Question

Which of the following statements is not true?

• A. the ratio of the mean speed to the rms speed is independent of the temperature.
• B. the square of the mean speed of the molecules is equal to the square of rms speed at a certain temperature.
• C. mean kinetic energy of the gas molecules at any given temperature is independent of the mean speed.
• D. the difference between rms speed and mean speed at any temperature for different gases diminishes as larger and yet larger molar masses are considered.

Answer 1

Answer: (B)

(a) $V_{AV}=\sqrt{\frac{8RT}{\pi M}}$

$V_{rms}=\sqrt{\frac{3RT}{M}}$

$\frac{V_{av}}{V_{rms}}=\frac{\sqrt{8/\pi }}{\sqrt{3}}$,

$\therefore$ independent of temperature

$\therefore$ True

(b) $\frac{8RT}{\pi M}=\frac{3RT}{M}$

$\frac{T}{T^{\prime }}=\frac{3\pi }{8}$

$T\ne T^{\prime };$

$\therefore$ False

(c) mean kinetic energy is

$\frac{1}{2}m{v}^2$ or $\frac{1}{2}m{V}_{rms}^2.$

When we change $V_{\text{av }}{V}_{\text{rms }}$ gets effected

$\therefore$ True

(d) True. This is because molecular weight occurs in the denominator of the expression.