Starting with the definition of the Helmholtz energy, A = U-TS , and following the example of question 27, derive the Maxwell relation in Eq. 3.60 .

Question 27 (for context): Starting with the definition of enthalpy, H = U + pV , and additional relations based on the First and Second Laws of Thermodynamics, derive the following:

a. dH as a function of T, S, V, and p

b. Equations for (0H>0p)S and (0H>0S )p

c. The equation (0T >0p)S (0V >0S )p

d. The result of part (a) starting from Eq. 3.35 and the definition G K H - TS