Editing Ideal gas (section)

=== Microscopic model ===

In order to switch from macroscopic quantities (left hand side of the following equation) to microscopic ones (right hand side), we use
: <math>nR=N k_\mathrm{B}</math>
where
* <math>N</math> is the number of gas particles
* <math>k_\mathrm{B}</math> is the [[Boltzmann constant]] ({{val|1.381|e=−23|u=J·K<sup>−1</sup>}}).

The probability distribution of particles by velocity or energy is given by the [[Maxwell speed distribution]].

The ideal gas model depends on the following assumptions:
* The molecules of the gas are indistinguishable, small, hard spheres
* All collisions are elastic and all motion is frictionless (no energy loss in motion or collision)
* Newton's laws apply
* The average distance between molecules is much larger than the size of the molecules
* The molecules are constantly moving in random directions with a distribution of speeds
* There are no attractive or repulsive forces between the molecules apart from those that determine their point-like collisions
* The only forces between the gas molecules and the surroundings are those that determine the point-like collisions of the molecules with the walls
* In the simplest case, there are no long-range forces between the molecules of the gas and the surroundings.

The assumption of spherical particles is necessary so that there are no rotational modes allowed, unlike in a diatomic gas. The following three assumptions are very related: molecules are hard, collisions are elastic, and there are no inter-molecular forces. The assumption that the space between particles is much larger than the particles themselves is of paramount importance, and explains why the ideal gas approximation fails at high pressures.