= Ideal gas
{wiki}
= Perfect gas
{synonym}
An ideal gas is a model of a dilute <gas> whose particle centres move according to <classical mechanics> and occupy negligible <volume (thermodynamics)> compared with their container. Treating the particles as <point masses> removes the molecular-size correction; neglecting interactions between separated particles removes the intermolecular contribution to <potential energy>. The usual <kinetic theory> model retains brief <elastic collisions> with the walls and, optionally, with other particles: these transfer <momentum> while conserving the total <kinetic energy> of the colliding bodies. There is no appreciable interaction <energy> stored between <collisions>. These assumptions lead to the <ideal gas law>, $PV=Nk_BT$. https://openstax.org/books/university-physics-volume-2/pages/2-1-molecular-model-of-an-ideal-gas[OpenStax University Physics Volume 2, section 2.1: molecular model and ideal gas law]{ref} https://openstax.org/books/university-physics-volume-2/pages/2-2-pressure-temperature-and-rms-speed[OpenStax University Physics Volume 2, section 2.2: kinetic-model assumptions]{ref}
The model's attraction is its universality: at the same <temperature> and <number density>, different classical <ideal gases> have the same <pressure>, even when their particle <masses> differ. In <ideal gas pressure from wall collisions>, heavier particles move more slowly at a given <temperature>, and the two effects cancel. For example, one <mole> of any <ideal gas> at $300\,\mathrm K$ in $0.025\,\mathrm{m^3}$ has <pressure> approximately $99.774\,\mathrm{kPa}$, as computed under the <ideal gas law>.
The <ideal gas law> describes the translational contribution to <pressure>; it does not specify all of the <internal energy> or the <heat capacity>. A <monatomic gas> has three classical translational <degrees of freedom>, whereas a <gas> of <molecules> can also store <rotational kinetic energy> and <energy> in vibrational <normal modes>. An <equation of state> alone therefore does not determine how much <heat> a chosen <temperature> increase requires. It also does not select a process: <isothermal expansion> and <adiabatic expansion> need different additional constraints. https://openstax.org/books/university-physics-volume-2/pages/2-3-heat-capacity-and-equipartition-of-energy[OpenStax University Physics Volume 2, section 2.3: internal degrees of freedom and heat capacity]{ref}
A <real gas> departs from this approximation when particle size or interactions become important, especially at high <number density> or low <temperature> near a <phase transition>. The <Van der Waals equation> adds such corrections. Independently, at sufficiently low <temperature> or high <number density>, <quantum statistics> can become essential: even particles with negligible interactions need not obey the classical <ideal gas law>. The classical statistical assumption is the <nondegenerate gas> regime, which is distinct from neglecting interactions. https://openstax.org/books/university-physics-volume-2/pages/2-1-molecular-model-of-an-ideal-gas[OpenStax University Physics Volume 2, section 2.1: departures from ideal-gas behavior]{ref} <Statistical Physics by David Tong/3 Quantum Gases>{ref}
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