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Gas in a box
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<p>In <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, the results of the quantum <a href="/facts/Particle_in_a_box/rezR97ky">particle in a box</a> can be used to look at the <a href="/facts/Equilibrium_solution/DgbGMPkg">equilibrium situation</a> for a quantum ideal gas in a box which is a box containing a large number of molecules which do not interact with each other except for instantaneous thermalizing collisions. This simple model can be used to describe the classical <a href="/facts/Ideal_gas/80EfYGFj">ideal gas</a> as well as the various quantum ideal gases such as the ideal massive <a href="/facts/Fermi_gas/D00lFTqW">Fermi gas</a>, the ideal massive <a href="/facts/Bose_gas/T3bsKjPS">Bose gas</a> as well as <a href="/facts/Black_body/f0fHghDy">black body</a> radiation (<a href="/facts/Photon_gas/0Q0x7Xqf">photon gas</a>) which may be treated as a massless Bose gas, in which thermalization is usually assumed to be facilitated by the interaction of the <a href="/facts/Photon/mFNhAEzA">photons</a> with an equilibrated mass. </p><p>Using the results from either <a href="/facts/Maxwell%25E2%2580%2593Boltzmann_statistics/l3Qf1Cxp">Maxwell–Boltzmann statistics</a>, <a href="/facts/Bose%25E2%2580%2593Einstein_statistics/Utb2jN3n">Bose–Einstein statistics</a> or <a href="/facts/Fermi%25E2%2580%2593Dirac_statistics/aLo4bton">Fermi–Dirac statistics</a>, and considering the limit of a very large box, the Thomas–Fermi approximation (named after <a href="/facts/Enrico_Fermi/cmYcY15H">Enrico Fermi</a> and <a href="/facts/Llewellyn_Thomas/cAzzHNCg">Llewellyn Thomas</a>) is used to express the <a href="/facts/Degenerate_energy_levels/ulrnMXTR">degeneracy of the energy states</a> as a differential, and summations over states as integrals. This enables thermodynamic properties of the gas to be calculated with the use of the <a href="/facts/Partition_function_(statistical_mechanics)/q65sJrrn">partition function</a> or the <a href="/facts/Grand_partition_function/q65sJrrn">grand partition function</a>. These results will be applied to both massive and massless particles. More complete calculations will be left to separate articles, but some simple examples will be given in this article. </p>