9867

Bose-Einstein Condensation (Free Boson Gas)

This Demonstration shows the thermal population of the ground orbital and all the excited orbitals for a gas of free bosons as a function of temperature. The populations according to the classical Maxwell–Boltzmann statistics can also be shown. The temperature is measured in units of Einstein's condensation temperature.
  • Contributed by: Olivier Espinosa (Universidad Técnica Federico Santa María, Valparaíso, Chile)

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Einstein's condensation temperature is the temperature below which the ground orbital of a gas of free bosons is occupied by a macroscopic number of particles. This temperature is determined by the mass of the particles and their concentration. For atoms of Helium-4 in the liquid state this temperature is about 3.1 degrees Kelvin.
Note that in the case of Maxwell–Boltzmann statistics, the number of particles in the ground orbital is much smaller than the number of particles in excited orbitals for all temperatures except those much smaller than Einstein's temperature. For the parameters of snapshots 2 and 3, for instance, the classical occupations of the ground orbital are 10.3 and 5.2, respectively. Both numbers are too small in comparison with the total number of particles to be represented by a small bar.
For details of the statistical-mechanics calculations relevant to this problem, see
C. Kittel and H. Kroemer, Thermal Physics, New York: W. H. Freeman and Company, 1980.

PERMANENT CITATION

    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+