# The Specific Heat of a Free-Electron gas calculated by using the Fermi

1. Feb 20, 2013

### nboogerz

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

Here g(ε_f) is the density of levels at the Fermi energy and T is the temperature. Calculate the specific heat of the electron gas in potassium (K) treating it as a free gas. For a free gas the density of electrons at ε_f is: g(ε_f)=(3/2)(n/E_f) where n is the electron density in the gas. Why is the contribution of the electron specific heat so hard to measure?

2. Relevant equations

C_v=(1/3)(∏^2)(k_B)^2Tg(ε_f)

3. The attempt at a solution

Okay I'm taking n to be the total number of electrons in potassium(19) I still can't calculate a value for g(ε_f) as I still don't know what to put in for E_f as its not given in the problem. Also I'm not sure what to put in for T. Can I take this as another arbitary value as putting 0K for the temperature at the fermi level causes the equation to collapse.

2. Feb 20, 2013

### sankalpmittal

Re: The Specific Heat of a Free-Electron gas calculated by using the F

It would be better if you consult from these sites:

http://www.cmmp.ucl.ac.uk/~ikr/3225/Section 6.pdf
http://www2.binghamton.edu/physics/docs/note-free-electron-gas.pdf
http://www.theo3.physik.uni-stuttgart.de/lehre/ss08/sst/Script-AHCN-Chap-6.pdf
http://phy.ntnu.edu.tw/~changmc/Teach/SS/SSG_note/mchap06.pdf
http://www2.binghamton.edu/physics/docs/note-free-electron-gas.pdf

3. Feb 21, 2013

### nboogerz

Re: The Specific Heat of a Free-Electron gas calculated by using the F

I'll have a look at them thanks.