The Flory and Flory-Huggins Models (7:05) (msu.edu)

Flory recognized the importance of molecular size on entropy, and the Flory equation is an important building block for many equations in Chapter 13. Flory introduced the importance of free volume. The Flory-Huggins model combines the Flory equation with the Scatchard-Hildebrand model using the degree of polymerization and the parameter χ. The Flory-Huggins model is used widely in the polymer industry.

Comprehension Questions:

Assume δ_P=δ_S for polystyrene, where δ_S is the solubility parameter for styrene. Also, polystyrene typically has a molecular weight of about 15,000. Room temperature is 25°C.

1. Estimate the infinite dilution activity coefficient of styrene in polystyrene.
2. Estimate the infinite dilution activity coefficient of toluene in polystyrene.
3. Estimate the infinite dilution activity coefficient of acetone in polystyrene.
4. Which of the above would be the "best" solvent for polystyrene? Explain quantitatively.

Refrigeration Cycle Introduction (LearnChemE.com, 3min) explains each step in an ordinary vapor compression (OVC) refrigeration cycle and the energy balance for the step. You might also enjoy the more classical introduction (USAF, 11min) representing your tax dollars at work. The musical introduction is quite impressive and several common misconceptions are addressed near the end of the video.
Comprehension Questions: Assume zero subcooling and superheating in the condenser and evaporator.
1. An OVC operates with 43 C in the condenser and -33 C in the evaporator. Why is the condenser temperature higher than than the evaporator temperature? Shouldn't it be the other way around? Explain.
2. An OVC operates with 43 C in the condenser and -33 C in the evaporator. The operating fluid is R134a. Estimate the pressures in the condenser and evaporator using the table in Appendix E-12.
3. An OVC operates with 43 C in the condenser and -33 C in the evaporator. The operating fluid is R134a. Estimate the pressures in the condenser and evaporator using the chart in Appendix E-12.
4. An OVC operates with 43 C in the condenser and -33 C in the evaporator. The operating fluid is R134a. Estimate the pressures in the condenser and evaporator using Eqn 2.47.
5. An OVC operates with 43 C in the condenser and -33 C in the evaporator. Assume the compressor of the OVC cycle is adiabatic and reversible. What two variables (P,V,T,U,H,S) determine the state at the outlet of the compressor?

Rankine Cycle Introduction (LearnChemE.com, 4min) The Carnot cycle becomes impractical for common large scale application, primarily because H2O is the most convenient working fluid for such a process. When working with H2O, an isentropic turbine could easily take you from a superheated region to a low quality steam condition, essentially forming large rain drops. To understand how this might be undesirable, imagine yourself riding through a heavy rain storm at 60 mph with your head outside the window. Now imagine doing it 24/7/365 for 10 years; that's how long a high-precision, maximally efficient turbine should operate to recover its price of investment. Next you might ask why not use a different working fluid that does not condense, like air or CO2. The main problem is that the heat transfer coefficients of gases like these are about 40 times smaller that those for boiling and condensing H2O. That means that the heat exchangers would need to be roughly 40 times larger. As it is now, the cooling tower of a nuclear power plant is the main thing that you see on the horizon when approaching from far away. If that heat exchanger was 40 times larger... that would be large. And then we would need a similar one for the nuclear core. Power cycles based on heating gases do exist, but they are for relatively small power generators.
     With this background, it may be helpful to review the relation between the Carnot and Rankine cycles. (LearnChemE.com, 6min) The Carnot cycle is an idealized conceptual process in the sense that it provides the maximum possible fractional conversion of heat into work (aka. thermal efficiency, ηθ).
Comprehension Questions:
1. Why is the Carnot cycle impractical when it comes to running steam through a turbine? How does the Rankine cycle solve this problem?
2. Why is the Carnot cycle impractical when it comes to running steam through a pump? How does the Rankine cycle solve this problem?
3. It is obvious which temperatures are the "high" and "low" temperatures in the Carnot cycle, but not so much in the Rankine cycle. The "boiler" in a Rankine cycle actually consists of "simple boiling" where the saturated liquid is converted to saturated vapor, and superheating where the saturated vapor is raised to the temperature entering the turbine. When comparing the thermal efficiency of a Rankine cycle to the Carnot efficiency, should we substitute the temperature during "simple" boiling, or the temperature entering the turbine into the formula for the Carnot efficiency? Explain.

Peng-Robinson Properties - Excel (6:56) (msu.edu)

Provides an overview of using the Peng-Robinson spreadsheet Preos.xlsx for calculation of H, U, S and use of solver.

Comprehension Questions:

1. For liquid propane at 298K and 1 MPa, and a reference state of 298K and 1bar propane vapor, what is the ideal gas contribution to "H-H_R" (J/mol)?
2. For liquid propane at 298K and 1 MPa, and a reference state of 298K and 1bar propane vapor, what is the ideal gas departure contribution: "H-H^_ig" (J/mol)?
3. For liquid propane at 298K and 1 MPa, and a reference state of 298K and 1bar propane vapor, what is the tabulated value of "H" (J/mol)?
4. Explain the similarity and difference between the numerical values of "H" and "H-H^_ig".
5. Ethane at 350K and 5 bars is expanded through an adiabatic, reversible turbine to 1 bar. What is the temperature (K) at the turbine outlet?