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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, η_{θ}). 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: η_{θ} = (T_{H}  T_{C})/TH, where T_{H} is the hot temperature and T_{C }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). Comprehension Questions: 
11.06  RedlichKister and the Twoparameter Margules Models  Click here.  56.6667  6 
Twoparameter Margules Equation (5:05) (msu.edu) An overview of the two parameter Margules equation and how it is fitted to a single experiment. 
01.2 Molecular Nature of Temperature, Pressure, and Energy  Click here.  56.25  16 
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 (U^{ig}, discussed above), gives the total "U."
Comprehension Questions:
For 14, assume 100 molecules are held in a cylinder with solid walls. A piston in the cylinder can move to adjust the density. 
10.04  Multicomponent VLE & Raoult's Law Calculations  Click here.  55  4 
This example shows how to use VLookup with the xls Solver to facilitate multicomponent VLE calculations for ideal solutions: bubble, dew, and isothermal flash. (15min, uakron.edu) The product xls file serves as a starting point for multicomponent VLE calculations with activity models and for adiabatic flash and stream enthalpy calculations. This video shows sample calculations for the bubble, dew, and flash of propane, isobutane, and nbutane, like Example 10.1. 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." Comprehension Questions  Assume the reboiler composition for the column in Example 10.1 was zi={0.2,0.3,0.5} for nbutane, isopentane, and npentane, respectively. a) Calculate the temperature at which the boiler must operate in order to boil the bottoms product completely at 8 bars. 
07.06 Solving The Cubic EOS for Z  Click here.  53.3333  3 
4. Selecting Stable Roots (1:11) (msu.edu) Selecting stable roots is often one of the confusing aspects in working with cubic equations of state. This screencasts gives a visual picture of how the roots and stability are related to the vapor pressure and EOS humps at subcritical temperatures. 
11.02  Calculations with Activity Coefficients  Click here.  53.3333  3 
Bubble Pressure (5:25) (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. As the easiest routine to apply, the bubble pressure method should be studied first. The recommended order of study is 1) Bubble Pressure; 2) Bubble Temperature; 3) Dew Pressure; 4) Dew Temperature. Note that an entire Pxy diagram can be generated with bubble pressure calculations; no dew calculations are required. 
04.02 The Microscopic View of Entropy  Click here.  53.3333  3 
Connecting Microstates, Macrostates, and the Relation of Entropy to Disorder (uakron.edu, 14min). For small systems, we can count the number of ways of arranging molecules in boxes to understand how the entropy changes with increasing number of molecules. By studying the patterns, we can infer a general mathematical formula that avoids having to enumerate all the possible arrangements of 10^23 molecules (which would be impossible within several lifetimes). A surprising conclusion of this analysis is that entropy is maximized when the molecules are most evenly distributed between the boxes (meaning that their pressures are equal). Is it really so "disordered" to say that all the molecules are neatly arranged into equal numbers in each box? Maybe not in a literary world, but it is the only logical conclusion of a proper definition of "entropy." It is not necessary to watch the videos on probability before watching this one, but it may help. And it might help to rewatch the probability videos after watching this one. Moreover, you might like to see how the numbers relate to the equations through sample calculations (uakron, 15min). These sample calculations show how to compute the number of microstates and probabilities given particles in Box A, B, etc and also the change in entropy. Comprehension Questions: 1. What is the number of total possible microstates for: (a) 2 particles in 2 boxes (b) 5 particles in 2 boxes (c) 10 particles in 3 boxes. 2. What is the probability of observing: (a) 2 particles in Box A and 3 particles in Box B? (b) 6 particles in Box A and 4 particles in Box B? (c) 6 particles in Box A and 4 particles in Box B and 5 particles in Box C? 
04.02 The Microscopic View of Entropy  Click here.  53.3333  3 
Relating the microscopic perspective on entropy to macroscopic changes in volume (uakron.edu, 11min) Through the introduction of Stirling's approximation, we arrive at a remarkably simple conclusion for changes in entropy relative to the configurations of ideal gas molecules at constant temperature: ΔS = Rln(V_{2}/V_{1}). This makes it easy to compute changes in entropy for ideal gases, even for subtle changes like mixing. Comprehension Questions: 1. Estimate ln(255!). 2. A system goes from 6 particles in Box A and 4 particles in Box B to 5 particles in each. Estimate the change in S(J/K). 3. A system goes from 6 moles in Box A and 4 moles in Box B to 5 moles in each. Estimate the change in S(J/molK). 
02.03 Work Associated with Flow  Click here.  52  5 
Energy and Enthalpy Misunderstandings (LearnChemE.com) (3:20) Three examples related to enthalpy and work changes that are often confusing...

04.02 The Microscopic View of Entropy  Click here.  50  2 
Molecular Nature of S: Thermal Entropy (uakron.edu, 20min) We can explain configurational entropy by studying particles in boxes, but only at constant temperature. How does the entropy change if we change the temperature? Why should it change if we change the temperature? The key is to recognize that energy is quantized, as best exemplified in the Einstein Solid model. We learned in Chapter 1 that energy increases when temperature increases. If we have a constant number of particles confined to lattice locations, then the only way for the energy to increase is if some of the molecules are in higher energy states. These "higher energy states" correspond to faster (higher frequency) vibrations that stretch the bonds (Hookean springs) to larger amplitudes. We can count the number of molecules in each energy state similar to the way we counted the number of molecules in boxes. Then we supplement the formula for configurational entropy changes to arrive at the following simple relation for all changes in entropy for ideal gases: ΔS = Cv ln(T_{2}/T_{1}) + R ln(V_{2}/V_{1}). Note that we have related the entropy to changes in state variables. This observation has two significant implications: (1) entropy must also be a state function (2) we can characterize the entropy by specifying any two variables. For example, substituting V = RT/P into the above equation leads to: ΔS = Cp ln(T_{2}/T_{1})  R ln(P_{2}/P_{1}). Comprehension Questions: 