# Kinetic Theory of Gases

Pressure is caused by the constant bombardment of the many individual molecules of a gas.

The ideal gas law can be explained by the constant bombardment of the many individual molecules of a gas.

Pressure is caused by the collisions of gas molecules with the walls of the container holding the gas.

Assume one-third of the molecules move along the x-axis at constant speed v.

This is the average force exerted by each single molecule. But we have N/3 molecules hitting this wall. Therefore, the total force on the wall is

Now, to get the pressure. Remember, in our simplified model, we are looking at a cube with edge length L,

P V = (1/3) N m v2

The kinetic energy of each molecule is KE = (1/2) m v2 so we can rewrite this as

P V = (2/3) N (1/2) m v2

P V = N k T

so this means

(2/3) N (1/2) m v2 = N k T

or

(1/2) m v2 = (3/2) k T

Let us replace our constant speed v with an average speed <v>,

(1/2) m <v>2 = (3/2) k T

(1/2) m <v>2 = Eint

Eint, tot = N (3/2) k T

Eint, tot = (3/2) N k T = (3/2) n R T