# Ideal gas

An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of negligible volume, with no intermolecular forces. Additionally, the constituent atoms or molecules undergo perfectly elastic collisions wih the walls of the container. The real gases that actually exist do not exhibit these exact properties, although the approximation is often good enough to treat real gases as ideal gases.

There are basically three types of ideal gas:

## Classical ideal gas

The equation of state of a classical ideal gas is the ideal gas law. The internal energy of an ideal monatomic gas consists entirely of the translational kinetic energy of its particles. The total internal energy of a monatomic ideal gas is therefore simply:

[itex]U = \frac{3}{2}nRT = \frac{3}{2}NkT[itex]

where U is internal energy,

n is the number of particles in moles,

R is the ideal gas constant,

T is the absolute temperature,

N is the number of particles,

and k is the Boltzmann constant.

The probability distribution of particles by velocity or energy is given by the Boltzmann distribution.

The ideal gas law is an extension of primitive experimentally discovered gas laws. While, strictly speaking, only an ideal gas obeys these gas laws exactly, at low density and high temperature, real fluids roughly approximate the behavior of a classical ideal gas. However, at lower temperature or higher density, a real fluid deviates strongly from the behavior of an ideal gas, particularly as it condenses from a gas into a liquid or solid. These deviations are often approximated through quantum-mechanical statistical methods.

## Ideal quantum gases

At extremely low temperature or high density, where the thermal wavelength of gas particles is comparable to the distances between them, quantum effects become apparent. Under such conditions, an ideal gas of bosons will be governed by Bose-Einstein statistics and the distribution of energy will be in the form of a Bose-Einstein distribution. An ideal gas of fermions will be governed by Fermi-Dirac statistics and the distribution of energy will be in the form of a Fermi-Dirac distribution.cs:Ideální plyn de:Ideales Gas eo:Ideala gaso fr:Gaz parfait it:Gas ideale he:גז אידאלי nl:Ideaal gas ja:理想気体 lv:Ideāla gāze pl:Gaz doskonały pt:Gás perfeito ru:Идеальный газ sl:Idealni plin fi:Ideaalikaasu sv:Perfekt klassisk gas

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