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)

The square of the mean speed of the molecules is equal to the square of rms speed at a certain temperature.

Answer 2

(i) V_AV= $\sqrt{\frac{8RT}{\pi M}}$

V_rms = $\sqrt{\frac{3RT}{M}}$

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

∴ independent of temperature

∴ True

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

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

T≠T′; ∴False

(iii) mean kinetic energy is $\frac{1}{2}mv^{2}$or $\frac{1}{2}$m V²_rms. When we change V_av, V_rms gets effected

∴ True

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