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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(T2/T1) + R ln(V2/V1). 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(T2/T1) - R ln(P2/P1).

Comprehension Questions:
1. Show the steps required to derive ΔS = Cp ln(T2/T1) - R ln(P2/P1) from ΔS = Cv ln(T2/T1) + R ln(V2/V1).
2. We derived a memorable equation for adiabatic, reversible, ideal gases in Chapter 2. Hopefully, you have memorized it by now! Apply this formula to compute the change in entropy for adiabatic, reversible, ideal gases as they go through any change in temperature and pressure.
3. Make a table enumerating all the possibilities for 3 oscillators with 4 units of energy. 
4. Compute the change in entropy (J/k) for 100 oscillators going from 3 units of energy to 50 units of energy.
5. Compute the change in entropy (J/K) for 100 particles going from 3 boxes to 50 boxes. (This is a review of configurational entropy.)
07.02 Corresponding States Click here. 50 8

Principles of Corresponding States (10:02) (msu.edu)
An overview of use of Tc and Pc and acentric factor to create corresponding states correlation. The relation between acentric factor and deviations from spherical fluids is highlighted.

Comprehension Questions:

1. What is the value of the reduced vapor pressure for Krypton at a reduced temperature of 0.7? How does this help us to characterize the vapor pressure curve?

2. Sketch the graph of vapor pressure vs. temperature as presented in this screencast for the compounds: Krypton and Ethanol. Be sure to label your axes completely and accurately. Draw a vertical line to indicate the condition that defines the acentric factor.
10.03 - Binary VLE using Raoult's Law Click here. 50 2

This screencast shows binary bubble, dew, and flash sample calculations (uakron, 19min) for methanol and ethanol. It complements the previous video by showing how the bubble and dew pressures relate to the Pxy diagram. It supplements the previous video with examples of numerical results for the bubble and dew temperatures. An isothermal flash calculation requires a different approach, but it also encompasses the bubble and dew temperature and pressure calculations. In a flash calculation, the bubble result is recovered when V/F = 0. The dew result is recovered when V/F=1.

Comprehension Questions (Assume the ideal solution SCVP model.):

1. Estimate the bubble pressure (mmHg) and vapor composition of methanol+ethanol at 50 C and xM = 0.4. (Note that the SCVP model should be used now.)
2. Estimate the dew temperature (C) and vapor composition of methanol+benzene at 50 C and yM = 0.4.
3. Estimate the vapor fraction and vapor/liquid compositions of methanol+benzene at 50 C, 355mmHg, and zM = 0.45.
4. Estimate the vapor fraction and vapor/liquid compositions of methanol+benzene at 50 C, 365mmHg, and zM = 0.45. (Hint: think carefully.)
04.09 Turbine calculations Click here. 50 10

General procedure to solve for steam turbine efficiency. (LearnChemE.com, 5min) This video outlines the procedure without actually solving any specific problem. It shows how inefficiency affects the T-S diagram and how to compute the actual temperature at the turbine outlet.
Comprehension Questions:
1. In this video, the entropy at the outlet of the actual turbine is to the right of the entropy for the reversible turbine. Suppose we were interested in the T-S diagram for a 75% efficient compressor. Would the outlet entropy of the actual compressor be to the right of the entropy for the reversible turbine, to the left, or about the same? Explain.
2. In the video, Prof. Falconer states that the outlet entropy must be the same as the inlet entropy because the process is reversible and one other property. What is the other requirement for the turbine to be isentropic? Explain.
3. Will inefficiency in the turbine always cause the temperature at the outlet to be higher than the inlet? Explain.
03.6 - Energy Balance for Reacting Systems Click here. 50 2

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.

Comprehension Questions:
1. Use this approach to compute the heat of reaction for 2 CH3OH = CH3OCH3 + H2O at 250C and 1 bar. Compare to your answer when using the pathway of Figure 3.5a. 
2. Methanol is a liquid at 45C and 2bars. Compute the enthalpy of a stream that is 100 mol/h of pure methanol at 45 C and 2 bars according to the method of Figure 3.5b. Hint: this is different from the pathway of Figure 2.6c because it includes the heat of formation.
05.4 - Refrigeration Click here. 50 8

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?
13.02 - Wilson's Equation Click here. 49.2308 13

Wilson's model concepts (2:44) (msu.edu)

The background on the assumptions and development of Wilson's activity coefficient model.

Comprehension Questions:

1. What value is assumed by Wilson's model for the coordination number (z)?
2. What are the values of Λ21 and Λ12 at infinite temperature, according to Wilson's equation?
3. Solve for x1+x2Λ12 in terms of volume fraction (Φ1) and mole fraction (x1) at infinite temperature.
4. What type of phase behavior is impossible to represent by Wilson's equation?
08.01 - The Departure Function Pathway Click here. 49.2308 13

Departure Function Overview (11:22) (msu.edu)
The philosophy and overall approach for using departure functions.
06.2 Derivative Relations Click here. 49.0909 11

Exact Differentials and Partial Derivatives (LearnChemE.com, 5min) This math review puts into context the discussion of exact differentials in Section 6.2 of the textbook using an example related to the volume of a cylinder.

Comprehension Questions:

1. Given that dU = TdS - PdV, what derivative relation comes from setting ∂2U/(∂S∂P) = ∂2U/(∂P∂S)?

2. Given that dA = -SdT - PdV, what derivative relation comes from setting ∂2A/(∂T∂V) = ∂2A/(∂V∂T)?

3. Given that dG = -SdT + VdP, what derivative relation comes from setting ∂2G/(∂T∂P) = ∂2G/(∂P∂T)?
01.5 Real Fluids and Tabulated Properties Click here. 49.0909 11

P-V and P-T diagrams (LearnChemE.com) (5:52) Describes distinctions and trends between solid, vapor, liquid, gas.

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