Chapter 22, Problem 28A

A friend says that, in a mixture of gases in thermal equilibrium, the molecules have the same average speed. Do you agree or disagree? Defend your answer.

To determine

To explain: If the molecules in a mixture of gases at thermal equilibrium have the same average speed.

Explanation of Solution

Introduction:

Kinetic energy is given by,

  $\text{KE}=\frac{1}{2}m{v}^2$

Hence, kinetic energy depends on mass and speed of a body.

If a mixture is at thermal equilibrium, all gases have the same temperature and hence same kinetic energy. But different gases have different mass. For gases with different masses to have the same kinetic energy, velocity changes accordingly. Lighter gases have greater velocity while heavier gases have slower velocity for kinetic energy to be same.

Conclusion:

The molecules in a mixture of gases at thermal equilibrium do not have the same average speed.