Molecular Nature of Energy and Temperature (msu.edu) (3:34)
This introduction shows the connection with temperature and kinetic energy.  When applying Eqn. 1.1, you must be careful to keep your units straight, as illustrated in this sample calculation of the molecular temperature for xenon (Mw=131). (uakron, 5min).

Comprehension Questions:

1. A 1m3 vessel contains 0.5m3 of saturated liquid in equilibrium with 0.5 m3 of saturated vapor. Which molecules are moving slower? (a) the vapor (b) the liquid (c) they are all the same.

2. A glass of ice water is sitting in your freezer, set to 0C and fully equilibrated. Which molecules are moving slower? (a) the gas (b) the liquid (c) the solid (d) they are all the same.

3. You walk into the kitchen in the morning to get some breakfast. The ceiling fan is on. You forgot your slippers. Which one is "hotter?" (a) the floor (b) the ceiling (c) the granite counter top (d) the air in the room (e) they are all the same.

Intermolecular Potential Energy (msu.edu) (7:11)

The intermolecular potential energy is distinct from the gravitational potential energy of the center of mass. Further, understanding of the potential energy relation with intermolecular force is important.

Comprehension Questions:

1. 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.)

2. The potential, u(r), represents the work of bringing two molecules together from infinite distance to distance r. So, what is the force law between two molecules according to the Lennard-Jones potential model? Hint: W=∫F*dx

3. 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?

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.

The objectives for Chapter 1 were:

1. Explain the definitions and relations between temperature, molecular kinetic energy,
molecular potential energy and macroscopic internal energy, including the role of intermolecular potential energy and how it is modeled. Explain why the ideal gas internal energy
depends only on temperature.
2. Explain the molecular origin of pressure.
3. Apply the vocabulary of thermodynamics with words such as the following: work, quality,
interpolation, sink/reservoir, absolute temperature, open/closed system, intensive/extensive
property, subcooled, saturated, superheated.
4. Explain the advantages and limitations of the ideal gas model.
5. Sketch and interpret paths on a P-Vdiagram.
6. Perform steam table computations like quality determination, double interpolation.

To these, we could add expressing and explaining the first and second laws. Make a quick list of these expressions and explanations in your own words, including cartoons or illustrations as you see fit,  starting with the first and second laws.

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.

Energy and Enthalpy Misunderstandings (LearnChemE.com) (3:20) Three examples related to enthalpy and work changes that are often confusing...
Comprehension Questions:
1. During one stroke of a steam engine, the pressure inside the (~frictionless) cylinder is maintained at 3MPa from a supply line at 500 C while the pressure created by the force on the cam shaft and atmosphere combined is 2.5 MPa.  The volume swept by the cylinder during one stroke is 10 L.  Compute the work achieved by this process (kJ).  
2. Was there any "lost work" in the above process? If so, compute its magnitude (kJ) and explain where those kJ are now.
3. Consider N2 in a closed cylinder with a piston initially at 1 bar and 300K. The system is heated to 400K such that the piston moves to maintain constant pressure. Is it true that Q = Cp dT for this system or should it be Cv dT or something else? Explain using a detailed analysis of the energy balance.

The reversible process is a common conception throughout discussions of thermodynamics. One very common illustration has to do with grains of sand being removed from a piston (KhanAcademy, 15min). It is also helpful to put the relation of reversibility into context with the work as a path function. (YouTube, 1.5min).

Comprehension Questions
1. Describe what happens when you knock a complete block off a piston under pressure. Assume the piston has mass roughly equal to the block, the cylinder is infinitely tall and everything is adiabatic, the gas in the cylinder is ideal, and the open side of the cylinder is at atmospheric pressure. In particular, does the piston go monotonically to its equilibrium position or does it do something else? If not, then what causes it to approach in a different way and why does it eventually reach its equilibrium state?
2. Consider the same piston/cylinder as above but compare it to a piston/cylinder with grains of sand. Is the final height of the piston the same, lower, or higher when you remove the weight one grain at a time vs. knocking the block off all at once? Hint: write the energy balance and carefully consider the work accomplished in each case.

State functions explained (LearnChemE.com, 5min). Properties like those listed in the steam tables are functions of P, V, T, etc. They depend only on the state variables and knowing two of the variables is enough to figure out all the rest. Other functions are like heat and work; they depend on the path by which you proceed to evaluate their changes. Path function sample calculations (uakron, 9min) are useful in providing concrete illustrations of how the path matters for work and heat.

Comprehension Questions:
1. Consider a monatomic ideal gas in an insulated piston/cylinder with a vaccuum outside the piston, originally at 300K and 1bar. Suppose the volume is suddenly doubled with zero resistance against the piston. Compute the change in U and the work accomplished.
2. Consider the same ideal gas etc as above. Now suppose the volume is slowly doubled (e.g. using grains of sand). Compute the change in U and the work accomplished.
3. Continuing from #2 above, the insulation is removed and the piston/cylinder is allowed to equilibrate to its original temperature in #1 above. Compute the change in U and the work accomplished for this stage.
4. Compare the entire process from 2-3 above with the process in #1. Compute the change in U and the work accomplished overall. Also compare the final pressures. Is pressure a state function or a path function?

Constant pressure process using steam (LearnChemE.com, 5min). 2000 kJ of heat is isobarically added to steam piston/cylinder starting at 0.45MPa with 0.9kg as vapor and 0.1kg as liquid. Compute the final temperature, work, and state of the steam. Once we have our general energy balance defined, we can straigntforwardly reduce it to its simplest applicable form to solve problems. The energy balance is the same regardless of whether the process uses an ideal gas, steam, or some other working fluid. But the method of solving the problem changes quite a bit depending on the working fluid.
Hint: "steam" and H2O are the same thing. So "liquid steam" is also known as "water."

Comprehension questions:
1. Describe how you would solve this problem if the H2O was replaced with a monatomic ideal gas (MW=40). Use the same starting pressure and temperature as the steam, but obviously the entire 1.0 kg will be gas, with no liquid.
2. Describe how you would write the energy balance if the cylinder was 5m3 total, open to the atmosphere, and the pressure was suddenly reduced to 1 bar. Assume the piston has a mass of 0.1kg.

Adiabatic, Reversible Compression of an Ideal Gas in a Piston/Cylinder (LearnChemE.com, 5min). The standard formula for an adiabatic, reversible, ideal gas is derived here in the T,V form. You should be able to rearrange the given equation into the usual form:
(T2/T1) = (P2/P1)^(R/Cp) to show they are equivalent. (Hint: PV=RT and Cp=Cv+R). The interesting part of this video is during the last 10 seconds. Watch what happens!

Comprehension Questions:

1. My bicycle pump is about 50cm tall and 2.0cm diameter. When I pump it down, the pressure goes to 100psig (after pumping once or twice). What is the temperature of the air that goes into the tire at that point?

2. What is the length (cm) remaining in the pump?

Understanding Enthalpy (uakron.edu, 6min) The vocabulary just keeps on coming. Usually, it helps to picture the physical process and think about what is happening with the molecules. Then the names applied nearly always make sense as they refer to some specific part of the overall picture. This is not the case for enthalpy. Enthalpy is merely a convenient lumping of other more fundamental terms. It has purely a mathematical definition. There is nothing physical about it. Keep in mind that this kind of arbitrary definition is the exception, not the rule. The rule is: try to understand each aspect of vocabulary in terms of its physical meaning. An exception is enthalpy. Enthalpy has no physical meaning.

The complete energy balance is convenient in the sense that it provides a comprehensive list of everything you need to check to ensure that you have accounted for all energy flows, but it can appear to be a little overwhelming at first glance. Common energy balances (uakron, 14 min) of the energy balance can be used in many situations, but don't forget that the process of analyzing a system and determining its proper model equations is an important part of thermodynamics, and engineering in general. Focus on learning the process, not memorizing the final equations. Energy balance practice (uakron, 18min) with Chapter 2 systems can help you build confidence and quickly prepare for mastering all the example problems in Chapter 2. Try to push pause after each problem statement and work it out for yourself, then resume to provide a check on your analysis.

