- #1

Coffee_

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à

##n_j=\frac{1}{exp(\frac{\epsilon_j-µ}{kT}) - 1}## (1)

(Here comes argument 1)

We conclude that the maximal value that µ can take is equal to ##µ=\epsilon_0##. This means that the distribution

##n_j=\frac{1}{exp(\frac{\epsilon_j-\epsilon_0}{kT})- 1}## (2)

Is an upper limit on any real distribution.

So using (2) we can calculate a statistical upper limit on the expected amount of particles in the excited states ##N_{exc}##.

Questions:

1) What explanation should come in the placeholder for 'argument 1' to conclude that µ is between 0 and ##\epsilon_0##? I've seen one on the net that already uses the result of having a macroscopic amount of particles in the groundstate to conclude this, which is kind of a circular reasoning.

2) Am I correct in thinking about this in terms of (2) being an upper limit? The problem that I then have is this - the upper limit on the state ##\epsilon_0## is infinite right? How to conclude that this state will only start getting a macroscopic occupation after the number of particles has exceede ##N_{exc}## - if we see an upper limit of infinity here how can we know that we won't get a big occupation in the groundstate from the very beginning?