Relation between pressure and Kinetic energy

we know that work done equals the change in kinetic energy

so,

W = dE

and work done is also equal to the produce of pressure and change in volume. So,

W = P.dV

thus, from (1) and (2), we get

dE = P.dV

or pressure

P = dE/dV

which is proportional the change of energy with volume