Comprehension Questions. Write the simplified energy balance for the following:

1. High pressure steam flows through an adiabatic turbine to steadily produce work. 

2. High pressure steam flows into a piston-cylinder to produce work. 

3. Steam at 200 bars and 600°C flows through a valve and out to the atmosphere. 

4. A gas is filling a rigid tank from a supply line.

5. A gas is leaking from a rigid tank into the air. 

6. A sunbather lays on a blanket. At 11:30 a.m., the sunbather begins to sweat. System: the sunbather at 12 noon.

Common Property Change Calculations (uakron, 11min). When we need to compute a change in energy or enthalpy, we may quickly resort to CvΔT or CpΔT, but you should also note that large changes can occur due to phase change. These considerations motivate careful consideration of the definitions of Cv and Cp, and the development of convenient equations for estimating heat of vaporization. To know when to apply the heat of vaporization, you need to know the saturation conditions, for which a quick estimate can be obtained from the short-cut vapor pressure (SCVP) equation. When the chemical of interest is H2O, these hand calculation methods can be compared to the properties given in the steam tables. Sample calculations of property changes (uakron, 21min) can be used to illustrate the precision of the quick estimates obtained from Eqs. 2.45, 2.47 and the back flap. These calculations provide practice with the steam tables at unusual conditions as well as validating your skills with the hand calculation formulas.

Comprehension Questions:
1. Develop an adaptation of props.xlsx that is most convenient for you personally to compute quick estimates of saturation temperature, saturation pressure, ideal gas enthalpy changes. You might want to view the props.xlsx and shortcut Antoine coefficients software tutorials.
2. Quickly estimate the change in enthalpy as CO2 goes from 350K, 1bar to 300K, 1bar.
3. Quickly estimate the change in internal energy as CO2 goes from 350K, 1bar to 300K, 1bar.
4. Quickly estimate the change in enthalpy as CO2 goes from 350K, 1bar to 300K, 100bar. Hint: the change in enthalpy to go from a saturated liquid to a compressed liquid can be computed from the adiabatic, reversible pump work.

We can streamline process calculations by defining a common reference state and computing values of enthalpy for all streams. A convenient path for tabulating properties relative to a reference state is illustrated in Figure 2.6c. It is very similar to the common calculation of DH illustrated in section 2.10. We define the common reference state to be the ideal gas at 25C (298K). Then (1) compute the change in ideal gas properties to the temperature of the stream. (2) Use Eqn. 2.47 to check Psat/Tsat in case a liquid may be forming (3) if liquid, use Eqn. 2.45 to compute the change from the ideal gas to the saturated liquid (4) if P^Liq >> P^sat, compute ΔH = V_LΔP. This process is easy to automate using a spreadsheet and you can quickly tabulate all the stream enthalpies of interest, as illustrate using sample calculations for DME (uakron, 17min). Remember to push the pause button as soon as you read the problem statement and see if you can perform the calculation on your own. Then use the screencast to catch any mistakes you might have made. The procedure for a single component can be extended to multiple components to provide a spreadsheet utility for quickly performing energy balance calculations for an entire process (uakron, 7min) Note that an entire process may involve mixtures or reactions. The extension to mixtures is presented in Section 3.5.

Comprehension Questions:
1. Tabulate the stream enthalpies of methanol relative to the ideal gas reference state at (298K,1bar) at: (a) 300K,1bar (b) 350K,1bar.
2. Compute ΔH for going between these states (a) and (b) and compare to the similar problem in Section 2.10.

Energy Balance Around a Turbine (LearnChemE.com, 7min) performs an energy balance around a turbine accounting for flow work

Throttle Temperature Change (LearnChemE.com, 3min). Shows the temperature change of non-ideal gases through an adiabatic throttle due to Joule-Thomson expansion

Heat Removal to Condense a Vapor Mixture (LearnChemE.com, 5min) uses state functions to explain how to determine heat of vaporization for binary mixture

Energy Balance on a Heat Exchanger (LearnChemE.com, 7min) do an energy balance on a heat exchanger that has superheated steam fed to it. Use the steam tables.

Adiabatic Compression of an Ideal Gas (LearnChemE.com, 6min) calculate adiabatic temperature for compression of an ideal gas, both reversibly and irreversibly.

Comprehension Questions:
1. 10 mol/s of air is compressed adiabatically and reversibly from 298K and 1bar to 5 bar.
(a) Compute the exit temperature (K). (Hint: check out Eqn. 2.51.)
(b) Compute the power requirement (kW) for this compressor.
(c) Suppose the compressor was only 75% efficient, where efficiency≡W_rev/W_act for compression. Is the temperature of the irreversible compressor higher or lower than that of the reversible compressor? Explain.
(d) Calculate the temperature exiting a 75% efficient compressor.
2. Air is expanded adiabatically and reversibly (through a turbine) from 298K and 5 bar to 1 bar.
(a) Is the outlet temperature higher or lower than 298K?
(b) Suppose the air was expanded through a 50% efficient turbine. Would the temperature be higher or lower than the reversible turbine? Explain.

Reversible Adiabatic Compression of Ideal Gas (LearnChemE.com, 5min) calculate the final conditions for adiabatic, reversible compression of an ideal gas. Here, we derive an important equation that should be memorized: (T2/T1)=(P2/P1)^(R/Cp).

Energy Balance: Filling a Tank (LearnChemE.com, 5min) determine the final properties of a tank to which steam is added.

Comprehension Questions:

1. An empty tank is filled by opening a valve and allowing steam at 300°C and 8MPa to flow into it until the pressure equalizes. Estimate the final temperature (°C).

2. An empty tank is filled by opening a valve and allowing steam at 350°C and 8MPa to flow into it until the pressure equalizes. Estimate the final temperature (°C).

3. An empty tank is filled by opening a valve and allowing steam at 300°C and 6MPa to flow into it until the pressure equalizes. Estimate the final temperature (°C).

Evaporative Cooling Energy Balance (LearnChemE.com, 6min) apply the energy balance to liquid water that is evaporating and undergoing evaporative cooling.

Tank filling: Steam, Unevacuated (uakron.edu, 15min) Unsteady state problems are relatively easy to solve for ideal gases, especially when the tank is empty to begin. The solution process becomes more difficult using steam with some H2O already in the vessel. This demonstration shows how to adapt to the new situation. The point is to learn the manner of adapting, not so much answer for this particular problem. You may not be filling many tanks with steam in your life, but you will certainly be adapting to new situations. The steps of analysis, identifying pieces of the puzzle, and putting them together are key components of any such adaptation.

Work and Enthalpy Misunderstandings (LearnChemE.com, 3min) discusses three examples related to enthalpy and work changes that are often confusing.

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:
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 T_C discussed 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 T_H would be necessary to approach 100% efficiency, even for this idealized, maximally efficient process? What are the practical limitations on T_H? Explain.
5. How can the formula for Carnot efficiency help us to calculate the "lost" work in the presence of a temperature gradient?

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, η_θ). 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.

Props.xlsx has a lot of data, but usually we are only interested in a few components at a time. Adding a few lines at the top and applying the VLookup function makes it easy to tabulate the properties you need. (8min, uakron.edu)

Comprehension questions

1. Download the latest version of Props.xlsx from sourceforge. Add lines to support 8 components of interest and cells to compute Psat given T as input and Tsat given P as input by appropriately arranging Eqn. 2.47. Add a column for computing Hvap at Tsat for each component by Eqn. 2.45.

2. Insert a sheet(tab) called Hrxn in Props.xlsx. Types the names for components in the reaction CO+0.5O2=CO2. Use VLookup to tabulate the Hf values for each component. To the left of the name column, insert cells to represent the stoichiometric coefficients. Then calculate the heat of reaction by using the sumproduct() function applied to the stoichiometric coefficients and Hf values. Check your result with a hand calculation.

3. Download the latest versions of PREOS.xls and Props.xlsx from sourceforge. Update the Props tab appropriately. Then implement the VLookup function on the ThermoProps tab of PREOS so all you need to do is type the name of the compound of interest in order to update the ThermoProps sheet to all properties of interest. We discuss how to use PREOS.xls to solve problems in Unit II.

Use VLookup and Eqn. 2.47 to tabulate shortcut estimates of Antoine coefficients. (5min, uakron.edu) By calculating these in a distinct location, then referencing those estimates in the cells that will actually be used for later calculations, you can type in precise estimates when you have them. When no precise values are available, recover the shortcut estimates by simply typing "=" and referencing the cell with the shortcut estimate.

