It is possible to write an approximate expression for the partition function of a protein molecule by including contributions from only two states: the native and denatured forms of the polymer. Proceeding with this crude model gives us insight into the contribution of denaturation to the heat capacity of a protein. According to this model, the total energy of a system of N protein molecules is 

where ε is the energy separation between the denatured and native forms.

(a) Show that the constant-volume molar heat capacity is

(b) Plot the variation of C_V,m with temperature.

(c) If the function C_V,m(T) has a maximum or minimum, derive an expression for the temperature at which it occurs.

Ne-E/KT 1+e-/kT E=-