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Grand Canonical Ensemble

Grand Canonical, V,T, m. There are A identical replicas with same m ,V, and T. 1. 2. 3. A. heat bath(T) and large N reservoir. Grand Canonical Ensemble. The walls are permeable to the passage of particles. To describe each system, we have to identify j and N

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Grand Canonical Ensemble

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  1. Grand Canonical, V,T,m There are A identical replicas with same m,V, and T 1 2 3 A heat bath(T) and large N reservoir Grand Canonical Ensemble The walls are permeable to the passage of particles To describe each system, we have to identify j and N For each N, there is a set of energies {EN,j(V)} {aN,j} number of systems with N particles and is energy state j For each N, there is a set of j states  first specify N, then j

  2. Distributions in a Grand canonical ensemble

  3. from where we can extract the first undetermined multiplier Partition function

  4. Mechanical Properties

  5. What is the Lagrange Multiplier g Derivation of g

  6. infinitesimal changes in ENj are produced by reversible work, dENj = -pNj dV Derivation of g

  7. Derivation of g III From knowing X(grand partition function) we can obtain the mechanical functions (p, N, E) and non-mechanical functions as S

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