Stream enthalpies for the DME process (uakron, 7min) can be estimated using the "heat of reaction" pathway (Fig 3.5a) or the "heat of formation" pathway (Fig 3.5b). This presentation is based on Fig 3.5b, which is very similar to Fig 2.6c. The main difference is the inclusion of the heat of formation for each compound relative to its elements. Including the heat of formation puts the reference state for each compound on the same basis of comparison (ie. the elements). If one stream (e.g. "products") possesses more enthalpy than another stream (e.g. "reactants") then the energy difference between the streams (e.g. "heat of reaction") would be accounted for by simply subtracting the two stream enthalpies. Reactions inherently involve multiple components, so including the heats of formation in the stream enthalpies, as well as the other enthalpic contributions represented in Fig 2.6c, is inevitable. These sample calculations are illustrated for all the streams appearing in the DME process. The presentation follows up on the discussion of Fig 2.6c for pure fluids. Once you understand the calculations for each pure fluid, the mixture property simply involves taking the molar average, so: H ≈ ∑(x_i*Hf_i+Cp_i^igΔT+(q_i-1)*H_i^vap). In this equation, (q_i-1)*H_i^vap accounts crudely for departures from ideal gas behavior. For example, if a stream is a vapor, then q=1 and H^vap doesn't matter. If q=0, then the stream is a liquid and H^vap must be subtracted. We will study more accurate models of ideal gas departures in Unit II.

Comprehension Questions:

1. Compute the enthalpy, H(J/mol), of methanol at 250C and 2 bars relative to its ideal gas standard state elements.

2. Compute the enthalpy, H(J/mol), of DME at 250C and 2 bars relative to its ideal gas standard state elements.

3. Compute the enthalpy, H(J/mol), of water at 250C and 2 bars relative to its ideal gas standard state elements.

4. Compute the enthalpy, H(J/mol), of a stream that is 50% methanol, 25% DME, and 25% water at 250C and 2 bars relative to its ideal gas standard state elements.

You can turn Excel into a crude process simulator (e.g. ASPEN, ChemCAD, ProSim, HYSYS, ...) by implementing an xls feature that is often overlooked. (7min, uakron.edu) You need to enable the iteration feature and then you simply need an initial guess about the masses of any recycle streams. This presentation illustrates the mass balance calculation for the dimethyl ether process (2CH3OH = CH3OCH3 + H2O). A subsequent video (below) shows how to add stream enthalpy calculations using the path of Figure 2.6c and Eqn 3.5. Then you can easily perform the energy balances. One important feature of having the energy balance is to facilitate performing an adiabatic reactor calculation, also illustrated below. You should also be mindful of tear stream control to ensure that your iterations do not diverge.

Comprehension questions:
1. Choose any process flow diagram from your material and energy balances (MEB) textbook that has a recycle stream. Solve the problem using this technique and compare to the answer you obtained in MEB class.
2. A process for decaffeination requires us to know: (A) the amount of decaffeination solvent (DCS) and (B) composition of the DCS recycle stream. In the process, coffee beans are fed directly to a mixing tank. The DCS is mixed with the DCS recycle stream then fed to the mixing tank. The solution is filtered and the wet coffee beans are sent to a dryer in which 90% of the DCS is recovered and returned to the mixing tank; the other 10% of DCS exits with the coffee beans. (This is NOT "the DCS recycle stream" mentioned above.) The liquid from the filtration is fed to a separation unit where the caffeine exits at 95wt% and "the DCS recycle stream" exits at a concentration that needs to be determined as (B). Additional information(assume a basis of 100kg coffee beans): (a) Coffee beans contain 1.5wt% caffeine. (b) Coffee beans exiting the filtration are 90% caffeine-free. (c) For each 100kg of coffee beans entering the mixing tank, 20kg of DCS go with them, hence the need for the dryer. (d) The concentration of DCS entering the mixing tank (after mixing recycle with fresh DCS) is 95% DCS and 5% caffeine. (e) The DCS-rich stream exiting the mixing tank is 88%DCS and 12% caffeine. Solve for (A) and (B) above. The process flow diagram and complete solution are available, (Learncheme.com, 12min) but try to solve as much as possible on your own by using the pause button frequently.

In case you need a little extra help on energy balances after iterating mass balances, this video walks you through the process. (8min, uakron.edu) for the same process flow diagram related to dimethyl ether synthesis.

Comprehension Questions:

1. Choose any process flow diagram from your material and energy balances (MEB) textbook that has a recycle stream. Solve the problem using this technique and compare to the answer you obtained in MEB class. Estimate stream enthalpies for every stream and compute the overall energy balance of all product streams to all feed streams. Does the process require net heat addition or removal?
2. Suggest limitations of this approach. What are the assumptions? Which assumptions seem most suspect?

Heat Removal from a Chemical Reactor (LearnChemE.com, 8min) determines heat removal so that a chemical reactor is isothermal following the pathway of Figure 3.5a. The reaction is N2 + 3H2 = 2NH3 at 350C and 1 bar. The pathway to go from products to reactants is to cool the products to 25C (the reference temperature), then "unreact" them back to their initial feed state (reactants), then to heat the reactants back to the inlet condition of the reactor (350C,1bar). Summing up the enthalpy changes over these three steps gives the overall change in enthalpy at the reactor conditions.

Comprehension Questions:
1. Suppose the reaction had been carried out at 2 bars. How would we compute the enthalpy change then?
2. Use this approach to compute the heat of reaction for 2 CH3OH = CH3OCH3 + H2O at 250C and 1 bar.
3. Methanol, dimethyl ether, and water are all liquids at 25C and 1 bar. Did you account for the heat of vaporization when answering Question #2 above? Explain.

Adiabatic Reactor Temperature (LearnChemE.com, 7min) calculate the adiabatic temperature for a reactor with 30% conversion. The reaction is NO + 0.5 O2 = NO2. The strategy is to guess the temperature at which the reactor operates, then compute the heat evolved at that temperature by either method of Fig 3.5a or 3.5b (see above). If the heat evolved is equal to the heat required to warm the products to that reactor temperature, then you have guessed the right temperature. If the heat evolved is negative, then you need to guess a higher temperature.

Comprehension Question:
1. Estimate the adiabatic reactor temperature for the ammonia synthesis reactor discussed above.  

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.

Adiabatic reactor temperature for an equilibrium limited reaction (LearnChemE.com, 7min) In many situations, the extent of reaction is not specified outright. Instead, a problem might be specified as operating at or near equilibrium in an adiabatic reactor. The problem is that the equilibrium constant that relates "products/reactants" changes with temperature according to ln(Ka/K_ref) = -(ΔH_rxn/R)*(1/T-1/T_ref) For example, in an exothermic reaction, the equilibrium constant decreases with temperature. This leads to a coupling between the adiabatic constraint to determine the temperature and the equilibrium constraint to determine the extent of reaction: two equations and two unknowns. The methodology is presented here for a hypothetical reaction of A->B in a liquid phase reactor where Cp^A=Cp^B=const.

Comprehension Questions:

1. What name is mentioned in the video for the equation that relates the equilibrium constant to temperature?
2. Why does the version of this equation in the video reverse the order of the reciprocal temperature subtraction, ie. (1/T_ref-1/T)? Is this a typographical error?
3. How would your solution change if Cp^A = 50 and Cp^B = 40?
 

Adiabatic reactors in chemical processes (uakron.edu, 6min) are not uncommon. Therefore, it is useful to illustrate how to perform the calculation in the context of the dimethyl ether process. Fortunately, the calculation is greatly simplified by the stream enthalpy calculations presented above. All we really need to do is iterate on the reactor outlet temperature until the stream enthalpy of the outlet stream equals that of the inlet stream. This is easy because our choice of thermodynamic pathway refers back to the formation elements at standard conditions. Hence, any changes in composition and component enthalpies are automatically reflected in the enthalpy of the stream. This provides a powerful illustration of the benefits of thermodynamic pathway analysis.

Comprehension Questions:

1. 100 kmol/h of N2 is reacted with 300 kmol/h of H2 to form NH3 with 55% conversion. Only a single distillation column is required to provide a 99.99% split on N2 (the light key) and 1% split on NH3. On the other hand a purge stream is required with a 20:1 recycle ratio. The inlet to the reactor needs to be at 200C and the reactor operates adiabatically. Compute the molar flow rates and enthalpies of all streams and the outlet temperature of the reactor.

Equilibrium limited adiabatic reaction in a process (uakron.edu, 9min) In practical applications, it is not feasible to achieve the equilibrium extent of reaction because the rate of reaction becomes very slow as equilibrium is approached. In this illustration for the dimethyl ether process, the adiabatic reactor temperature is determined for the case where the actual conversion approaches 75% of the equilibrium value. This means that we need to solve for the equilibrium conversion first, then multiply it by 0.75 to get the actual conversion. In an actual process, however, the stream compositions depend on the conversion and the amount of recycle. In particular, the inlet to the reactor changes as well as the outlet when the conversion changes because of the recycle stream. This leads to complicated coupling between the extent of reaction and the reactor outlet temperature that must be solved using the equilibrium constant and the energy balance.

