# Statistical mechanics average energy

1. Mar 20, 2008

### sarahger9

1. The problem statement, all variables and given/known data

average energy per particle u = (Eo + E1 e^(-B deltaE)) / (1 + e^(-B deltaE))
B = 1/T

2. Relevant equations

Possibly relevant: e^x = 1 + x^2 / 2! + x^3 / 3! ......

3. The attempt at a solution

It tells me the average energy is about u = Eo + (deltaE)e^(-B delatE) as t approaches 0, and u = (1/2)(Eo + E1) - (1/4)B(delataE)^2 as T approaches infinity.

I can easily derive the first term in both of these equations, but the second is giving me some trouble. I tried to Taylor expand the exponential, but everything seems to cancel out and appear as before.

2. Mar 20, 2008

### kdv

What is the question???

3. Mar 20, 2008

### sarahger9

Sorry, I am attempting to derive the solution that was given to me, the energy as T approaches 0 and infinity from the average energy per particle

4. Mar 20, 2008

### kdv

You might want to try the T-> infinity first. I got their answer. Just Taylor expand. And you will also need to use that

$$\frac{1}{1+x} \approx 1-x$$

If you don't get it, post your steps