Consider a simple thermodynamic system in which particles can occupy only two states: a lower state, whose energy we define as 0, and an upper state, energy Eu.
(a) Cany out the sum (with only two states, integration is certainly not valid) giving the average particle energy E, and plot your result as a function of temperature.
(b) Explain qualitatively why it should behave as it does.
(c) This system can be used as a model of paramagnetism, where individual atoms' magnetic moments can cither be aligned or antialigned with an external magnetic field, giving a low or high energy, respectively. Describe how the average alignment or antialignment depends on temperature. Does it make sense?
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