Comprehension Questions:

1. This presentation makes a mistake in calculating the partial pressures relevant to the equilibrium, but it turns out not to make a difference. What is the mistake and why doesn't it make a difference?
2. 100 kmol/h of N2 is fed with 300 kmol/h of H2 to a process forming NH3 with 85% of the equilibrium conversion. Only a single distillation column is required to provide a 99.99% split on N2 (the light key) and 2% split on NH3. On the other hand a purge stream is required with a 19:1 recycle ratio. The inlet to the reactor needs to be at 400K and the reactor operates adiabatically at 100 bars. Compute the molar flow rates and enthalpies of all streams and the outlet temperature of the reactor. (Hint: you might want to check the process flow diagram illustrated in this presentation.)

Connecting a recycle stream through the iteration feature is actually trickier than might have been evident from the introductory lesson.  A better procedure is to recognize this recycle stream as a "tear" stream and to carefully control how the iterations are implemented, especially during the early stages of analyzing a process. This video (UA, 10min) shows how to implement a "guess" and "try" approach that keeps the iterations under control until automatic iteration is ready.

Comprehension Questions:

1. Set the split fractions for DME and Methanol correctly in the first distillation column, but reverse them in the second.  What is the "guess" value of flowrate for methanol in stream 7 in that case?

2. Set the split fractions for DME and Methanol reversed in the first distillation column, but correctly in the second.  What is the "guess" value of flowrate for methanol in stream 7 in that case?

Composite Systems: Iterating Mass Balances of a Process Flow Diagram (PP3.1) (uakron.edu) You may be surprised by how easy it is to solve all the mass balances of a fairly sophisticated chemical process using the xls "iteration" feature. In about 10 minutes, you can solve an entire project complete with a reactor, distillation columns, and recycle. And if you need to change something like the reactor conversion or column splits, that will take about 3 seconds.
 
Comprehension Question:20kmol/h of propylene with 2kmol/hr of propane is fed with 21kmol/h of Benzene to produce Cumene (isopropylbenzene). Conversion of the propylene is 90%, but the benzene needs to be fed such that the ratio entering the reactor is 6:1 Benzene:propylene. Also 0.1 mol of diisopropylbenzene (DIPB) is produced for every mol of cumene. A flash occurs at 90C and 1.75 bars after the reactor to purge excess propane. A distillation column separates the benzene for recycle with a split of 99.5%. The cumene is recovered in the bottoms at 99%. Compute the flow rates in all the streams.

Principles of Probability.

This is supplemental Material from "Molecular Driving Forces, K.A. Dill, S. Bromberg", Garland Science, New York:NY, 2003, Chapter 1. See the next three screencasts. This content is useful for graduate level courses that go into more depth or for students interested in more background on probability.

Download Handout Notes to Accompany Screencasts (msu.edu)

Heat and entropy in a glass of water (uakron, 9min) Taking a glass from the refrigerator causes heat to flow from the room to the water. The temperature of the water slowly rises while the temperature of the (relatively large) room remains fairly constant. Applying the macroscopic definition of entropy makes it easy to compute the entropy changes, but is one larger than the other? Are all entropy changes greater than zero? What does the second law mean exactly?

Comprehension Questions:

1. Describe your own example of a process with an entropy decrease and explain why it doesn't violate the second law.

You might better understand the macroscopic definition of entropy (uakron, 9min) if you consider isothermal reversible expansion of an ideal gas. Note the word "isothermal" is different from "adiabatic." If the expansion was an adiabatic and reversible expansion of an ideal gas, then we know from Chapter 2 that the temperature would go down, ie. T2/T1=(P2/P1)^(R/Cp)=(V1/V2)^(R/Cv). Therefore, holding the temperature constant must require the addition of heat. We can calculate the change in entropy for this isothermal process from the microscopic balance, then show that the amount of heat added is exactly equal to the change in entropy (of this reversible process) times the (isothermal) temperature. Studying the energy and entropy balance for the irreversible process helps us to appreciate how entropy is a state function. As suggested by the hint at the end of this video, you can turn this perspective around and infer the relation of entropy to volume by starting with the macroscopic definition and calculating exactly how much heat must be added after adiabatic, reversible expansion in order to recover the original (isothermal) temperature. Through this thought process, you should start to appreciate that the micro and macro definitions are really interchangeable expressions of the same quantity.

Comprehension Questions: (Hint: entropy is a state function.)

1. Use the macroscopic definition of entropy to compute the change in entropy (J/mol-K) of N2 in a piston/cylinder from 450K and 1cm3/mol to 450K and 4cm3/mol.

2. Use the macroscopic definition of entropy to compute the change in entropy (J/mol-K) of N2 in a piston/cylinder from 450K and 4cm3/mol to 258.46K and 4cm3/mol.

3. Use the macroscopic definition of entropy to compute the change in entropy (J/mol-K) of N2 in a piston/cylinder from 450K and 1cm3/mol to 258.46K and 4cm3/mol.

4. Use the macroscopic definition of entropy to compute the change in entropy (J/mol-K) of N2 in a piston/cylinder from 450K and 1cm3/mol to 300K and 3 cm3/mol.

Once we establish equations relating macroscopic properties to entropy changes, it becomes straightforward to compute entropy changes for all sorts of situations. To begin, we can compute entropy changes of ideal gases (learncheme, 3 min). Entropy change calculations may also take a more subtle form in evaluating reversibility (learncheme, 3min). 

Comprehension Questions: 

1. Nitrogen at 298K and 2 bars is adiabatically compressed to 375K and 5 bars in a continuous process. (a) Compute the entropy change. (b) Is this process reversible, irreversible, or impossible?
2. Nitrogen at 350K and 2 bars is adiabatically compressed to 575K and 15 bars in a piston/cylinder. (a) Compute the entropy change. (b) Is this process reversible, irreversible, or impossible?
3. Steam at 450K and 2 bars is adiabatically compressed to 575K and 15 bars in a continuous process. (a) Compute the entropy change. (b) Is this process reversible, irreversible, or impossible?
4. Steam at 450K and 2 bars is isothermally compressed to 8 bars in a continuous process. (a) Compute the entropy change. (b) Is this process reversible, irreversible, or impossible?

Simplifying the complete entropy balance (uakron, 11min) is analogous to simplifying the complete energy balance. In general, there are fewer terms to worry about because the system's kinetic and gravitational energy are not involved. This presentation focuses on the same three most common systems as for energy applications.

Comprehension Questions. Write the simplified entropy balance for the following:

1. An isothermal reversible compressor.

2. The expansion stroke of an 80% efficient piston/cylinder.

3. An adiabatic, reversible, ideal gas expanding in a piston/cylinder.

4. Steam expanding through an adiabatic, reversible turbine.

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.

Compressor efficiency using an ideal gas assumption (uakron.edu, 13min) Propane is compressed from -100F and 1 bar to 180F and 10 bar. This is enough information to compute the efficiency of the compressor. In this video, we use the ideal gas assumption. We solve the same problem later using more accurate property estimates. Re-watching this video after you have solved the problem using the chart will help you to understand a lot about the influences of molecular interactions and their significance in accounting for the work that goes into designing a chemical engineering process.

Comprehension Questions:
1. An ordinary vapor compression cycle (OVC) is to be considered for cryogenic cooling. The process fluid is to be propane with a compression/expansion ratio (ie. P^Hi/P^Lo) of 5.2. The evaporator coils operate at 0.148MPa. The adiabatic compressor's actual exit temperature is 120°F. You may assume the ideal gas law. Hint: what temperature is implied by the pressure of 0.148MPa for the "evaporator." (cf. Eqn. 2.47).
(a) Write the energy balance for the compressor.
(b) Estimate the actual work required for this compressor.
(c) Write the entropy balance required to estimate the efficiency of the compressor.
(d) Estimate the reversible work required for this compressor.
(e) Estimate the compressor's efficiency.
2. HFC134a is to be considered as the working fluid in a prospective refrigeration system. HFC134a (MW=102) is compressed in an adiabatic compressor from 244K and saturated vapor to 316K and 0.9856MPa. Assume the ideal gas law.
(a) Write the energy balance for the compressor.
(b) Estimate the actual work required for this compressor.
(c) Write the entropy balance required to estimate the efficiency of the compressor.
(d) Estimate the reversible work required for this compressor.
(e) Estimate the compressor's efficiency.

How to read a pressure-enthalpy chart (uakron.edu, 9min) In principle, reading properties from a chart is no different from looking them up in a table (like the steam tables). In some ways, you could argue that it is easier because interpolation is unnecessary. On the other hand, there are so many lines of the propane chart, all going in different directions, it can be a little confusing at first. In general, the best approach is to use the saturation table when you can, and read the chart when necessary. This video walks you through the process.

