Question

The relation between velocity of sound in gas $\left(v\right)$ and r.m.s velocity of molecules of gas $v_{r.m.s}$ is

• A. $v=v_{r.m.s}(\gamma /3{)}^{1/2}$
• B. $v_{r.m.s}=v(2/3{)}^{1/2}$
• C. $v=v_{r.m.s}$
• D. $v=v_{r.m.s}(3/\gamma {)}^{1/2}$

Answer 1

The correct option is A $v=v_{r.m.s}(\gamma /3{)}^{1/2}$

Velocity of sound in a gas is

$v=\sqrt{\frac{\gamma P}{\rho }}$

and from $P=\frac{1}{3}\rho v_{rms}^2$

$v_{rms}=\sqrt{\frac{3P}{\rho }}$

Thus

$\frac{v}{v_{rms}}=\sqrt{\frac{\gamma }{3}}$

Ans: A