Editing Ideal gas law (section)

=== Statistical mechanics ===
In [[statistical mechanics]], the following molecular equation (i.e. the ideal gas law in its theoretical form) is derived from first principles:
: <math> p = nk_\text{B}T, </math>
where {{math|''p''}} is the absolute [[pressure]] of the gas, {{math|''n''}} is the [[number density]] of the molecules (given by the ratio {{math|1=''n'' = ''N''/''V''}}, in contrast to the previous formulation in which {{math|''n''}} is the ''number of moles''), {{math|''T''}} is the [[absolute temperature]], and {{math|''k''<sub>B</sub>}} is the [[Boltzmann constant]] relating temperature and energy, given by:
: <math> k_\text{B} = \frac{R}{N_\text{A}} </math>
where {{math|''N''<sub>A</sub>}} is the [[Avogadro constant]].
The form can be furtherly simplified by defining the kinetic energy corresponding to the temperature:
: <math> T := k_\text{B}T, </math>
so the ideal gas law is more simply expressed as:
: <math> p = n \, T, </math>

From this we notice that for a gas of mass {{math|''m''}}, with an average particle mass of {{math|''μ''}} times the [[atomic mass constant]], {{math|''m''<sub>u</sub>}}, (i.e., the mass is {{math|''μ''}}&nbsp;[[Dalton (unit)|Da]]) the number of molecules will be given by
: <math> N = \frac{m}{\mu m_\text{u}}, </math>
and since {{math|1=''ρ'' = ''m''/''V'' = ''nμm''<sub>u</sub>}}, we find that the ideal gas law can be rewritten as
: <math> p = \frac{1}{V}\frac{m}{\mu m_\text{u}} k_\text{B} T = \frac{k_\text{B}}{\mu m_\text{u}} \rho T. </math>

In SI units, {{math|''p''}} is measured in [[Pascal (unit)|pascals]], {{math|''V''}} in cubic metres, {{math|''T''}} in kelvins, and {{math|1=''k''<sub>B</sub> = {{physconst|k|ref=no|round=2}}}} in [[SI unit]]s.