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Entropy Balances: Solving for Turbine Efficiency Sample Calculation. (uakron.edu, 10min) Steam turbines are very common in power generation cycles. Knowing how to compute the actual work, reversible work, and compare them is an elementary part of any engineering thermodynamics course.

Comprehension Questions:

1. An adiabatic turbine is supplied with steam at 2.0 MPa and 600°C and it exhausts at 98% quality and 24°C. (a) Compute the work output per kg of steam.(b) Compute the efficiency of the turbine.

2. A Rankine cycle operates on steam exiting the boiler at 7 MPa and 550°C and expanding to 60°C and 98% quality. Compute the efficiency of the turbine.

The objectives for Chapter 1 were:

1. Explain the definitions and relations between temperature, molecular kinetic energy,
molecular potential energy and macroscopic internal energy, including the role of intermolecular potential energy and how it is modeled. Explain why the ideal gas internal energy
depends only on temperature.
2. Explain the molecular origin of pressure.
3. Apply the vocabulary of thermodynamics with words such as the following: work, quality,
interpolation, sink/reservoir, absolute temperature, open/closed system, intensive/extensive
property, subcooled, saturated, superheated.
4. Explain the advantages and limitations of the ideal gas model.
5. Sketch and interpret paths on a P-Vdiagram.
6. Perform steam table computations like quality determination, double interpolation.

To these, we could add expressing and explaining the first and second laws. Make a quick list of these expressions and explanations in your own words, including cartoons or illustrations as you see fit,  starting with the first and second laws.

When expressing the derivative of the total Gibbs energy by chain rule, there is one particular partial derivative that relates to each component in the mixture: the "chemical potential." By adapting the derivation from Chapter 9 of the equilibrium constraint for pure fluids, we can show that the equilibrium constraint for mixtures is that the chemical potential of each component in each phase must be equal. That is fine mathematically but it is not very intuitive. By translating the chemical potential into a rigorous definition of fugacity of a component in a mixture, we recognize that an equivalent equilibrium constraint is that the fugacity of each component in each phase must be equal. (8min, Live, uakron.edu) This offers the intuitive perspective of, say, molecules from the liquid escaping to the vapor and molecules from the vapor escaping to the liquid; when the "escaping tendencies" are equal, the phases experience no net change and we call that equilibrium.

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?

Group contributions are used widely in property prediction. The volumes and surface areas have been determined by x-ray data and high-temperature collision data. The UNIQUAC and UNIFAC activity coefficient methods use these quantities to calculation volume fractions and surface area fractions. The assignment of functional groups for a molecule must be done carefully to assure agreement with the groups used by the model developers.

Comprehension Questions:

1. Estimate R and Q for 1,4 dihydroxy benzene.

2. Estimate R and Q for n-propyl alcohol and compare them to the values for IPA.

3. Estimate R and Q for methyl-npropyl ketone.

Keys to the Kingdom of Chemical Engineering (uakron.edu, 11min) Sometimes it helps to reduce a subject to its simplest key elements in order to "see the forest instead of the trees." In this presentation, the entire subject of Chemical Engineering is reduced to three key elements: sizing a reactor (Uakron.edu, 7min), sizing a distillation column (uakron.edu, 9min), and sizing a heat exchanger (uakron.edu, 9min). In principle, these elements involve the independent subjects of kinetics, thermodynamics, and transport phenomena. In reality, each element involves thermodynamics to some extent. Distillation involves thermodynamics in the most obvious way because relative volatility and activity coefficients are rarely discussed in a kinetics or transport course. In kinetics, however, the rate of reaction depends on the partial pressures of the reactants and their nearness to the equilibrium concentrations, which are thermodynamical quantities. In heat exchangers, the heat transfer coefficient is important, but we also need to know the temperatures for the source and sink of the heat transfer; these temperatures are often dictated by thermodynamical constraints like the boiling temperature or boiler temperature required to run a Rankine cycle (cf. Chapter 5). In case you are wondering about the subject of "mass and energy balances," the conservation of mass is much like the conservation of energy; therefore, we subsume this subject under the general umbrella of thermodynamics. Understanding the distinctions between thermodynamics and other subjects should help you to frame a place for this knowledge in your mind. Understanding the interconnection of thermodynamics with subjects to be covered later should help you to appreciate the necessity of filing this knowledge away for the long term, such that it can be retrieved at any time in the future.

If you would like a little more practice with reactor mass balances and partial pressure, more screencasts are available from LearnChemE.com, MichiganTech, and popular chemistry websites.

Concepts for General Phase Equilibria (12:33) (msu.edu)

The calculus used in Chapter 6 needs to be generalized to add composition dependence. Also, we introduce partial molar properties and composition derivatives that are not partial molar properties. We introduce chemical potential These concepts are used to show that the chemical potentials and component fugacities are used as criteria for phase equilibria.

14.09 - Numerical procedures for binary, ternary LLE Click here. 100 1

LLE flash using Matlab/Chap14/LLEflash.m (5:54) (msu.edu)

An overview of the LLE flash routine in Matlab, including an overview of the program logic and then an example of how to run the program.

See also - Supplement on Iteration of LLE with Excel and Matlab.

VLE Routines - General Strategies (4:49) (msu.edu)

Deciding which routine to use is more challenging than it appears. Also understanding the strategy used to solve the problems is extremely helpful in being able to develop the equations to solve instead of trying to memorize them.

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 δP=δS for polystyrene, where δS 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.