The specific internal energy u of a substance is given as u(s, v) = u0 + k1 s ln ( v/v0) + k2 v ln( s/s0) where u0 is the value of the specific internal energy at a reference state s0 and v0 (i .e., u0, s0, and v0 are constants), and k1 and k2 are positive constants. a. (2 points) Determine the expression for the pressure P (s, v) and the temperature T (s, v) for this substance. b. (1 point) Derive the expression for the specific Helmholtz free energy f (T, v) of this substance. c. (1 point) How would you obtain an Equation of State for this substance? (Describe the approach without explicit computations.) d. (1 point) Develop the expression for the heat capacity Cv of this sub- stance as a function of T , v, and the constants. Does this fundamental equation makes sense physically and why? 3