# Lect18 - Lecture 18 p 1 Miscellaneous Notes Miscellaneous...

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Unformatted text preview: Lecture 18, 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) Lecture 18, p 2 Lecture 18 Review & Examples Lecture 18, p 3 Example: Solid “Solutions” In equilibrium, some A atoms are in the B crystal and vice versa. Assume: • There are M “A” sites, N of which are occupied by “B” atoms. N << M. • The only entropy is due to site counting (ignore vibrations, etc. ) • The energy increase when a “B” goes to an “A” site is ∆. Let’s call the chemical potential of the B atoms in their own crystal 0, by choosing a convenient zero for energy. Then, in equilibrium, the chemical potential of the B’s in A must also be zero: , , , ln . So, if : kT V T V T V T F U S M N N T kT N M e N N N N M μ ∆- ∂ ∂ ∂- = = =- = ∆ - = ∂ ∂ ∂ = A B Important for real devices e.g. , silicon-gold, tin-lead ! ln !( )! M S k N M N = - Lecture 18, p 4 Work from Free Energy Due to Non-equilibrium μ Mechanical Work (isothermal expansion of N particles at temp T) n 1 n 2 Quasi-static expansion (an external force on the piston prevents it from being free expansion): W by = - ∆ F = - ∆ U + T ∆ S = NkT ln(V f /V i ) Constant T ⇒ ∆ U = 0 (ideal gas) Look familiar? Same old physics, different language. Can we use these concepts to do something new ??? vacuum Thermal Bath, T Lecture 18, p 5 Consider this situation. Two different ideal gases, at equal pressures . If one starts on the left, and one on the right , each will expand to fill the volume. In his situation, how much work, if any, could be extracted? A ) 0 B ) (N G - N P ) kT C ) (N G +N P ) kT*ln(2) Thermal Bath, T N G N P ACT 1 Lecture 18, p 6 Consider this situation. Two different ideal gases, at equal pressures . If one starts on the left, and one on the right , each will expand to fill the volume. In his situation, how much work, if any, could be extracted? A ) 0 B ) (N G - N P ) kT C ) (N G +N P ) kT*ln(2) Thermal Bath, T N G N P Each of the components individually loses free energy in the expansion (after the expansion, there’s obviously no longer the possibility of expanding and doing work!); therefore, each component individually could do work up to ∆ F = N kT ln2....
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Lect18 - Lecture 18 p 1 Miscellaneous Notes Miscellaneous...

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