Understanding Einstein's Solid: Calculating Multiplicity of Energy States

[aaaa202]

Reading about einstein's model of a solid as being made up by quantum harmonic oscillators.

Now while the idea is VERY interesting, I think my book's explanation of the multiplicity of an energy state is quite flawed. One can easily derive a simple formula using the binomial coefficient. However, as far as I can see the multiplicity of an energy state tends to increase as the total energy tends to inifinity. But surely that is nonsense, because the multiplicity must somehow be limited by the total energy in the system as a whole.

Why does it even make sense to calculate the multiplicty of different amounts of total energy, when there is always ONE total amount of energy, that can't change.

Maybe I should have continued to the next pages before asking this question though..

 

[jtbell]

I think you should continue reading for a while.

You'll probably encounter an example based on two solids that are in thermal contact and can exchange energy. Each solid's energy can vary randomly, but the total energy is fixed.

If (for example) you have two solids containing the same number of oscillators, the most likely distribution of energy between them is obviously half-and-half. The interesting question is, if you have N oscillators in each solid, sharing q units of energy, what is the probability that the distribution is different from half-and-half, by 1%, 0.01%, etc.? What if N is one mole (6.02 x 10^23) and q is a similar number?

 

[zhangyang]

However, as far as I can see the multiplicity of an energy state tends to increase as the total energy tends to inifinity

Very interesting.I also think that the energy of every oscillator must be finite.Because every particle can't be faster than light.And if they have a so high energy ,the solid will chenge itself into liquid or gas.