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BITSAT 2024

Exam: BITSAT
Year: 2024
Subject: Physics
Chapter: Kinetic Theory of Gases

BITSAT 2024 · Physics · Kinetic Theory of Gases

In a mixture of gases, the average number of degree of freedoms per...

In a mixture of gases, the average number of degree of freedoms per molecule is 6. The rms speed of the molecule of the gas is

c

, then the velocity of sound in the gas is

Options

A $\frac{c}{\sqrt{3}}$
B $\frac{c}{\sqrt{2}}$
C $\frac{2 c}{3}$
D $\frac{3 c}{3}$

Correct answer

C. $\frac{2 c}{3}$

Step-by-step solution

(

v_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}}

and

v_{\text{sound }}=\sqrt{\frac{\gamma R T}{M}}\frac{v_{\text{sound }}}{v_{\text{rms }}}=\sqrt{\frac{\gamma}{3}}

Degree of freedom is 6 .

\begin{array}{lr} \therefore & \gamma=1+\frac{2}{f}=1+\frac{2}{6}=\frac{4}{3} \\ \therefore & v_{\text{sound }}=\sqrt{\frac{4 / 3}{3}} v_{\text{rms }}=\frac{2}{3} v_{\text{rms }}=\frac{2 c}{3} \end{array}

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