Can you explain the fugacity of boson gas in Bose-Einstein Condensation?

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SUMMARY

The discussion centers on the fugacity of boson gas in the context of Bose-Einstein Condensation (BEC). It establishes that BEC occurs when the temperature of bosons drops below a critical temperature (T_{c} > 0K), leading to a phase where all bosons condense at absolute zero. The conversation clarifies that between 0K and T_{c}, there exists a mixture of ideal boson gas and condensed bosons. It concludes that the fugacity of the boson gas is 1 when the chemical potential is 0, indicating that the density of non-condensed bosons is solely a function of temperature for T < T_{c}.

PREREQUISITES
  • Understanding of Bose-Einstein Condensation principles
  • Familiarity with thermodynamic concepts such as temperature and critical temperature
  • Knowledge of statistical mechanics, particularly regarding bosons
  • Basic grasp of chemical potential and fugacity in thermodynamic systems
NEXT STEPS
  • Study the mathematical formulation of Bose-Einstein statistics
  • Explore the implications of critical temperature (T_{c}) on bosonic systems
  • Investigate the relationship between chemical potential and fugacity in quantum gases
  • Learn about the experimental observations of Bose-Einstein Condensation
USEFUL FOR

Students of physics, particularly those studying quantum mechanics and thermodynamics, as well as researchers interested in the properties of bosonic systems and Bose-Einstein Condensation.

Ang Han Wei
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Hi,
my course just provided an introduction to Bose-Einstein Condensation.

I was told that this phenomenon occurs when the temperature of Bosons go under a certain critical temperature T_{c} > 0K. At absolute zero, all the Bosons go into the condensed phase.

However, at temperatures between 0K and T_{c}, there is a mixture of an ideal Boson gas and condensed bosons.

What then is the fugacity of the boson gas in such an instance?
 
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The chemical potential is exactly 0, which corresponds to fugacity 1, I suppose. Hence the density of non-condensed bosons becomes a function of T, only for T<Tc.
 

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