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|07.06 Solving The Cubic EOS for Z||Click here.||60||4||
5. Peng Robinson Using Solver for PVT and Vapor Pressure - Excel (4:42) (msu.edu)
Describes use of the Goal Seek and Solver tools for Peng-Robinson PVT properties and vapor pressure.
1. Which of the following represents the vapor pressure for argon at 100K?
|05.5 Liquefaction||Click here.||60||2||
Joule-Thomson Expansion (LearnChemE.com, 7min) describes the Joule-Thomson coefficient - (dT/dP)H. For non-ideal fluids (including liquids), the temperature usually drops as the pressure drops. From a molecular perspective, it requires energy to rip molecules apart when they are in their attractive wells, and this energy must be taken from the thermal energy of the molecules themselves if the system is adiabatic. This video refers to the PREOS.xls spreadsheet to be used more in Unit II, but you can get the idea of how the Joule-Thomson expansion provides a basis for any liquefaction of any chemical, including the liquefaction that occurs in refrigeration and the one that occurs in a process designed to simply recover liquid product (e.g. liquefied natural gas (LNG), aka. methane).
1. Referring to the table for R134a in Appendix E-12, compute the fraction liquid at 252K after throttling from a saturated liquid at 300K.
2. Referring to the table for R134a in Appendix E-12, compute the fraction liquid at 252K after expanding a saturated liquid at 300K through a reversible turbine.
|09.10 - Saturation Conditions from an Equation of State||Click here.||60||1||
We can combine the definition of fugacity in terms of the Gibbs Energy Departure Function with the procedure of visualizing an equation of state to visualize the fugacity as characterized by the PR EOS. (21min, uakron.edu) This amounts to plotting Z vs. density, similar to visualizing the vdW EOS. Then we simply type in the departure function formula. Since the PR EOS describes both vapors and liquids, we can calculate fugacity for both gases and liquids. Taking the reciprocal of the dimensionless density ( V/b=1/(bρ) ) gives a dimensionless volume. When the dimensionless pressure (bP/RT) is plotted vs. the dimensionless volume, the equal area rule indicates the pressure where equilibrium occurs and this can be checked by comparing the ln(f/P) values for the liquid and vapor roots. When the pressure is not exactly saturated, we may still be in the 3-root region. Then you need to check the fugacity to determine which phase is stable.
1. What equation can we use to estimate the fugacity of a compressed liquid relative to its saturation value?
|01.2 Molecular Nature of Temperature, Pressure, and Energy||Click here.||60||9||
Molecular Nature of Internal Energy: Configurational Energy. (uakron.edu, 19min) Making the connection between "u" and "U" requires the concept configuring the molecules such that their potentials overlap. Then it is a simple matter (conceptually) to count the number of overlaps that occur and multiply by the energy of the overlap to get the "configurational energy." Adding the configurational energy to the translational (and vibrational) energy (Uig, discussed above), gives the total "U."
For 1-4, assume 100 molecules are held in a cylinder with solid walls. A piston in the cylinder can move to adjust the density.
|01.5 Real Fluids and Tabulated Properties||Click here.||60||2||
Steam Tables (LearnChemE.com) (5:59) calculate enthalpy of steam by interpolation
|10.03 - Binary VLE using Raoult's Law||Click here.||60||2||
Raoult's Law (5:39) (msu.edu)
|11.02 - Calculations with Activity Coefficients||Click here.||60||2||
This example shows how to predict activity coefficients in Excel using the Margules Acid-Base (MAB) model.(8min, uakron.edu) Sometimes you just need a quick estimate of whether to suspect an azeotrope or LLE or some other anomalous behavior. If the MAB model indicates a possible problem, it's time to go to the library or the lab and validate your model with experimental data.
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."
|03.6 - Energy Balance for Reacting Systems||Click here.||60||1||
Heat Removal from a Chemical Reactor (uakron, 8min) determines heat removal so that a chemical reactor is isothermal following the pathway of Figure 3.5b using the pathway of Figure 2.6c if a heat of vaporization is involved. The reaction is: N2 + 3H2 = 2NH3 at 350C and 1 bar. The pathway to go from products to the reference condition is to correct for any liquid formation at the conditions of the product stream then cool/heat the products to 25C (the reference temperature), then "unreact" them back to their elements of formation. Summing up the enthalpy changes over these steps gives the overall enthalpy of the reactor outlet stream. The same procedure applied to the reactor inlet gives the overall enthalpy of reactor inlet stream. Then the heat duty of the reactor is simply the difference between the two stream enthalpies.
|11.06 - Redlich-Kister and the Two-parameter Margules Models||Click here.||56.6667||6||
Two-parameter Margules Equation (5:05) (msu.edu)
An overview of the two parameter Margules equation and how it is fitted to a single experiment.
|03.1 - Heat Engines and Heat Pumps: The Carnot Cycle||Click here.||56.6667||6||
Introduction to the Carnot cycle (Khan Academy, 21min). 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). Note that Khan uses the absolute value when referring to quantities of heat and work so his equations may look a little different from ours. By systematically adding up the heat and work increments through all stages of the process, we can infer an approximate equation for thermal efficiency (Khan Academy, 14min) The steps are isothermal and reversible expansion, adiabatic and reversible expansion, isothermal and reversible compression, and adiabatic/reversible compression. We know how to compute the heat and work for ideal gases of each step based on Chapter 2. In this presentation by KhanAcademy, an additional proof is required (17min) to show that the volume ratio during expansion is equal to the volume ratio during compression. (Note that the presentation by KhanAcademy uses arbitrary sign conventions for heat and work. They prefer to change the sign to minimize the use of negative numbers but it doesn't always work out.) When we put it all together, the equation we get for "Carnot efficiency" is remarkably simple: ηθ = (TH - TC)/TH, where TH is the hot temperature and TC is the cold temperature. We can use this formula to quickly estimate the thermal efficiency for many processes. We will show in Chapter 5 that this formula remains the same, even when we use working fluids other than ideal gases (e.g. steam or refrigerants).