# The Partition Fuction

1. May 4, 2014

### lmanri

1. The problem statement, all variables and given/known data
Consider a system at 290 K for which the energy of the nth state is En=n(.01 eV). Using 1+a+a2+a3...=1/(1-a) for a <1 where necessary, Find the value of the partition function.

2. Relevant equations

3. The attempt at a solution

Z=∑e-βE$_{}n$

β=1/κT

I don't know what the energy of the state would be so I can't figure out the problem.

2. May 4, 2014

### tman12321

What do you mean you don't know what the energy of the state is? You wrote it already: E(n) = (0.01 eV)*n. It is linear in n.

3. May 4, 2014

### lmanri

So, I would then have
Z=(sum)e^(-(1/((1.38*10^-23)(290)))(n(0.01))

4. May 4, 2014

### tman12321

No. You have incompatible units.

5. May 4, 2014

### lmanri

I don't understand it.

6. May 4, 2014

### Matterwave

tman means, your units of energy is in eV, but your Boltzmann constant is using units of J/K. You should convert one or the other to have the same units.

7. May 4, 2014

### lmanri

Oh ok, which is 8.625*10^-5 eV/K