Statistical thermodynamics MOC

Grand canonical ensemble

The grand canonical ensemble represents an otherwise closed system in thermal and chemical equilibrium with a heat bath and particle reservoir. As such, its natural variables are

• — Chemical potential
• — System volume
• — Temperature of the heat bath (and thus the system)

and microstates of all energies and particle numbers are accessible to the system, with probabilities at equilibrium given by the distribution

where is the grand canonical partition function, related to the Landau free energy . The determination of depends on the statistics used.

• Maxwell-Boltzmann statistics
• Modified Boltzmann approximation
• Fermi-Dirac statistics
• Bose-Einstein statistics

Derivation

derivation

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