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

[nboogerz]

Homework Statement

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?

Homework Equations

C_v=(1/3)(∏^2)(k_B)^2Tg(ε_f)

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.

 

[sankalpmittal]

Homework Statement

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?

Homework Equations

C_v=(1/3)(∏^2)(k_B)^2Tg(ε_f)

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.

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

 

[nboogerz]

I'll have a look at them thanks.