# A4 - PHYS 258 Thermal Physics Assignment 4 Due February 7 Student ID Last Name 1[4 Two-State Paramagnet The following questions deal with a two

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PHYS 258 - Thermal Physics: Assignment 4 Due February 7 Student ID: Last Name: 1. [4]. Two-State Paramagnet . The following questions deal with a two state paramagnetic system comprising N magnetic dipoles in an external magnetic field, such that for each magnetic dipole the energy of its ground state (aligned, ) is 0 and the energy of its excited state (antialigned, ) is ε . Thus, if n quanta of energy are in the system, its total energy is U = n . (a) [0.5] Suppose that N = 5. How many macrostates are there, and what are their corresponding values of U ? For each macrostate, explicitly write down all possible microstates (e.g. ↑↑↓↑↓ ) and so define its multiplicity. What is Ω (all), the total number of microstates? (b) [0.5] Suppose that the system exchanges energy with its environment in such a way that each of these microstates is equally likely to occur, like flipping five fair coins. What is the probability, at any instant of time, of finding the system in the microstate: ↑↑↓↑↓ ?

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(c) [0.5] What are the probabilities, P(n), at any instant of time, of finding the system
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## This note was uploaded on 06/11/2011 for the course PHYS 258 taught by Professor Yurileonenko during the Winter '11 term at Waterloo.

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A4 - PHYS 258 Thermal Physics Assignment 4 Due February 7 Student ID Last Name 1[4 Two-State Paramagnet The following questions deal with a two

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