# Lect20 - Misce ous Note llane s The end is near dont get...

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Lecture 20, p 1 Miscellaneous Notes The end is near – don’t get behind. All Excuses must be taken to 233 Loomis before noon, Friday, Dec. 3. The PHYS 213 final exam times are * 7-9 PM, Monday, Dec. 13 and * 8-10 AM, Tuesday, Dec. 14 . The deadline for changing your final exam time is 10pm, Tuesday, Nov. 30. Homework 6 is due Saturday , Dec. 4 at 8 am. Course Survey = 2 bonus points (accessible at the top of HW6) Review Lecture: Thursday, Dec. 9, 3-5 PM in 228 NHB.

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Lecture 20, p 2 Lecture 20 Phase Transitions Phase diagrams Latent heats Phase-transition fun Freezing point depression/Boiling point elevation Superheated/cooled water Reading for this Lecture: Elements Ch 13
Lecture 20, p 3 Remember: It’s negative, because (unless highly compressed) n Q >> n and p Q >> p . For helium at T = 300K and p = 1 atm: So, All ideal gases will behave similarly, with a logarithmic pressure dependence and an approximately linear temperature dependence. (The curvature is due to the T dependence of n Q . ) Here’s a graph: Chemical Potential of an Ideal Gas ln ln , where Q Q g Q Q n p kT kT p n kT n p μ = = = 6 ln ln(3.10 10 ) (.026 eV)( 12.69) 0.33 eV Q He p kT kT p μ - = = × = - = - ( 29 ( 29 1.5 4 5 4.04 10 atm 4 3.23 10 atm Q p = × = × μ 0 -0.33 eV T 300 K p = 1 atm p < 1 atm p > 1 atm Increase the temperature, holding p constant:: μ decreases. Increase the pressure, holding T constant:: μ increases.

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Lecture 20, p 4 Vapor Pressureof a Solid and thep-T PhaseDiagram Last lecture we saw that μ solid is constant (- ). We can use this to determine graphically the equilibrium pressure (vapor pressure) of the solid as a function of T. For a given temperature, at what pressure does the curve cross μ = - ? From this, we can plot the equilibrium curve, p(T), where the two phases can coexist. This graph is called a p-T phase diagram. It tells us what regions in the (p,T) plane make a gas and which make a solid. The equilibrium curve separates them. It’s just a way to visualize the equilibrium equation: / ln Q kT g s Q p kT p p e p μ μ -∆ = = = -∆ At low T or high p, equilibrium is all solid. The phases coexist on the equilibrium curve. At high T or low p, equilibrium is all gas. μ T p = 1 atm p < 1 atm p > 1 atm - Equilibrium T p Solid Gas
Lecture 20, p 5 We ignored the entropy of the solid, because the entropy of the gas was so much larger. When comparing solids and liquids, we can’t ignore entropy. The entropy is small, but not completely negligible. Compare solids and liquids (for a given substance) : S > L . Atoms in the solid are more strongly bound. S S < S L . Atoms in the liquid have more available microstates (due to motion). Compare the chemical potentials: Remember that F = U-TS, and μ is the free energy per particle. At very low T, the entropy is not important, so μ S < μ L . As T increases, both chemical potentials decrease, but the liquid decreases faster.

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