(1) What is the change in molar entropy of liquid toluene at 25oC when the pressure is raised from 1 to 1000 bar? The coefficient of thermal expansion β is 1.14 x 10-3 K-1, the density is 0.923 g cm-3, and the molar mass is 92.14 g mol-1 (note: these values for β and ρ are fictitious). Hint: consider what you know about the pressure dependence of S (try a Maxwell relation)
(2) In class we derived a expression for the entropy in terms of T and V that was valid for any fluid, dS = (Cv/T)dT + (β/κ)dV .
Using a similar procedure, derive the analogous expression in terms of T and P. Compare this result with the expression specific to an ideal gas.
(3) Suppose 1.00 mol of water initially at 27oC and 1 bar undergoes a process whose final state is 100oC and 50 bar. Using the data below and the approximation that the temperature and pressure variations of β, κ, and Cp,m can be neglected, calculate (a) ΔH, (b) ΔU, and (c) ΔS. (β = 3.04 x 10-4 K-1, κ = 4.52 x 10-5 bar-1, Cp,m = 75.3 J K-1 mol-1,Vm = 18.1 cm3 mol-1). Hint: Break this change of state into 2 steps, 270C, 1 bar → 1000C, 1bar and then 1000C, 1 bar → 1000C, 50 bar.
(4) In the thermodynamics of rubberlike elasticity( e.g.,polymer stetching), the differential change in the Helmholtz free energy is given by dA= -SdT + fdL, where f is the restoring force and L is the displacement. Obtain a general expression for the change in entopy for isothermal stretching, i.e., ΔS for L= L1 → L2 at fixed T.
(Hint: first derive the appropriate Maxwell relation.)