PHYSICS 112 Midterm: physics112-sp2009-mt2-Sadoulet-soln
Document Summary
Time yourself and move to the next problem after a number of minutes equal to the number of points. Entropy (10 points): a) (5 points) show from our general definition of the entropy (which applies both to isolated and non isolated systems) that the entropy of a system in contact with a thermal bath at temperaturer, is a(rlogz) (1 ; E+ = mb, eo = 0 and e_ = mb, depending whether it points along, perpendicular to or opposite to the magnetic field. a) (5 points) write down the partition flmetion of each spin and probabilities of it pointing along, perpendicular to or opposite to the magnetic field. 1" b) (10 points) from the partition fnnction of a single spin, deduce that the total entropy of the system is (at small mb/"t) as ~ ns(1og3-~-2)" 10g(1 + e) e+ 0(e2 cosh(e) 1 + + 0( 3).
