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  • 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. The velocity of sound in the gas is   

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. The velocity of sound in the gas is 

 

Option: 1

\frac{C}{\sqrt{3}}


Option: 2

\frac{C}{\sqrt{2}}


Option: 3

\frac{2 C}{3}


Option: 4

\frac{3C}{3}


Answers (1)

best_answer

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

\therefore \frac{V_{\text {sound }}}{V_{\text {rms }}}=\sqrt{\frac{\gamma}{3}}

Degree of freed om is 6 .

\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}
 

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