Question

On the basis of kinetic theory of gases, obtain an expression for pressure exerted by gas molecules enclosed in a container on its walls.

Hint:

The pressure in a gas is a result of the constant collisions of molecules with the walls of the container. The higher the velocity and the number of molecules, the higher the pressure.

Answer 1

Step 1: Kinetic Theory of Gases.
According to the kinetic theory of gases, gas molecules are in continuous random motion, colliding with the walls of the container. These collisions exert a force on the walls, and the pressure exerted by the gas on the walls is the average force per unit area.
Step 2: Kinetic Energy and Pressure.
The kinetic energy of a single molecule is \( \frac{1}{2} m v^2 \), where \( m \) is the mass of the molecule and \( v \) is its velocity. The rate at which a molecule strikes the walls of the container is proportional to the velocity of the molecules. The pressure \( P \) is the force per unit area. Using the kinetic theory, we derive the expression for pressure as: \[ P = \frac{1}{3} n m \overline{v^2} \] where \( n \) is the number of molecules per unit volume and \( \overline{v^2} \) is the mean square velocity.
Step 3: Conclusion.
Thus, the pressure exerted by gas molecules on the walls of the container is proportional to the number of molecules, the mass of each molecule, and the mean square velocity of the molecules.