Statistical mechanics average energy

[sarahger9]

Homework Statement

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

Homework Equations

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

 

[kdv]

Homework Statement

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

Homework Equations

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

What is the question?

 

[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

 

[kdv]

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

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