How to Solve for Average Energy as T Approaches 0 and Infinity

[sarahger9]

I'm having some difficulties with a problem. Based on the constraints, I have found that the average energy per particle is u = (Eo + E1 e^(-B deltaE)) / (1 + e^(-B deltaE)). I know this is correct. However, I am having problems solving as T approaches 0 and infinity. B = 1/T
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 was able to easily get the first term in these expressions, but how the second term is coming out I have no idea. I was trying taking a derivative for a while, but I don't believe that that is the way to go. Does anybody have any ideas?

Thanks

 

[SeniorTotor]

Would you, please, describe the physical problem you're trying to solve?

 

[kdv]

I'm having some difficulties with a problem. Based on the constraints, I have found that the average energy per particle is u = (Eo + E1 e^(-B deltaE)) / (1 + e^(-B deltaE)). I know this is correct. However, I am having problems solving as T approaches 0 and infinity. B = 1/T
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 was able to easily get the first term in these expressions, but how the second term is coming out I have no idea. I was trying taking a derivative for a while, but I don't believe that that is the way to go. Does anybody have any ideas?

Thanks

It's considered bad ethis to double post. You already started a thread with that excat same question, why not pursue the thread there? I already gave you pointers there. You have to show some of your work before people will help. I did tell you that the answer they give for the large T limit is correct and gave you a hint. Now show the first few steps that you try and if you are stuck I can point out what the next step is or if you made a mistake I can tell you what the mistake is. But show your attempt.