Kinetic Energy in relation to the ideal gas law

[vjk2]

I'm trying to fit this together.

For monotomic molecules, the avg kinetic energy is 3/2 k_b T

for diatomic, it is 5/2 k_b T

PV = n_particles * k_b T

Why is there no factor of 3/2 or 5/2 in the ideal gas law? How is it factored out?

 

[cepheid]

A simple answer might be that although pressure and energy density have the same dimensions, they are not the same quantity. For an ideal gas, its pressure and its energy density are not the same. Therefore:

pressure * total volume is not equal to total energy.

energy density * total volume is equal to total energy.