File:Quantum ideal gas chemical potential 3d.svg

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Captions

Captions

Chemical potential of classical ideal gas and quantum ideal gases (Fermi gas, Bose gas) in three dimensions as a function of temperature, for a fixed density of particles.

Summary

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Description
English: Chemical potential of classical ideal gas and quantum ideal gases (Fermi gas, Bose gas) as a function of temperature, for a fixed density of particles. This is for the case of non-relativistic (massive, slow) particles in three dimensions.

A few features can be seen:

  • As temperature increase, the Fermi and Bose gases approach the classical gas line, gradually.
  • The classical gas has an interesting non-monotonic behaviour, but the quantum gases are monotonic (note that in 1D, however, the Fermi gas is also non-monotonic).
  • The Fermi gas is always higher chemical potential, and Bose gas is lower chemical potential, compared to classical ideal gas.
  • The * marker indicates the upper temperature of Bose condensation. Moving below this temperature, the chemical potential is pinned to ε0, which is the energy of a particle at rest (i.e. the per-particle potential energy).
  • The Fermi gas at low T (far below Fermi temperature TF) saturates to a value ε0 + εF. This extra εF=kTF is its Fermi energy.

The figure has been scaled in a way that the particle degeneracy factor, density, mass, etc. are all factored out and irrelevant.

This was generated using the same source code as File:Quantum ideal gas pressure 3d.svg.
Date
Source Own work
Author Nanite

Licensing

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I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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current17:57, 20 January 2021Thumbnail for version as of 17:57, 20 January 2021270 × 207 (24 KB)Nanite (talk | contribs)Uploaded own work with UploadWizard

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