Relation between pressure and mean kinetic energy

Relation between pressure and mean kinetic energy

From earlier section, the internal energy of the gas is given by

The above equation can also be written as

From the equation (9.12), we can state that the pressure of the gas is equal to two thirds of internal energy per unit volume or internal energy density (u=U/V).

Writing pressure in terms of mean kinetic energy density using equation (9.6)

where ρ = nm = mass density (Note n is number density)

Multiply and divide R.H.S of equation (9.13) by 2, we get

From the equation (9.14), pressure is equal to 2/3 of mean kinetic energy per unit volume.