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.