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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."

Comprehension Questions:

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.
1. Suppose the range of the potential (λ) was increased. Would the configurational energy increase, decrease, or stay the same?
2. Suppose the density was decreased. Would the configurational energy increase, decrease, or stay the same?
3. Suppose the temperature was increased at constant density. Would the configurational energy increase, decrease, or stay the same?
4. Suppose the temperature was increased at constant density. Would the configurational energy characterized by (U-Uig)/RT  increase, decrease, or stay the same?
5. Molecules A and B can be represented by the square-well potential. For molecule A, σ = 0.2 nm and ε = 30e-22 J. For molecule B, σ = 0.35 nm and ε = 20e-22 J.  Sketch the potential models for the two molecules on the same pair of axes clearly indicating σ's and ε's of each species. Start your x-axis at zero and scale your drawing properly.  Make molecule A a solid line and B a dashed line. Which molecule would you expect to have the higher boiling temperature? (Hint: check out Figure 1.2.)
6. Sketch the potential and the force between two molecules vs. dimensionless distance, r/σ, according to the Lennard-Jones potential. Considering the value of r/σ when the force is equal to zero, is it greater, equal, or less than unity?

Steam Tables (LearnChemE.com) (5:59) calculate enthalpy of steam by interpolation

Txy Phase Diagram Showing LLE and VLE Simultaneously (9min,uakron.edu)

The binary Txy phase diagram of methanol+benzene is visualized with sample calculations of the SSCED model with several values of the nonideality (kij) parameter. The calculations show the liquid-liquid equilibrium (LLE) phase boundary as well as the vapor-liquid equilibrium (VLE) boundary. As the estimated nonideality (kij) increases, the LLE boundary crashes into the VLE. It is so exciting that it makes a thermo nerd wax poetic about the "valley of Gibbs."

Comprehension Questions:

1. The LLE phase boundary moves up as the nonideality increases. Which way does the VLE contribution move? Explain how this relates to the molecules' escaping tendencies.
2. How would this phase diagram change if the pressure was increased to, say, 10 bars?
3. What value of kij is required to make the LLE binodal barely touch the VLE at 1 bar?
4. What value of kij is required to make the LLE binodal barely touch the VLE at 10 bars?

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."

Comprehension Questions
1. Order the following binary systems from most compatible to least compatible according to the MAB model:
(Note: negative deviations from Raoult's law indicate greater "compatibility," although they may generate azeotropes.)
(a) ethanol+water (b) ethanol+benzene (c) ethanol+diethylamine (d) n-pentane+n-pentanol (e) n-hexane+benzene
2. Pick a couple of binary systems from the Korean Database (Hint: use Internet Explorer for KDB) and compare the experimental data to the MAB predictions. Refine your predicted M1 parameter by calling the solver to minimize the sum of squared deviations between the predicted and experimental pressures. If there was an azeotrope in one of your systems, did the MAB model miss it or was it qualitatively correct?

Raoult's Law (5:39) (msu.edu)
What type of components make an ideal solution that follows Raoult's Law? What does a diagram look like for a system that follows Raoult's Law? Can you identify the regions? What is the K-ratio for Raoult's Law? What simple principles must be followed for the K-ratios of the components in a binary mixture?

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).

Comphrehension Questions:

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.

03.1 - Heat Engines and Heat Pumps: The Carnot Cycle Click here. 60 2

Heat Engine Introduction (LearnChemE.com, 6min) introduction to Carnot heat engine and Rankine cycle. 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). But it is impractical for several reasons as discussed in the video. When operating on steam as the working fluid, as is common in nuclear power plants, coal fired power plants, and concentrated solar power plants, the Rankine cycle is much more practical, as explained here. This LearnChemE video is short and sweet, but it applies the property of entropy, which is not introduced until Chapter 4. All you need to know about entropy at this stage is that the change in entropy is zero for an adiabatic and reversible process and the change in entropy is greater than zero when you add heat or cause irreversibility. Since entropy is a state function, we can use the steam tables to facilitate accounting for inefficiencies. Entropy becomes essential when using steam as the working fluid because working out ∫PdV of steam is much more difficult than for an ideal gas. We reiterate this video in Chapter 5, where we discuss calculations for several practical cyclic processes.

Comprehension Questions:
1. Why is the Carnot cycle impractical when it comes to running steam through a turbine? How does the Rankine cycle solve this problem?
2. Why is the Carnot cycle impractical when it comes to running steam through a pump? How does the Rankine cycle solve this problem?
3. It is obvious which temperatures are the "high" and "low" temperatures in the Carnot cycle, but not so much in the Rankine cycle. The "boiler" in a Rankine cycle actually consists of "simple boiling" where the saturated liquid is converted to saturated vapor, and superheating where the saturated vapor is raised to the temperature entering the turbine. When comparing the thermal efficiency of a Rankine cycle to the Carnot efficiency, should we substitute the temperature during "simple" boiling, or the temperature entering the turbine into the formula for the Carnot efficiency? Explain.

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.

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 Tis 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:
1. Should we express temperature in Kelvins or Celsius when calculating the Carnot efficiency? Explain.
2. What value of TC would be necessary to achieve 100% efficiency, even for this idealized, maximally efficient process? Explain.
3. Why is it impractical to reject heat at the value of Tdiscussed in Question 2 above? What is a more practical temperature for rejecting heat? (Hint: what geographical feature is very closely located near most nuclear power plants? "Geographical features" might include mountains, desserts, large bodies of water, forests, ...)
4. What value of TH would be necessary to approach 100% efficiency, even for this idealized, maximally efficient process? What are the practical limitations on TH? Explain.
5. How can the formula for Carnot efficiency help us to calculate the "lost" work in the presence of a temperature gradient?

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.