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Set up a relation between speed of sound in a gas and root mean square velocity of the molecules of that gas. |
Answer» Speed of sound in a gas is \(v=\sqrt{\frac{\gamma P}{ρ}}\) …(i) According to kinetic theory of gases, root mean square velocity (c) of molecules of gas is obtained from the relation \(P=\frac{1}{3}ρc^2,\) \(c = \sqrt{\frac {3P}{ρ}}\) …(ii) Dividing (i) by (ii), \(\frac{v}{c}=\sqrt{\frac{\gamma}{3}}\) Or \(v=c \sqrt{\frac{\gamma}{3}}\) This is the required solution. |
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