Boltzmann constant and Ek

Remember:.

pV = nRT

Where:.

n = number of moles of gas

and

R = universal molar gas constant.

Boltzmann decided it would be useful if we know what the gas constant was per molecule, not per mole. He came up with a new constant - named the Boltzmann constant, of course - which was:

Where:.

k = the Boltzmann constant

R = the universal molar gas constant

N_A = Avogadro's number, the number of particles in one mole.

Then it was possible to rewrite

pV = nRT

as

pV = NkT

Where:.

N = no of atoms or molecules involved.

If you combine

and

pV = NkT

to give

or, in words

The average E_k of the particles = a constant x temperature (in kelvin).

This confirms what we've mentioned a number of times in this section, that the temperature of a gas depends only on the Ek of the molecules that make it up.