Comprehension Questions:
1. HFC134a is to be considered as the working fluid in a prospective refrigeration system. HFC134a (MW=102) is compressed in an adiabatic compressor from 244K and saturated vapor to 316K and 0.9856MPa. (a) Estimate the pressure(MPa), enthalpy (J/g) and entropy(J/g-K) for the compressor inlet. (b) Estimate the enthalpy (J/g) and entropy(J/g-K) for the compressor outlet.

Compressor efficiency using real propane (uakron.edu, 11min) Propane is compressed from -100F and 1 bar to 180F and 10 bar. This time we solve for the compressor efficiency using the chart to estimate the thermodynamic properties.

Comprehension Questions:
1. Re-watch the video showing the solution of this problem based on the ideal gas law. What is the temperature exiting an adiabatic, reversible compressor assuming the propane inlet above? How does that compare to the temperature for an adiabatic, reversible ideal gas? Explain why one is higher than the other.
2. HFC134a is to be considered as the working fluid in a prospective refrigeration system. HFC134a (MW=102) is compressed in an adiabatic compressor from 244K and saturated vapor to 316K and 0.9856MPa. (a) Write the relevant energy balance. (b) Write the relevant energy balance. (c) Solve for the actual work (J/g) (d) Estimate the efficiency of the compressor.

Isothermal compression of steam (uakron, 11min) Compute the work of isothermally and reversibly compressing steam from 5 bars and 224°C to 25 bars. Pay close attention to the problem statement!

Comprehension Questions:
1. Two moles of methane at 3bar and 200K are isothermally and reversibly compressed to 30 bar in a piston/cylinder.
Assume the ideal gas law.
(a) Write the energy and entropy balances.
(b) Estimate the change in entropy (J/K) and enthalpy (J).
(c) Solve for the work(J/g).
2. Two moles of methane at 3bar and 200K are isothermally and reversibly compressed to 30 bar in a piston/cylinder.  Use the chart and table for methane.
(a) Write the energy and entropy balances.
(b) Estimate the change in entropy (J/K) and enthalpy (J).
(c) Solve for the work(J/g).
(d) Compare the changes in entropy and enthalpy for real methane to those for ideal gas methane.

Using the NIST WebBook for the propane compression problem (uakron, 14min). The NIST WebBook makes it just as easy to solve problems for propane (and 50 other fluids) as it is for steam. They effectively provide "steam" tables for 50 fluids besides steam.

Comprehension Questions:
1. Re-solve the R134a problem above using the WebBook.
2. Re-solve the methane problem above using the WebBook.

Rankine Cycle Introduction (LearnChemE.com, 4min) The Carnot cycle becomes impractical for common large scale application, primarily because H2O is the most convenient working fluid for such a process. When working with H2O, an isentropic turbine could easily take you from a superheated region to a low quality steam condition, essentially forming large rain drops. To understand how this might be undesirable, imagine yourself riding through a heavy rain storm at 60 mph with your head outside the window. Now imagine doing it 24/7/365 for 10 years; that's how long a high-precision, maximally efficient turbine should operate to recover its price of investment. Next you might ask why not use a different working fluid that does not condense, like air or CO2. The main problem is that the heat transfer coefficients of gases like these are about 40 times smaller that those for boiling and condensing H2O. That means that the heat exchangers would need to be roughly 40 times larger. As it is now, the cooling tower of a nuclear power plant is the main thing that you see on the horizon when approaching from far away. If that heat exchanger was 40 times larger... that would be large. And then we would need a similar one for the nuclear core. Power cycles based on heating gases do exist, but they are for relatively small power generators.
     With this background, it may be helpful to review the relation between the Carnot and Rankine cycles. (LearnChemE.com, 6min) 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).
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.

Using XSteam Excel (4:46) (msu.edu)
This utility is helpful once you have learned how to interpolate reliably. It saves the tedium.

Using XSteam Matlab (4:20) (msu.edu)
This utility is helpful once you have learned how to interpolate reliably. It saves the tedium.

Improving Thermal Efficiency with a 2-Stage Rankine Modification (uakron.edu, 15min) Power is to be generated between temperatures of 500 C and 65 C (0.025MPa) with the steam quality not to drop below 100%. This coursecast compares a simple Rankine cycle and one modification in which the single turbine expansion is replaced with two turbine stages. The thermal efficiency increases from 27% to 39% as a result of this modification. Such an increase could equate to millions of dollars per year at a decent sized electric power plant. These considerations motivate careful analysis of thermal efficiency under multiple permutations of modifications. Ultimately, the Carnot efficiency cannot be surpassed, however. Also, the optimal configuration for a particular facility (like cogeneration at a chemical plant) will depend on other demands like the need for medium pressure steam dedicated to other purposes.
Comprehension Questions:
1. Do you think that turning this process into a 3-stage Rankine cycle would increase the thermal efficiency another 12%, from 39% to 51%? Explain.
2. Suppose the turbines were 85% efficient. How would you approach this problem in that case?

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?

How To Read the Pressure-Enthalpy (PH) Diagram for Propane (uakron.edu, 9min) A chemical process may need refrigeration to operate the condenser of a distillation column at cryogenic conditions. The process in this video operates between -100F and 80F in its refrigeration coils.
Comprehension Questions: Assume zero subcooling and superheating. (ie. The "approach temperature" is zero.)
1. Download the table of saturation properties for propane from the student supplements section of chethermo.net. Estimate the pressures and enthalpies exiting the condenser and evaporator. How do these compare to the values reported in the video?
2. Suppose the condenser outlet operated at 100 F. Estimate the condenser pressure (MPa).
3. Suppose the condenser outlet operated at 100 F. Estimate the condenser outlet enthalpy(J/g)
4. Suppose the condenser outlet operated at 100 F. Estimate the condenser inlet temperature(F)
5. Suppose the condenser outlet operated at 100 F. Estimate the condenser inlet enthalpy (J/g)

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.

Acceleration of an Airplane by a Turbojet Engine (LearnChemE.com, 10min) calculates the initial acceleration of an airplane powered by a turbojet engine. Demonstrates application of the energy and entropy balance for individual components of a composite system and for the system as a whole.

From the physical world to the realm of mathematics (uakron.edu, 15min) In Unit I, students develop the skills to infer simplified energy and entropy balances for various physical situations. In order to facilitate that approach for applications involving chemicals other than steam and ideal gases, we need to transform that approach into a realm of pure mathematics. In this context it suffices to apply the energy and entropy balance of a very simple system (piston/cylinder) then focus on the state functions that are involved (U,H,S,...). The mathematical realm is relatively abstract, but it is ideally suited for the generalizations required to extend our principles from steam and ideal gases to any chemical.

Comprehension Questions:

1. In example 4.16, we noted that the estimated work to compress steam was less when treated with the steam tables than when treated as an ideal gas. Explain why while referring to the molecular perspective.

2. In Chapter 5, we noted that the temperature drops when dropping the pressure across a valve when treating steam or a refrigerant with thermodynamic tables, but the energy balance suggests that the temperature drop for an ideal gas should be zero. Explain how these two apparently contradictory observations can both be true while referring to the molecular perspective.

3. What is the relation of the state variable dU to the state variables S and V according to the fundamental property relation?

4. What is the relation of the state variable dH to the state variables S and P according to the fundamental property relation?

5. What is the significance of writing changes of state variables in terms of changes in other state variables?

6. Why is the compressibility factor (Z=PV/RT) less than one sometimes?

7. Is it possible for Z to be greater than one? Explain.

8. What is the significance of having a relation for P = P(V,T)? How will that help us to solve problems involving chemicals other than steam and ideal gases?

State Functions Equation Check (LearnChemE.com, 3min) determines which form of various state functions is incorrect.

Comprehension Questions:

1. Which of the following relations is not valid (may be more than one)?
dA = dH - d(PV) - d(TS); dA = dG - d(PV); dG = -SdT + VdP; dA = dH - d(PV) - TdS

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)?

Using the NIST Webbook for Charts/Tables (uakron.edu, 14min) Shows how to access the NIST fluid properties as needed to design an OVC cycle. Demonstrates the procedure with a problem based on propane at -100F saturated vapor pressure being raised to 10 bars and 180F in an adiabatic compressor by solving for the compressor efficiency and the COP.

Comprehension Questions:

1. Chlorodifluoromethane is used as the working fluid of an OVC cycle at -100F saturated vapor pressure exiting the evaporator and 80F saturated liquid exiting the condenser. Assuming an adiabatic reversible compressor solve for the COP.

