Top-rated ScreenCasts

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04.02 The Microscopic View of Entropy Click here. 65 4

Principles of Probability II, Counting Events, Permutations and Combinations. This part discusses the binomial and multinomial coefficients for putting particles in boxes. The binomial and multinomial coefficient are used in section 4.2 to quantify configurational entropy. (msu.edu, 16min) (Flash) You might like to check out the sample calculations below before attempting the comprehension questions.
Comprehension Questions:
1. Write the formulas for the binomial coefficient, the multinomial coefficient, and the multinomial with repetition.
2. Ten particles are distributed between two boxes. Compute the number of possible ways of achieving 7 particles in Box A and 3 particles in Box B.
3. Note that the binomial distribution is a special case of the multinomial distribution where the number of categories is 2. Also note that the total number of events for a multinomial distribution is given by M^N where M is the number of categories (aka. outcomes, e.g. boxes) and N is the number of objects (aka. trials, e.g. particles). The probability of a particular observation is given by the number of combinations divided by the total number of events. Compute the probability of observing 7 particles in Box A and 3 Particles in Box B.
4. Ten particles are distributed between three boxes. Compute the probability of observing 7 particles in Box A, 3 particles in Box B, and zero particles in Box C.
5. Ten particles are distributed between three boxes. Compute the probability of observing 3 particles in Box A, 3 particles in Box B, and 4 particles in Box C.
11.02 - Calculations with Activity Coefficients Click here. 64.2105 19

Dew Pressure (7:41) (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 Pxy diagram can be generated with bubble pressure 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.
11.06 - Redlich-Kister and the Two-parameter Margules Models Click here. 62.8571 7

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.
01.4 Basic Concepts Click here. 62 20

Molecular Nature of U and PV=RT (msu.edu) (5:04)

Internal energy is the sum of molecular kinetic energy and intermolcular potential energy, which leads to the relation between internal energy and temperature for an ideal gas. Also, the ideal gas law can be derived by incoporating the relation between kinetic energy and temperature with the force due to the molecules bouncing off the walls.

Comprehension question:
One mole of Xenon molecules (MW=131g/mol) is flying back and forth in the x-direction of a three-dimensional cube of 1m³ volume with zero velocity in the y- or z- directions. The velocity of every molecule is 300 m/s. Estimate the pressure (MPa) in the x- and y- directions.
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.

Concept Questions:

1. What equation can we use to estimate the fugacity of a compressed liquid relative to its saturation value?
2. How accurate is that equation relative to the change in pressure when we are close to saturation?
3. The video shows a graph of ln(f/P) vs. P. Which phase gives the lower value of fugacity when you are to the right of the intersection point? (ie. vapor or liquid?)
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.
14.04 LLE Using Activities Click here. 60 2

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?
08.07 - Implementation of Departure Functions Click here. 60 2

Helmholtz Departure - PR EOS (uakron.edu, 11min) This lesson focuses first and foremost on deriving the Helmholtz departure function. It illustrates the application of integral tables from Apx. B and the importance of applying the limits of integration. It is the essential starting point for deriving properties involving entropy (S,A,G) of the PREOS, and it is a convenient starting point for deriving energetic properties (U,H).
01.6 Summary Click here. 60 4

Keys to the Kingdom of Chemical Engineering (uakron.edu, 11min) Sometimes it helps to reduce a subject to its simplest key elements in order to "see the forest instead of the trees." In this presentation, the entire subject of Chemical Engineering is reduced to three key elements: sizing a reactor (Uakron.edu, 7min), sizing a distillation column (uakron.edu, 9min), and sizing a heat exchanger (uakron.edu, 9min). In principle, these elements involve the independent subjects of kinetics, thermodynamics, and transport phenomena. In reality, each element involves thermodynamics to some extent. Distillation involves thermodynamics in the most obvious way because relative volatility and activity coefficients are rarely discussed in a kinetics or transport course. In kinetics, however, the rate of reaction depends on the partial pressures of the reactants and their nearness to the equilibrium concentrations, which are thermodynamical quantities. In heat exchangers, the heat transfer coefficient is important, but we also need to know the temperatures for the source and sink of the heat transfer; these temperatures are often dictated by thermodynamical constraints like the boiling temperature or boiler temperature required to run a Rankine cycle (cf. Chapter 5). In case you are wondering about the subject of "mass and energy balances," the conservation of mass is much like the conservation of energy; therefore, we subsume this subject under the general umbrella of thermodynamics. Understanding the distinctions between thermodynamics and other subjects should help you to frame a place for this knowledge in your mind. Understanding the interconnection of thermodynamics with subjects to be covered later should help you to appreciate the necessity of filing this knowledge away for the long term, such that it can be retrieved at any time in the future.

If you would like a little more practice with reactor mass balances and partial pressure, more screencasts are available from LearnChemE.com, MichiganTech, and popular chemistry websites.
01.5 Real Fluids and Tabulated Properties Click here. 60 2

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

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