# Boltzmann constant and Ek

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## 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.