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Open system

Open systems & The grand canonical ensemble. Open system. Particle exchange with the surrounding (particle reservoir) allowed e.g., a surface of a solid exchanging particles with a gas. V=const. Particle reservoir. Heat Reservoir R. T=const.

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Open system

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  1. Open systems & The grand canonical ensemble Open system Particle exchange with the surrounding (particle reservoir) allowed e.g., a surface of a solid exchanging particles with a gas V=const Particle reservoir Heat Reservoir R T=const. Thermodynamic potentials depend on variable particle number N

  2. Microcanonicalensemble Canonical ensemble Grand canonical ensemble E fixed average energy average energy constraint average particle number

  3. Deriving density function  and partition function ZG of the grand canonical ensemble Next we show with Partition function of the grand canonical ensemble is the chemical potential where From the constraint

  4. U N 1 With

  5. Expressing ZG with the help of N-particle canonical partition functions Sum over all states of 1 particle Sum over all states of 2 particle fugacity

  6. Ideal gases considered in the grand canonical ensemble We saw previously Remember canonical partition of ideal gas of fixed N particles

  7. With

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