P13E.18 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 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 E=Nɛe tikT /(1+et/kT ), where ɛ is the energy separation between the denatured and native forms. (a) Show that the constant-volume molar heat capacity is (ɛ/kT)eelkT Cy=f(T)R f(T)= (b) Plot the variation of Cym with temperature. (c) If the function Cym (T) has a maximum or minimum, calculate the temperature at which it occurs.

P13E.18 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 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 E=Nɛe tikT /(1+et/kT ), where ɛ is the energy separation between the denatured and native forms. (a) Show that the constant-volume molar heat capacity is (ɛ/kT)eelkT Cy=f(T)R f(T)= (b) Plot the variation of Cym with temperature. (c) If the function Cym (T) has a maximum or minimum, calculate the temperature at which it occurs.