set2 - Department of Physics The Ohio State University Prof...

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Department of Physics Prof. R. Bundschuh The Ohio State University Second Problem Set for Physics 847 (Statistical Physics II) Winter quarter 2004 Important dates: Feb 10 10:30am-12:18pm midterm exam, Mar 16 9:30am-11:18am final exam Due date: Tuesday, Jan 20 4. Two-state system 8 points A (very small) discrete system has only two states 1 and 2 with energies E 1 = - ε 0 and E 2 = ε 0 , respectively. This could, e.g., be a spin 1 / 2 particle in an external magnetic field. Since this system contains only one particle, the different thermodynamic ensembles do not provide equivalent descriptions of the physics. We want to explore this difference for this simplest possible system. a) If the system is isolated from the environment which are the possible values for the internal energy of the system? b) In the following we assume that the system is not isolated any more but instead inter- acting with a heat bath of temperature T . What are the probabilities p i to find the system in each of the two states in this case.
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