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In the text I showed that for an Einstein solid with three
Chapter 3, Problem 35P(choose chapter or problem)
In the text I showed that for an Einstein solid with three oscillators and three units of energy, the chemical potential is \(\mu=-\epsilon\) (where \(\epsilon\) is the size of an energy unit and we treat each oscillator as a “particle”). Suppose instead that the solid has three oscillators and four units of energy. How does the chemical potential then compare to \(-\epsilon\)? (Don’t try to get an actual value for the chemical potential; just explain whether it is more or less than \(-\epsilon\).)
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QUESTION:
In the text I showed that for an Einstein solid with three oscillators and three units of energy, the chemical potential is \(\mu=-\epsilon\) (where \(\epsilon\) is the size of an energy unit and we treat each oscillator as a “particle”). Suppose instead that the solid has three oscillators and four units of energy. How does the chemical potential then compare to \(-\epsilon\)? (Don’t try to get an actual value for the chemical potential; just explain whether it is more or less than \(-\epsilon\).)
ANSWER:Step 1 of 5
The multiplicity of the system is defined as follows
\(\Omega(N, q)=\frac{(q+N-1) !}{q !(N-1) !}\)
Here, N is the number of oscillators and q is the number of energy units.
Substitute 3 for N and 4 for q in the above expression.
\(\Omega(3,4)=\frac{(4+3-1) !}{4 !(3-1) !}=15\)
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