Experimental observation of the critical point (LearnChemE.com, 5min) Discusses the background of the critical point and its relation to the 2-phase envelope. Includes a video showing the transition of a 2-phase fluid as it is heated through the critical temperature, then cooled back again.

Comprehension Questions:

1. Based on watching the video, what is different about the behavior of the fluid when it is cooled through the critical point as opposed to being heated from subcritical to supercritical?

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.

Intro to the vdW EOS. (LearnCheme.com, 5min) Provides a brief overview of the van der Waals (vdW) 1873 equation of state (EOS), which served as a prototype for EOS development for over 100 years. Note: the vdW EOS is just one conjecture of how equations of state for real fluids may be formulated. In reality, each fluid has its own unique EOS. The vdW model conjectures that the pressure is altered relative to the ideal gas by the presence of attractive forces and repulsive forces.

Comprehension Questions:

1. Of the two parameters a and b, which is related to attractive forces and which is related to attractive forces?
2. How are the parameters a and b typically characterized/computed? ie. To what experimental constants are they related in order to compute them?
3. Is the vdW EOS an example of a 2-parameter EOS or 3-parameter EOS?
4. When writing the term (V-b) we subtract b because the molecules occupy volume and when V=b, all the "free volume" is gone. Can you explain the term (P+a/V²) in a similar manner?
5. In the presented example of CO2 at 0.2L and 269K, how does the pressure compare when computed by the ideal gas law vs. the vdW model? (Give both values.)
6. In the presented example of CO2 at 0.0L and 269K, how does the pressure compare when computed by the ideal gas law vs. the vdW model? (Give both values.)

Virial and Cubic EOS (11:18) (msu.edu)
Discusses the strategy of the virial EOS and the cubic EOS and the strategy used to solve as a cubic in Z. Gives formulas for calculating the a and b parameters of both the vdW and Peng-Robinson EOS's, as well as the virial EOS. You might want to watch the video on "Visualizing the vdW EOS" if you want to understand where the equations for a and b come from or how to make quantitative plots of isotherms.

Comprehension Questions:

1. To what region of pressure is the virial EOS limited at a given temperature? Why?
2. Is the Pitzer EOS limited to the same conditions as the virial EOS?
3. Is the virial EOS a 2-parameter or 3-parameter EOS?
4. Is the Peng-Robinson (PR) EOS a 2-parameter or 3-parameter EOS?
5. What is the primary shortcoming of the vdW EOS, as described on slide 4 of this presentation?
6. Is the PR EOS limited to the same conditions as the virial EOS? Explain.
7. How does the "fugacity" help you to identify the stable root of a cubic EOS?
8. When there are 3 real roots to a cubic EOS, what do we do with the center root? Why?

3. Using Preos.xlsx and Interpreting Output (11:38) (msu.edu)
This screencast includes discussion of what we mean by the casual terminology 'three root region' and 'one root region', and how to interpret screen output. Also, the screencast spends time dicussing selection of stable roots using fugacity.

Comprehension Questions:

1. Is it possible to have a 1-root region below the critical temperature?

2. Is it possible to have a 3-root region above the critical temperature?

3. How does fugacity help us to identify the proper root to select?

4. Would argon at 5 MPa be in the 1-root or 3-root region?

1. Peng-Robinson PVT Properties - Excel (3:30) (msu.edu)

Introduction to PVT calculations using the Peng-Robinson workbook Preos.xlsx. Includes hints on changing the fluid and determining stable roots.

Comprehension Questions:

1. At 180K, what value of pressure gives you the minimum value for Z of methane? Hint: don't call solver.

2. At 30 bar, what value of pressure gives Z=0.95 for methane?

3. Compute the molar volume(s) (cm³/mol) for argon at 100K for each of the following?
(a) 3.000 bars (b) 4.000 bars (c) 3.26903 bars.

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.

Comprehension Questions:

1. Which of the following represents the vapor pressure for argon at 100K?
(a) 3.000 bars (b) 4.000 bars (c) 3.26903 bars.

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.

Using a macro to create an isotherm (Excel) (msu.edu, 14:31) The tabular Excel display is convenient for viewing all the intermediate values, but no so good for building a table such as for an isotherm. This screencast shows how to write/edit a macro to build a table by copying/pasting values. The screencast creates an isotherm on a Z vs. Pr plot over 0.01 < Pr < 10.

Derivative Relations for the Peng-Robinson EOS (3:18) (msu.edu)
The derivatives (∂U/∂V)_T and (∂C_V/∂V)_T are evaluated for the Peng-Robinson EOS and the concept of expressing non-measurable properties in terms of measurable properties is discussed.

Comprehension Questions:

1. What derivative do we need to use when developing formulas for departure functions in Chapter 8?

Nature of Molecular Interactions - Macro To Nano(8min). (uakron.edu) Instead of matching the critical point, we can use experimental data for density vs. temperature from NIST as a means of characterizing the attractive energy and repulsive volume. A plot of compressibility factor vs. reciprocal temperature exhibits fairly linear behavior in the liquid region. Matching the slope and intercept of this line characterizes two parameters. This characterization may be even more useful than using the critical point if you are more interested in liquid densities than the critical point. In a similar manner, you could derive an EOS based on square-well (SW) simulations and use the SW EOS to match the NIST data(11min), as shown in this sample calculation of the ε and σ values for the SW potential. In this lesson, we learn how to characterize the forces between individual atoms, which may seem quite unreal or impractical when you first encounter it. On the other hand, "nanotechnology" is a scientific discipline that explores how the manipulation of nanostructure is now quite real with very significant practical implications. "The world's smallest movie" shows dancing molecules, (IBM, 2min) demonstrating the reality of molecular manipulation, and the accompanying text explains some of the practical implications. Along similar lines, researchers at LLNL and CalTech have developed 3D printers that can display "voxels" (the 3D analog of pixels) of ~1nm3. That's around 10-100 atoms per voxel. Since 2013-14, chemical/materials engineers have been building nanostructures (TEDX, 13min) in the same way that civil engineers build infrastructure.
Comprehension Questions:
1. What does the y-intercept represent in a plot of compressibility factor vs. reciprocal temperature?
2. What parameter does the y-intercept help to characterize, b or ε?
3. What does the x-intercept represent in a plot of compressibility factor vs. reciprocal temperature?
4. What parameter does the x-intercept help to characterize, b or ε?
5. Apply the SW EOS given in the second video to the isochore at 16.1 mol/L. Do you get the same values for ε/k and σ? Explain.

Simple Hard Disk Collisions. (5min) (uakron.edu) Deriving the formula for pressure from the motions of molecules was easy when we were talking about ideal gas molecules and we even got a compact, exact result (aka. the ideal gas law). The problem gets more complicated when the molecules can collide with each other as well as with the walls. This complexity undermines our ability to get an exact solution, but we can obtain a numerical solution by integrating all the collisions with respect to time and computing the average pressure as a result. The process begins with computing collision times of molecules with walls. This computation is simple enough that you should be able to do it even if you can't write a molecular simulation program.

Comprehension questions:

1. Two molecules with MW=16 and 0.36nm diameter are traveling in 2D with velocities: (643, -133) and (133, -643) m/s. Their initial positions in a 5 nm box are (2,4) and (3,1). Estimate the time (ns) and nature of the first collision, whether with a wall or with another molecule.
2. Two molecules with MW=16 and 0.36nm diameter are traveling in 2D with velocities: (133, -266) and (-133, 266) m/s. Their initial positions in a 5 nm box are (2,4) and (3,1). Estimate the time (ns) and nature of the first collision, whether with a wall or with another molecule.
3. A molecule with MW=16 and 0.36nm diameter is traveling in 2D towards the east wall of a box. Its velocity is given by (vx, vy) = (123, 345) m/s. It starts off being 2nm from the east wall. How far must the molecule travel before it contacts the wall?
4. A molecule with MW=16 and 0.36nm diameter is traveling in 2D towards the east wall of a box. Its velocity is given by (vx, vy) = (123, 345) m/s. It starts off being 2nm from the east wall. How much time(ns) before it contacts the wall?

