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.