Question

Which of the following statements is/are true?

• A. The ratio of the mean speed to the rms speed is independent of temperature of gas
• B. The square of the mean speed of the molecules is equal to the root mean square speed at a certain temperature
• C. Mean translational kinetic energy of the gas molecules at any given temperature is independent of the molecular mass of gas
• D. The square of the mean speed of the molecules is equal to the $u_{av}^2=\frac{8RT}{\pi M}$ at a certain temperature

Answer 1

Answer: (A), (C), (D)

The correct options are
A The ratio of the mean speed to the rms speed is independent of temperature of gas
C Mean translational kinetic energy of the gas molecules at any given temperature is independent of the molecular mass of gas
D The square of the mean speed of the molecules is equal to the $u_{av}^2=\frac{8RT}{\pi M}$ at a certain temperature

a)
$\frac{u_{av}}{u_{rms}}$ =$\frac{\sqrt{\frac{8RT}{\pi M}}}{\sqrt{\frac{3RT}{M}}}$ = $\sqrt{\frac{8}{3\pi }}$
Hence, ratio of the mean speed to the rms speed is independent of temperature of gas.
b), d)
$u_{av}^2$ =$\frac{8RT}{\pi M}\ne$ $\sqrt{\frac{3RT}{M}}$
$u_{av}^2\ne u_{rms}$
c)
Average KE = $\frac{3RT}{2}$
Hence, it is independent of molar mass of gas.