Lecture09-05.2-Gibbs_Factor_Sum

Lecture09-05.2-Gibbs - 1 Last Time A new conjugate pair chemical potential and particle number Definition of chemical potential Ideal gas chemical

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Unformatted text preview: 1 Last Time A new conjugate pair: chemical potential and particle number Definition of chemical potential Ideal gas chemical potential Total, Internal, and External chemical potential Example: Pressure vs. Altitude Example: Spins in magnetic field Example: Lead-Acid battery LECTURE 9 Today Chapter 5 (part 2) Gibbs Factor Chemical potential and entropy Gibbs Factor (Boltzmann factor with N) Gibbs Sum (Partition function with N) Adsorption (Al from a soda can) Semiconductor Impurity Sites LECTURE 9 2 Chemical potential and Entropy Analogy with temperature: Let dV = dN = 0: ( V and N are constant) L e c t u r e 3 Similar approach for μ : Let dV= dU = 0: ( V and U are constant) Summary of relations , V F N τ μ ∂ = ∂ : μ , U V N μ σ τ ∂ - = ∂ : p : τ ( ) , , U V N σ ( ) , , U V N σ ( ) , , F V N τ , 1 V N U σ τ ∂ = ∂ , V N U τ σ ∂ = ∂ independent , U N p V σ τ ∂ = ∂ , N U p V σ ∂ - = ∂ , N F p V τ ∂ - = ∂ , V U N σ μ ∂ = ∂ intensive extensive ( ) , , dU V N pdV d dN σ τ σ μ = - + + ( ) , , dF V N d pdV dN τ σ τ μ = -- + 3 Gibbs Factor ε g(U) g(U - ε ) Generalization of Boltzmann factor for systems that can trade energy and particles Energy and particles Boltzmann Factor ε g(U) g(U - ε ) Boltzmann Factor is for constant N L e c t u r e 4 4 Gibbs Factor Reservoir System System and Reservoir can trade energy and particles Multiplicity of system + reservoir when the system is completely specified Lets assume we specify the state of the system completely . Once this is done, multiplicity depends only on the reservoir: Multiplicity of reservoir depends on internal variables Probability of the system to be in this specified state N particles, energy ε S Total for R + S Probability of the system to be in state “ s” Probability of particular state depends on multiplicity of reservoir Gibbs Factor Reservoir System System and Reservoir can trade energy and particles 5...
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This note was uploaded on 12/14/2010 for the course PHYSICS 416 taught by Professor Savikhin during the Spring '10 term at Purdue University-West Lafayette.

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Lecture09-05.2-Gibbs - 1 Last Time A new conjugate pair chemical potential and particle number Definition of chemical potential Ideal gas chemical

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