An ideal gas (also called a perfect gas) is a hypothetical fluid consisting of particles that are identical to each other, occupy negligible volume and undergo perfect elastic collisions with each other, with no intermolecular forces and no intramolecular storage of energy, as opposed to a real gas, a gas that actually exists, which does not have these properties. There are basically three types of ideal gas:

• The classical or Maxwell-Boltzmann ideal gas
• The ideal quantum Bose gas, composed of Bosons
• The ideal quantum Fermi gas, composed of Fermions

Classical ideal gas

The equation of state of a classical ideal gas is the ideal gas law. The energy of an ideal gas consists entirely of the translational kinetic energy of its particles. The probability distribution of particles by velocity or energy is given by 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.

Quantum ideal gases

At extremely low temperature or high density, where thermal wavelength of gas particles are comparable to 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.