Lect14 - Physics 213: Lecture 14, Pg 1 Lecture 14 Lecture...

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Unformatted text preview: Physics 213: Lecture 14, Pg 1 Lecture 14 Lecture 14 Phase Transitions Phase Transitions Agenda for today Agenda for today • Phase diagrams • Latent heats • Phase-transition fun • Freezing point depression/Boiling point elevation • Superheated/cooled water Re fe re nc e fo r this Le c ture : Ele m e nts Ch 13 Physics 213: Lecture 14, Pg 2 Chemical Potential for an Ideal Gas Chemical Potential for an Ideal Gas It’s negative because n Q is much larger than n for a dilute gas. For an ideal gas at T = 300K and p = 1 atm: ln ln Q Q g n p kT kT n p μ = = % 9 ln ln(1.02 10 ) (.026eV)( 20.74) 0.54 Q g p kT kT eV p μ- = = × = - = - μ-.5 4 eV T 300K How does μ g depend on temperature? 3/2 3 ln ln ln ln 2 Q g n kT kT CT kT T kT C n μ =- =- =- - Increase T increase S decrease F decrease μ g How does μ g depend on pressure? (ln ln ) (ln ln ) Q Q g kT p p kT n n μ = - = - Decrease p, n decrease μ g p = 1atm p < 1atm Q Q p n kT ≡ % Physics 213: Lecture 14, Pg 3 Vapor Pressure of a Simple Model of a Solid Vapor Pressure of a Simple Model of a Solid and the p-T phase diagram and the p-T phase diagram First plot μ vs. T for different pressures. Simple solid has no internal motions, μ s = constant From the equilibrium crossings, we can plot p(T); “Vapor pressure” T p Q / kT p p e-∆ = = Equilibrium conditions Q g p kT n p μ = - ÷ l- s ∆ = μ μ T- ∆ p 1 p 2 p 3 5/2 Q Q p n kT T = μ Physics 213: Lecture 14, Pg 4 Chemical Potentials of Real Solids and Liquids Chemical Potentials of Real Solids and Liquids A real solid has internal motions and therefore non-zero entropy μ s decreases slowly with T. An atom in the liquid phase is less bound than in the solid (Δ L < Δ S ), but there is more entropy in the liquid. μ L starts higher, but changes less slowly with T. L μ s μ μ T-- s L ∆ ∆ Liquid-solid equilibrium T freeze Because the liquid and solid have about the same volume per particle, for now we can ignore p and just consider equilibria at different T. To minimize G state with the lowest μ At special values of (p,T), different phases can have the same μ and thus coexist. Physics 213: Lecture 14, Pg 5 2 ) The substance is in state C. What will happen? a. substance will melt b. free energy will minimize itself c. entropy will maximize Act 1 Act 1 1) Which point corresponds to a liquid? A B C L μ s μ T-- s L ∆ ∆ μ A B C Physics 213: Lecture 14, Pg 6 Constructing the p-T Phase Diagram for a Normal Liquid Constructing the p-T Phase Diagram for a Normal Liquid (actually not water) (actually not water) p 1 p 2 > p 1 p 3 > p 2 Solid μ s Liquid μ L Gas μ g p 4 p 3 p 2 p 1 T p Phase Diagram: Solid Liquid Gas T T c μ T T c T T c T c T T c p 4 > p 3 μ Physics 213: Lecture 14, Pg 7 How to interpret the graphs of How to interpret the graphs of μ μ (p,T): (p,T): At a given p, the system chooses the lowest branch At a given p, the system chooses the lowest branch...
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This note was uploaded on 12/11/2011 for the course PHYS 213 taught by Professor Kuwait during the Spring '09 term at University of Illinois at Urbana–Champaign.

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Lect14 - Physics 213: Lecture 14, Pg 1 Lecture 14 Lecture...

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