# HW_B - Homework B PHY3513 Due: Monday, Feb. 7, 2011 1....

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Homework B PHY3513 Due: Monday, Feb. 7, 2011 1. (4.2) 2. (4.4) Note that there is a factor of two error in the equations stated in the text for this problem. Also, recognize that dT/dE is related to an important thermodynamic quantity. 3. (4.7) Hint, use the relation, ln x x x e e ex α ⎛⎞ =− ⎜⎟ ⎝⎠ 4. Thermal Equilibrium of an Isolated System: Consider two macroscopic systems, A and B , in thermal contact an in equilibrium with each other but isolated from the surroundings. P(E A )dE is the probability that the system A has an energy between E A and E A +dE . Therefore, ) ( ) ( ) ( B B A A A E E C E P Ω Ω = ( E = E A + E B = constant). We are interested in the behavior of P(E A ) near E E A = where ) ( E P is maximum. Show that { } 2 / ) ( exp ) ( ) ( 2 E E E P E P γ where B A + = and 2 2 ) ( A A A A E E n Ω = A ( B similarly defined). Use the Taylor expansion, not around E = 0 but around EE = . Do you see that γ has to be positive?

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## This note was uploaded on 12/15/2011 for the course PHY 3513 taught by Professor Staff during the Fall '08 term at University of Florida.

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HW_B - Homework B PHY3513 Due: Monday, Feb. 7, 2011 1....

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