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Lecture11-06.2-Ideal_Gas-Classical_limit

# Lecture11-06.2-Ideal_Gas-Classical_limit - Last time...

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1 Last time Fermions: Pauli exclusion principle Bosons: no limitation of occupancy Fermi-Dirac Distribution Function Bose-Einstein Distribution Fermi level chemical potential μ ( τ ) Fermi energy ≡ μ (0) Classical limit gives ideal gas result Density of States 3D case: Today Chapter 6 (part 2) Ideal Gas: Classical limit Classical Limit, fermions and bosons: Free energy Pressure Internal Energy Heat Capacities: C V and C V Ideal gas with internal degrees of freedom LECTURE 11

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2 Fermions and Bosons ε μ τ - >> Free energy and chemical potential ( ) , , , V F N V N τ μ τ ( ) , , , , , V N N V F F F dF V N d dV dN V N τ τ τ τ τ = + + ( ) , , dF V N d pdV dN τ σ τ μ = - - + Lecture 8 ( ) ( ) , , , , , V F dF V N dN N V dN N τ τ μ τ = = Constant V, τ : ( ) ( ) 0 , , , , N F V N N V dN τ μ τ =
3 Free energy Constant V, τ : ( ) ( ) 0 , , , , N F V N N V dN τ μ τ = Ideal gas: n N V = log Q N n V μ τ = ( ) log log Q N n V μ τ = - log Q n n μ τ = log log xdx x x x = - Use this constant ( ) 0 0 log log N N Q NdN n V dN τ = - ( ) 0 log log N Q N N N n V N τ = - - ( ) log log Q N N N N n V τ = - - ( ) log Q N N n V N τ = - Ideal Gas Free Energy Pressure ( ) , , , , , V N N V F F F dF V N d dV dN V N τ τ τ τ τ = + + ( ) , , dF V N d pdV dN τ σ τ μ = - - + Lecture 8 , N F p V τ = - ( ) log 1 Q N N n V τ = - ( ) log log log 1 Q N N n V τ = - - - ( ) , log N p N V V τ τ = - N p n V τ τ = = World Famous Ideal Gas Law

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4 Internal Energy Lecture 8 U F τσ = + ( ) , , , , , V N N V F F F dF
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Lecture11-06.2-Ideal_Gas-Classical_limit - Last time...

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