ch2_03_Interacting_systems - The Second Law Interacting...

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The Second Law Interacting Systems PHYS 4050: Thermodynamics and Statistical Physics Prof. B. A. Foreman
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Interacting solids Consider now a system of two Einstein solids, labeled A and B The solids are allowed to interact and exchange energy: However, they are isolated from the rest of the universe N oscillators q units of energy hf
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Energy conservation The total energy of the combined system is therefore conserved: Since , we can also write the conservation law as However, the individual energies and are not conserved , because energy exchanges are allowed Although and are allowed to vary, the values of and are fixed
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Total multiplicity We already know how to find the individual multiplicities and : The total number of microstates of the interacting system is therefore given by the product But how do we find for the combined system? For each of the microstates of solid A , there are possible microstates of solid B
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Subsystem energy distribution The dependence of on the variable (or ) describes how energy is distributed between the two subsystems Taking account of energy conservation, this dependence is given by the function Let’s see what this function gives in a few simple cases
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Small system Consider first a small system with and :
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