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 molecules. (iv) The mean translational kinetic energy of a gas is proportional to its kelvin temperature.

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

Hint:

Always remember: kinetic energy depends only on absolute temperature.

Answer 1

The Correct Option is D

Step 1: Pressure of a gas is proportional to the mean square speed, not mean speed ⇒ (i) false.
Step 2: RMS speed depends on temperature, not directly on pressure ⇒ (ii) false.
Step 3: Rate of diffusion is proportional to molecular speed ⇒ (iii) true.
Step 4: Mean translational kinetic energy \(\propto T\) ⇒ (iv) true.