Question

In the kinetic theory of gases, which of these statements is/are true?
(i) The pressure of a gas is proportional to the mean speed of the molecules.
(ii) The root mean square speed of the molecules is proportional to the pressure.
(iii) The rate of diffusion is proportional to the mean speed of the molecules.
(iv) The mean translational kinetic energy of a gas is proportional to its Kelvin temperature.

• A. (i) and (ii) only
• B. (ii) and (iii) only
• C. (iii) and (iv) only
• D. (i) and (iii) only

Answer 1

Answer: (C)

(i) $v_{\text{mean }}=\sqrt{\frac{2P}{\rho }}$ or
$P\propto v_{\text{mean }}^2$
Hence $(i)$ is incorrect.
(ii) $v_{ms}=\sqrt{\frac{3P}{\rho }}$ or $v_{ms}\propto \sqrt{P}$
Hence $(ii)$ is incorrect.
(iii) Diffusion is proportional to the mean speed of molecules. Hence (iii) is correct.
(iv) $E_K=\frac{3}{2}\cdot kT$
$\Rightarrow E_K\propto T$ or (iv) is correct.