Nature of Molecular Parking Lots - RDFs(20min, uakron.edu) Molecules occupy space and they move around until they find their equilibrium pressure at a given density and temperature. Cars in a parking lot behave in a similar fashion except the parking lot is in 2D vs. 3D. Despite this exception, we can understand a lot about molecular distributions by thinking about how repulsive and attractive forces affect car parking. For example, one important consideration is that you should not expect to see two cars parked in the same space at the same time! That's entirely analogous for molecular parking. Simple ideas like this lead to an intuitive understanding of the number of molecules distributed at each distance around a central molecule. From there, it is straightforward to multiply the energy at a given distance (ie. u(r) ) by the number of molecules at that distance (aka. g(r) ), and integrate to obtain the total energy. A similar integral over intermolecular forces leads to the pressure. And, voila! we have a new conceptual route to developing engineering equations of state.
Comprehension questions:
1. Sketch u(r)/epsilon and g(r) vs. r/sigma for square well spheres at a very low density. Use a solid line for g(r) and a dashed line for u(r)/epsilon.
2. Sketch u(r)/epsilon and g(r) vs. r/sigma for hard spheres at a high density. Use a solid line for g(r) and a dashed line for u(r)/epsilon.
3. Sketch u(r)/epsilon and g(r) vs. r/sigma for square well spheres at a high density. Use a solid line for g(r) and a dashed line for u(r)/epsilon.

Nature of Molecular Energy - Example Calculation(8min, uakron.edu) Given an estimate for the radial distribution function (RDF) integrate to obtain an estimate of the internal energy. The result provides an alternative to the attractive term of the vdW EOS.

Nature of Molecular Pressure - Example Calculation(11min, uakron.edu) Similar to integrating intermolecular energy to obtain the macroscopic internal energy, integrating the intermolecular force per unit area leads to the macroscopic force per unit area (aka. pressure).

Departure Function Overview (11:22) (msu.edu)
The philosophy and overall approach for using departure functions.

The Internal Energy Departure Function (11min, uakron.edu) Deriving departure functions for a variety of equations of state is simplified by transforming to dimensionless units and using density instead of volume. This also leads to an extra simplification for the internal energy departure function.

Comprehension Questions:

1. What is the value of T(∂P/∂T)_V - P for an ideal gas?
2. What is the value of (∂U/∂V)_T for an ideal gas and how can you explain this result at the molecular scale?
3. The Redlich-Kwong (RK) EOS is: P=RT/(V-b) -a/(V²RT^1.5). Use Eqn. 8.13 to solve for (U-U^ig)/RT of the RK EOS.
4. The RK EOS can be written as: Z = 1/(1-bρ) - aρ/(RT^1.5). Use Eqn. 8.14 to solve for (U-U^ig)/RT of the RK EOS.

Departure Function Derivation Principles (8:03) (msu.edu)
This screencast covers sections 8.2 - 8.8. Concepts of using the equation of state to evaluate departure functions. The screencasts also discusses the choice of density integrals or pressure integrals. The use of a reference state is discussed.

Enthalpy Departure Function for the vdW Fluid (5min) (LearnChemE.com) This short video shows the application of Eqn. 8.24 and the van der Waals equation of state. This is a simple equation of state and the derivation is easy, so it is a good place to start in order to understand the process.

Departure Functions: PREOS.xls Compressor and OVC Design (11min) (uakron.edu) Redesign the ordinary vapor compression cycle (OVC) using propane as discussed in Chapter 5, this time applying PREOS.xls instead of the chart. In this sample calculation, the cycle operates from -100F in the evaporator with a compressor that takes the saturated vapor from the evaporator to 10 bars and 180F. With this procedure, applying PREOS.xls could be adapted to any compound in the database, not just propane. So PREOS.xls represents the equivalent of charts for roughly 200 compounds, and that's just what it can do for pure fluids.
Comprehension Questions: Assume a reference state of the saturated liquid at 1 bar. Use Eqn. 2.47 (SCVP eq) to estimate saturation conditions.
1. Compute the enthalpy (J/mol) of saturated vapor N2O at -100F.
2. Compute the enthalpy (J/mol) of saturated liquid N2O at 80F.
3. Compute the enthalpy (J/mol) of N2O at 60 bars and 350F.
4. Compute the COP for this OVC cycle.

Peng-Robinson Properties - Excel (6:56) (msu.edu)

Provides an overview of using the Peng-Robinson spreadsheet Preos.xlsx for calculation of H, U, S and use of solver.

Comprehension Questions:

1. For liquid propane at 298K and 1 MPa, and a reference state of 298K and 1bar propane vapor, what is the ideal gas contribution to "H-H_R" (J/mol)?
2. For liquid propane at 298K and 1 MPa, and a reference state of 298K and 1bar propane vapor, what is the ideal gas departure contribution: "H-H^_ig" (J/mol)?
3. For liquid propane at 298K and 1 MPa, and a reference state of 298K and 1bar propane vapor, what is the tabulated value of "H" (J/mol)?
4. Explain the similarity and difference between the numerical values of "H" and "H-H^_ig".
5. Ethane at 350K and 5 bars is expanded through an adiabatic, reversible turbine to 1 bar. What is the temperature (K) at the turbine outlet?

Peng-Robinson Properties - Matlab (13:10) (msu.edu)

This screencast shows the types of calculations that can be done usiing the Matlab GUI. Includes finding states at a given P and T, matching S, finding saturations, and developing a custom objective function. Selection of root stability is stressed and demonstrated several times.

Phase equilibrium in a pure fluid (uakron, 11min) can be contemplated in terms of the following question: Suppose propane exists at a set temperature in an uninsulated piston/cylinder with half the volume as vapor and half as liquid. What is the final pressure when the piston is pressed down. A proper thermodynamic answer leads to the consideration of the Gibbs energy, with implications that open up an entire new world of problems to be solved related to equilibrium partitioning for pure fluids and mixtures.

Comprehension Questions:

1. Write dG for the total piston/cylinder system in terms of the individual phases.
2. What is the criterion for equilibrium in a pure fluid?
3. What is the stable state (L,V,L=V) when G^L > G^V ?
4. For the vdW fluid at 62C, 0.35 MPa, the following roots were obtained: Z^L = 0.02598,
Z^V = 0.92718, A=0.08608, B=0.01820. What is the stable state (L,V,L=V)?
5. For the vdW fluid at 62C, 0.25 MPa, the following roots were obtained: Z^L = 0.01859,
Z^V = 0.94910, A=0.061487, B=0.013000. What is the stable state (L,V,L=V)?

Hint: (G-G^ig)/RT = -ln(Z-B)-A/Z + Z - 1 - ln(Z) where A=a*P/(R²T²); B=bP/RT; b=0.125*RT_c/P_c

Estimating the Heat of Vaporization from Antoine's Equation (3min, learncheme.com) The Clausius-Clapeyron equation shows that the heat of vaporization is slope of the vapor pressure curve. So you just need to differentiate the Antoine equation to estimate the heat of vaporization. This sample calculation shows how to compute the heat of vaporization of benzene given Antoine coefficients.

Comprehension Questions:

1. Estimate the vapor pressure (torr) of benzene at 55C using the equation given in the screencast.
2. Estimate (or report) the heat of vaporization (J/mol) of benzene according to the screencast.
3. Estimate the vapor pressure (torr) of benzene at 55C using the SCVP equation (2.47).
4. Estimate the heat of vaporization (J/mol) of benzene using the SCVP equation.
5. Estimate the heat of vaporization (J/mol) of benzene using Eq. 2.45.

Shortcut estimation of thermodynamic properties (sample calculation) can be very quick and sometimes reasonably accurate.(6min, uakron.edu) As a follow-up exercise, it is suggested to adapt the shortcut vapor pressure equation in combination with Eqn. 2.45 and the pathway of Fig. 2.6c to rapidly estimate stream properties. Briefly, all you need is an "IF" statement that checks whether the T is less than T^sat at the given P. If so, then H=H^ref+CpΔT+H_vap. If not, then H=H^ref+CpΔT. This can be a quick and convenient method to estimate stream attributes of a process flow diagram. One equation per cell and you're done. This sample calculation illustrates the process for the heat duty of a butane vaporizer and compares the PREOS to the methods of Chapter 2 (ie. Eq. 2.45 etc.)

Comprehension Questions: Suppose you want to tabulate the entropy (S) of your stream attributes by this approach.
1. How would you compute the S^ig(T,P)-S^ig(T^ref,P^ref) contribution?
2. How would you compute ΔS_vap?
3. Compute "S" for propane at 355K and 3MPa relative to the liquid at 230K and 0.1MPa by this approach.
4. Compute "H" for propane at 355K and 3MPa relative to the liquid at 230K and 0.1MPa by this approach.
5. Compute H and S for the same conditions/reference using the PREOS.
6. Explain the discrepancies between the two approaches. e.g. compare the H_vap values and the (H^V-H^ig) values, where H^V represents the enthalpy of the vapor phase, not the heat of vaporization (H_vap).

Gibbs Energy - Nuts to Soup. (learncheme.com, 8min) It is straightforward to start from the definition of Gibbs Energy and derive all the changes in Gibbs energy. These can be graphed for H2O to see how familiar quantities from the steam tables relate to changes in this unfamiliar property.

