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) $V_{ AV }=\sqrt{\frac{8 R T}{\pi M}}$

$V_{ rms }=\sqrt{\frac{3 R T}{M}}$

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

$ \therefore $ independent of temperature

$\therefore $ True

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

$\frac{T}{T'}=\frac{3 \pi}{8}$

$T \neq T' ;$

$ \therefore $ False

(c) mean kinetic energy is

$\frac{1}{2} m v^{2}$ or $\frac{1}{2} m V_{r ms }^{2} .$

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.