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# Lect16 - Misce ous Note llane s The end is near dont get...

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Lecture 16, p 1 Miscellaneous Notes Miscellaneous Notes The end is near – don’t get behind. All Excuses must be taken to 233 Loomis before noon, Tuesday, Nov. 30. 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)

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Lecture 16, p 2 Lecture16 Equilibrium Between Particles Free Energy and Chemical Potential Simple defects in solids Ideal gases, revisited Reference for this Lecture: Elements Ch 11 Reference for Lecture 12: Elements Ch 12
Lecture 16, p 3 Thumbnail review of free energy: Equilibrium corresponds to maximum S tot = S reservoir + S small system . When we calculate S, we only need to know the temperature of the reservoir. In minimizing F (equivalent to maximizing S tot ) we don’t have to deal explicitly with S reservoir . Consider exchange of material (particles) between two containers. These are two small systems in equilibrium with a reservoir (not shown) at temperature T. In equilibrium, dF/dN 1 = 0: The derivative of free energy with respect to particle number is so important that we define a special name and symbol for it: For two subsystems exchanging particles, the equilibrium condition is: A New Process: Particle Exchange Maximum Total Entropy Minimum Free Energy Equal chemical potentials 1 2 1 2 1 1 1 1 2 1 2 1 2 0 dF dF dF dF dF dN dN dN dN dN dF dF dN dN = + = - = = 1 N F = F 1 +F 2 N 1 N 2 The chemical potential of subsystem “i” i i i dF dN μ 1 2 μ μ =

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Lecture 16, p 4 Why Bother with Yet Another Definition? Answer: It makes the various equilibrium conditions look the same: Exchange of: Volume: p 1 = p 2 Energy: T 1 = T 2 Particles: μ 1 = μ 2 Why does the last equation use dF/dn, instead of d σ /dN? Remember that there is a thermal reservoir (not shown). When particles are exchanged, the reservoir’s entropy might change. (It might gain or lose energy.) That’s what F System 1 System 2 The two systems can exchange volume, energy, or particles. 1 2 1 2 d d dV dV σ σ = 1 2 1 2 d d dU dU σ σ = 1 2 1 2 dF dF dN dN =
Lecture 16, p 5 ThePath Ahead... Having considered thermal equilibrium when volume and energy exchanged, now we’ll consider systems in which particles can be exchanged. Some examples: Particles can move from place to place. Particles can combine into new types ( e.g. , chemical reactions). This will lead to the concept of “chemical equilibrium”. And lots and lots of applications... Let’s start with a concrete example.

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Lecture 16, p 6 Simple defects in solids Atoms in a crystal can pop out of position and sit in interstitial sites. These defects (and others) play a crucial role in the thermal properties of materials.
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Lect16 - Misce ous Note llane s The end is near dont get...

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