CHEN 354- HW #1- Due Wednesday, January 28, 2015
Problem 1. Verify concepts of phase equilibrium and phase transitions using the steam tables.
a. Establish by direct calculation this equality between molar Gibbs free energies for steam at 2.5
MPa and 224oC : Gl = Gv
b. Calculate Gv at 2.5 MPa for temperatures between 225 and 400oC and extrapolate this curve
below 224 oC.
c. Find Gl at 160, 170, 180, 190, 200, and 210 oC. Plot in the same graph used for part b and
extrapolate above 224 oC. Hint: for a liquid, H and S can be taken as independent of P.
d. Plot the molar volume V vs. T at P =2.5 MPa over the T range between 150 and 400 oC, and
show that V is discontinuous.
e. Plot Cp vs. T at P =2.5 MPa over the T range between 150 and 400 oC, and show that Cp is
discontinuous.
f. Using the data in the steam tables, show that the Gibbs energies per unit mass of steam and
liquid water in equilibrium at 300 oC are equal.
Problem 2. Prove that Cp > Cv for any fluid, and identify conditions where Cp = Cv. Hints:
 V   P 
 P 
 


  0 for a fluid to be stable; Show that Cp  Cv  T 
 V T
 T  P  V T
2
Problem 3. The following figure shows the P-V diagram for a pure fluid according to the van
der Waals EOS. Within the vapor-liquid coexistence envelope one can draw another envelope
representing the limits of supercooling of the vapor and superheating of the liquid that can be
 P 
observed in the laboratory; along each isotherm these are the points where 
  0.
 V T
Obtain this envelope for the van der Waals fluid. This is the spinodal curve. The region between
the coexistence curve and the spinodal curve is the metastable region of the fluid.
Problem 4. Using modified Raoult’s law, estimate the boiling pressure and mole fractions in the
vapor phase that is in equilibrium with a liquid having 0.1238 mol fraction of ethanol, in a
mixture ethanol/water at 85.3oC. The activity coefficients in the liquid phase are ethanol= 2.9235,
and water = 1.0388.
Problem 5. Using modified Raoult’s law, estimate the boiling temperature and mole fractions in
the vapor phase that is in equilibrium with a liquid having 0.2608 mol fraction of ethanol, in a
mixture ethanol/water at P = 1 atm. The activity coefficients in the liquid phase are ethanol=
1.8859, and water = 1.1506.
Problem 6. Estimate the condensing pressure and the liquid mole fractions in equilibrium with a
vapor having 0.6122 mol fraction of ethanol, in a mixture ethanol/water at 80.7oC. The activity
coefficients in the liquid phase are ethanol= 1.4809, and water = 1.2866.