1. In your own words, describe what a "partition function" is. Is it likely that it has lots of terms which are equal, or very few terms which are equal? Briefly explain.
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2. Think about a system of N magnetic atoms which are placed in an external magnetic field B and which can each be in two possible states. Let the "+" state be the state for which B and the magnetic moment of an atom, m, are aligned (parallel), and let the "-" state be the state for which B and m are anti-aligned (anti-parallel).
Write expressions for the magnetic energy E+ and E- of an atom in each of the two states, and write also write expressions for the probability of finding an atom in each of these states. (These expressions should be very simple.)
What do your answers tell you about the likelihood of finding an atom in each of these two states? Does this make physical sense to you?
3. The probability P(Es) = (1/Z)*exp(-Es/kT)
Check the correct answer: a) gives the probability of finding the system with energy Esb) gives the probability of finding the system in a particular state s with energy Esc) is normalized because Z is summed over all energies Esd) is sharply peaked about the most probable energy E Below is a space for your thoughts, including general comments about today's assignment (what seemed impossible, what reading didn't make sense, what we should spend class time on, what was "cool", etc.): You may change your mind as often as you wish. When you are satisfied with your responses click the SUBMIT button.
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