This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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: LeadAcid 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...
View
Full
Document
This note was uploaded on 12/14/2010 for the course PHYSICS 416 taught by Professor Savikhin during the Spring '10 term at Purdue UniversityWest Lafayette.
 Spring '10
 SAVIKHIN
 Physics

Click to edit the document details