Question

If nrms is the rms speed of molecules in a gas and n is the speed of sound waves in the gas, then the ratio $\frac{\nu_{rms}}{\nu}$ is

• A. $\sqrt{\frac{3}{\gamma}}$
• B. $\sqrt{\frac{\gamma}{3}}$
• C. $\sqrt{3\gamma}$
• D. $\frac{\sqrt{3}}{\gamma}$

Answer 1

Answer: (A)

$\sqrt{\frac{3}{\gamma}}$

Answer 2

rms speed of gas molecules is

$v_{rms}\sqrt{\frac{3P}{\rho}}$ ….. (i)

Speed of sound in the gas is

$v = \sqrt{\frac{\gamma P}{\rho}}$ ….. (ii)

Divide (i) by (ii),we get

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