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|01.5 Real Fluids and Tabulated Properties||Click here.||100||2||
Double interpolation (uakron, 8min) is exactly what it sounds like: to find a steam property when neither the pressure nor temperature are among the tabulated values, you need to interpolate twice. We interpolate first on pressure, then on temperature. It is a bit tedious, but straightforward.
|12.04 - The Flory-Huggins Model||Click here.||100||2||
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.
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.
|05.2 - The Rankine cycle||Click here.||100||1||
Thermal Efficiency with a 1-Stage Rankine Cycle. (uakron.edu, 12min) Steam from a boiler enters a turbine at 350C and 1.2MPa and exits at 0.01MPa and saturated vapor; compute the thermal efficiency (ηθ) of the Rankine cycle based on this turbine. (Note that this is something quite different from the turbine's "expander" efficiency, ηE.) This kind of calculation is one of the elementary skills that should come out of any thermodynamics course. Try to pause the video often and work out the answer on your own whenever you think you can. You will learn much more about the kinds of mistakes you might make if you take your best shot, then use the video to check yourself. Then practice some more by picking out other boiler and condenser conditions and turbine efficiencies. FYI: the conditions of this problem should look familiar because they are the same as the turbine efficiency example in Chapter 4. That should make it easy for you to take your best shot.
1. The entropy balance is cited in this video, but never comes into play. Why not?
2. Steam from a boiler enters a turbine at 400C and 2.5 MPa and exits a 100% efficient turbine at 0.025MPa; compute the Rankine efficiency. Comment on the practicality of this process. (Hint: review Chapter 4 if you need help with turbine efficiency.)
|10.07 - Nonideal Systems||Click here.||100||1||
This screencast shows how to quickly visualize Pxy phase diagrams for nonideal systems using Excel (5min, uakron.edu). These sample calculations for methanol+benzene apply the simplest nonideal solution model: ΔHmix = A12*x1*x2. Rigors of this model are discussed in Chapter 11. Nevertheless, its basic elements are simple enough that they can be understood in Chapter 10. When x1=0 or x2=0, a pure fluid is indicated, corresponding to no mixing and zero heat of mixing. When A12=0, the ideal solution approximation is recovered. When A12>0, the model indicates an endothermic interaction (like 2-propanol+water, Fig. 10.8c), giving rise to "positive deviations from Raoult's Law." When A12<0, the model indicates an exothermic interaction (like acetone+chloroform, Fig. 10.9c), giving rise to "negative deviations from Raoult's Law." With this spreadsheet, you can quickly change your components and A12 values to see how the phase diagram changes and gain "hands-on" familiarity with the principles discussed in Section 10.7.
Note: This is a companion file in a series. You may wish to choose your own order for viewing them. For example, you should implement the first three videos before implementing this one. Also, you might like to see how to quickly visualize the Txy analog of the Pxy phase diagram. If you see a phase diagram like the ones in section 11.8, you might want to learn about LLE phase diagrams. The links on the software tutorial present a summary of the techniques to be implemented throughout Unit3 in a quick access format that is more compact than what is presented elsewhere. Some students may find it helpful to refer to this compact list when they find themselves "not being able to find the forest because of all the trees."
|10.07 - Nonideal Systems||Click here.||100||1||
Nonideal Mixtures (4:58) (msu.edu)
Raoult's law is an easy way to calculate VLE, but it is inaccurate for most detailed VLE calculations. This screencast provides an overview of the problems, and introduces the concept of an azeotrope. The VLE K-ratio is shown to be less than one or greater than one dependenting on the overall system concentration relative to the azeotrope composition where K=1. The concept of positive and negative deviations is introduced.
|08.07 - Implementation of Departure Functions||Click here.||100||1||
Derive the internal energy departure function (uakron.edu, 20min) for the following EOS:
Comprehension: Given (A-Aig)TV/RT = -2ln(1-ηP) - 16.49ηPβε/[1-βε(1-2ηP)/(1+2ηP)^2 ]
1. Derive the internal energy departure function.
2. Derive the expression for the compressibility factor.
3. Solve the EOS for Zc.
|10.01 - Introduction to Phase Diagrams||Click here.||96||5||
Introduction to Phase Behavior (9:37) (msu.edu)
1. Referring to the Txy diagram on slide 3, estimate T, nature (ie. L,V, V+L, L+L), composition(s), and amount of the phase(s) for points: a, b. d, g.
|11.02 - Calculations with Activity Coefficients||Click here.||96||5||
Dew Temperature (7:57) (msu.edu)
The culmination of the activity coefficient method is application of the fitted activity coefficients to extrapolate from limited experiments in a Stage III calculation. The recommended order of study is 1) Bubble Pressure; 2) Bubble Temperature; 3) Dew Pressure; 4) Dew Temperature. Note that an entire Txy diagram can be generated with bubble temperature calculations; no dew calculations are required. However, many applications require dew calculations, so they cannot be avoided. The dew calculations are more complicated than bubble calculations, because the liquid activity coefficients are not known until the unknown liquid mole fractions are found. This screencast describes the procedure and how to implement the method in Matlab or Excel.
|14.10 Solid-liquid Equilibria||Click here.||93.3333||3||
SLE using Excel with the M1 model (7min, uakron.edu)
Similar to LLE in Excel, the iteration feature can be used to quickly solve for SLE at multiple temperatures.
|07.06 Solving The Cubic EOS for Z||Click here.||93.3333||3||
1. Peng-Robinson PVT Properties - Excel (3:30) (msu.edu)
Introduction to PVT calculations using the Peng-Robinson workbook Preos.xlsx. Includes hints on changing the fluid and determining stable roots.
1. At 180K, what value of pressure gives you the minimum value for Z of methane? Hint: don't call solver.
2. At 30 bar, what value of pressure gives Z=0.95 for methane?
3. Compute the molar volume(s) (cm3/mol) for argon at 100K for each of the following?