Lecture 7 - Grand Canonical V,T μ 1 2 A 3 heat bath(T and...

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Unformatted text preview: Grand Canonical, V,T, μ 1 2 A 3 heat bath(T) and large N reservoir There are A identical replicas with same μ ,V, and T The walls are permeable to the passage of particles { a N,j } number of systems with N particles and is energy state j For each N , there is a set of j states r first specify N , then j = = = ∑∑ ∑∑ ∑∑ N j N j N j Nj Nj Nj Nj E N a a a A E N To describe each system, we have to identify j and N For each N , there is a set of energies {E N,j (V)} { } ( 29 = ∏∏ the number of states in a particular distribution is W ! N j Nj Nj a A! a { } ( 29 ( 29 β α γ-- +- = ⋅ ⋅ ( ) 1 using the Legendre undetermined multipliers, we find the distribution that maximizes W a s Nj Nj E V N Nj e e e a a Normalization α β γ Constraint Type Lagrange multiplier ∑ ∑ Nj P N j = ∑ ∑ Nj P Nj N j E E = ∑ ∑ Nj P N j N N from where we can extract the first undetermined multiplier ( 29 α β γ- +-- = ⋅ ∑∑ 1 ( ) Nj E V N N j e e e A β γ β γ β γ β γ-...
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This note was uploaded on 05/29/2011 for the course CHM 6461 taught by Professor Bowers during the Spring '08 term at University of Florida.

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Lecture 7 - Grand Canonical V,T μ 1 2 A 3 heat bath(T and...

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