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 dont 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 . Lets 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 Bs 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 - - = = =- = - = = 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 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, theres 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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