What is fugacity? (10min) (learncheme.com) Defines fugacity in terms of Gibbs Energy and describes the need for defining this new property as a generalization of how pressure affects ideal gases.
Comprehension Questions
1. The phases in this video start with concentrations 0.0007kg/L and 1.0 kg/L, when not at equilibrium. What are the equilibrium concentrations?
2. Why is concentration an unreliable indicator for the direction of mass transfer?
3. Name two indicators for the direction of mass transfer that are superior to concentration.  

In a contest for "the most hated word in Chemical Engineering," fugacity won by a landslide. This video (15min, uakron.edu) reviews how the term was developed and why it's not really as bad as all that. In fact, it's a nice word that sets the stage for all of phase and reaction equilibrium with a straightforward extension of the same conceptual basis to mixtures. On second thought, perhaps the power of that conceptual basis and all that it implies is what really intimidates new students. Many perspectives have been offered to help overcome the frustration that students feel toward fugacity. If you like a comic book perspective, even that is available.

Comprehension Questions:

1.What is the fugacity of a vapor phase component in a mixture according to Raoult's law?
2.What is the fugacity of a liquid phase component in a mixture according to Raoult's law?
3. What word is modern usage is closely related to the latin root "fuga-"?
4. Water is in VLE at 0.7 bars in a fixed volume vessel. Five cm³ of air are injected into the vessel and the temperature is allowed to return to its original value. Does the water in the vapor phase increase, decrease, or remain the same? (Learncheme.com, 2min) (Hint: you may assume that air does not dissolve in the liquid water and the pressure is sufficiently low that the vapor can be assumed to behave as an ideal gas.)

When liquid is added to an evacuated tank of fixed volume, equilibrium is established between the vapor and liquid. (3min,learncheme.com) The fugacity criterion characterizes this equilibrium as occurring when the escaping tendency from each phase is equal.

We occasionally require the fugacity in the vapor phase by an EOS other than the PR EOS. (learncheme, 3min) This becomes especially common in Unit 3 when we extend our methods to mixtures. Another skill demonstrated in this screencast is a sample derivation using the pressure dependent formulas. Note that there is a typo in the initial problem statement. The equation of state should be: PV = (1-0.05 P)RT.

Comprehension Questions:

1. Rearrange the given EOS to solve for Z and apply Eq. 9.23 to solve for the change in fugacity. Compare your answer to that given in the screencast. Which method seems easier to you?
2. Use Eq. 7.5 with Eq. 9.23 to derive an expression for the fugacity.
3. Apply the result of #2 to evaluate the fugacity of n-pentane at 398 K and 1 MPa.
4. Does this condition for pentane satisfy Eq. 7.10? Explain.

Liquid fugacity relative to vapor fugacity. (LearnChemE, 5 min) This screencast shows a sample derivation and sample calculation for the vapor equation of state given by: Z = 1-0.01P, solve for: (a) the vapor fugacity at 500K and 30 bar (b) the liquid fugacity in equilibrium with the same vapor at 500K and 30bar (c) the liquid fugacity at 500K and 60 bar. Data: V^L = 25 cm³/mol.

Comprehension Questions:

1. How much did raising the pressure to 60 bar change the liquid fugacity (bars) (+/- 1%)?
2. Estimate the fugacity (bars) of the vapor at 500 K and 60 bar and compare it to the liquid. Which is smaller? Which state do you think best characterizes the fluid (ie. V or L)?
3. Estimate the fugacity (bars) of n-pentane vapor at 30 bar and 460 K by Eqn. 7.5.
4. Assuming V^L=229cm³/mol, estimate the fugacity of liquid n-pentane at 460K and 600bar.
5. Compare your answers for 3 and 4 to the PREOS.

The fugacity of a solid (uakron, 19min) follows a similar trend to that of a liquid, but there can be unexpected implications. The impact of pressure requires careful consideration. NIST Webbook lists the melting temperature of xenon as 161.45K and the Antoine equation as log₁₀P^sat(bars) = 3.80675 - 577.661/(T(K)-13.0), Cp^V=22.7 J/mol-K, Cp^L=44.4 J/mol-K, ρ^L=2.9662 g/cm3. Wikipedia lists the solid density as 3.540 g/cm3 (and the liquid density as 3.084) and the heat of fusion as 2270 J/mol. You may assume Cp^L=Cp^S. Use Eq. 7.06 to describe the vapor phase. You may assume ω = 0 for the purpose of these calculations. This screencast shows a sample calculation to solve for: (a) the vapor fugacity at 162 K and 0.085 MPa (b) the liquid fugacity in equilibrium with the same vapor at 162 K and 0.085 MPa (c) the liquid fugacity at 162 K and 8.5 MPa (d) the solid fugacity at 161.45 K and 0.082 MPa (e) the solid fugacity at 162 K and 8.5 MPa. If you are still having trouble understanding the ways that all these fugacities relate, you might like to view the phase diagram implications of VLSE (uakron, 9min).

Comprehension Questions:

1. How much did raising the pressure to 8.5 MPa change the liquid fugacity (bars)?
2. Estimate the fugacity (MPa) of the vapor at 162 K and 1.15 MPa and compare it to the liquid. Which is smaller? Which state do you think best characterizes the fluid (ie. V or L or S)?
3. Estimate the fugacities (MPa) of methane vapor, liquid, and solid at its triple point using PREOS. Compare the vapor pressure from PREOS at the triple point to that from NIST.
4. Assuming V^S=V^L/1.1, estimate the fugacity of solid methane at 92K and 10 MPa using PREOS for all fluid properties. Consult the NIST Webbook for T and H_fus at the triple point.

Solving for the saturation pressure using PREOS.xls simply involves setting the temperature and guessing pressure until the fugacities in vapor and liquid are equal. (5min, learncheme.com) It is not shown, but it would also be easy to set the pressure and guess temperature until the fugacities were equal in order to solve for saturation temperature. One added suggestion would be to type in the shortcut vapor pressure (SCVP) equation to give an initial estimate of the pressure. Rearranging the SCVP can also give an initial guess for Tsat when given P. This presentation illustrates a sample calculation for toluene to explore when the vapor is the stable, when the liquid is the stable phase, and when the phases are roughly in equilibrium.

Comprehension Questions:

1. Estimate the vapor pressure (MPa) of n-pentane at 450K according to the PREOS. Compare your result to the value from Eq. 2.47 (SCVP) and to the Antoine equation using the coefficients given in Appendix E. What do you think explains the observations that you make?
2. Estimate the saturation temperature (K) of n-pentane at 3.3 MPa according to the PREOS. Compare your result to the value from Eq. 2.47 (SCVP) and to the Antoine equation using the coefficients given in Appendix E. What do you think explains the observations that you make?
3. Estimate the vapor pressure (MPa) of n-pentane at 223K according to the PREOS. Compare your result to the value from Eq. 2.47 (SCVP) and to the Antoine equation using the coefficients given in Appendix E. What do you think explains the observations that you make?
4. Estimate the saturation temperature (K) of n-pentane at 3.3 kPa according to the PREOS. Compare your result to the value from Eq. 2.47 (SCVP) and to the Antoine equation using the coefficients given in Appendix E. What do you think explains the observations that you make?

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?)

Introduction to Phase Behavior (9:37) (msu.edu)
Students tend to be distracted with the algorithms for bubble, dew, and flash, and often miss the important concepts of the relation of the calculations to the phase diagram. This screencast discusses the pure component endpoints, the trends in phase behavior at the bubble and dew conditions, and the qualitative relation between the P-x-y and T-x-y diagrams.

Comprehension Questions:

1. Referring to the Txy diagram on slide 3, estimate T, nature (ie. L,V, V+L, L+L), composition(s), and amount of the phase(s) for points: a, b. d, g.
2. Referring to the Txy diagram on slide 3, suppose we had T = 340K and zA = 0.40. Estimate T, nature (ie. L,V, V+L, L+L), composition(s), and amount of the phase(s) for that point.
3. Which component is more volatile, A or B?

Bubble, Dew, Flash Concepts and the Lever Rule (4:01) (msu.edu)

Understanding what is present (known) and not present (unkown) for a given state of a system will help you decide which routine to use. Notation is introduced for liquids, vapor, and overall compositions. Also, the lever rule concept is used throughout the chemical engineering curriculum, but it is important to see how to use compositions for the lever rule.

Comprehension Questions:

1. Which variables are fixed and which do you need to find in each of the following:
a. Bubble temperature
b. Bubble pressure
c. Dew temperature
d. Dew pressure
e. Isothermal flash
f. Adiabatic flash