{3} Further rrms = \sqrt{(\frac{3 RT}{M_{0}})} = C and v_{s} = \sqrt{(\frac{γRT}{M_{0}})} Dividing eq (2) by eq (1) we get \frac{V_{S}}{C} = \sqrt{(\frac{γ}{3})} = \sqrt{(\frac{4}{3 \times 3})} = \frac{2}{3} or v_{s} = 2 C / 3$

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