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Entropy of Einstein solids

  • Thread starter d2x
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d2x
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This is the problem:
Consider a system of two Einstein solids, with NA = 300, NB = 200, and qtotal = 100. Compute the entropy of the most likely macrostate and of the least likely macro state.

I only have a doubt. Is the most likely macro state when each solid has half the energy (in this case qA=qB=50 units of energy)? Or does NA get a larger amount of energy for having a larger number of oscillators (In which case I assume that ΩA = ΩB)?
 

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jfizzix
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The most likely macrostate will be when the energy is uniformly distributed over all the oscillators of each solid.

If there are 500 oscillators in total and 100 units of energy then each oscillator will have on average a fifth of a unit of energy.

In the most likely macrostate, solid A would have 60 units of energy, and solid B would have 40 units of energy.

You can't assume that [itex]\Omega_{A}=\Omega_{B}[/itex] since [itex]N_{A}\neq N_{B}[/itex] and [itex]q_{A}\neq q_{B}[/itex].

Knowing what [itex]q_{A}[/itex] and [itex]q_{B}[/itex] are for the most likely macrostate, and knowing [itex]N_{A}[/itex] and [itex]N_{B}[/itex], you can figure out [itex]\Omega_{A}[/itex] and [itex]\Omega_{B}[/itex]
 
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