Molecular Nature of Internal Energy: Configurational Energy. (uakron.edu, 19min) Making the connection between "u" and "U" requires the concept configuring the molecules such that their potentials overlap. Then it is a simple matter (conceptually) to count the number of overlaps that occur and multiply by the energy of the overlap to get the "configurational energy." Adding the configurational energy to the translational (and vibrational) energy (U^ig, discussed above), gives the total "U."

Comprehension Questions:

For 1-4, assume 100 molecules are held in a cylinder with solid walls. A piston in the cylinder can move to adjust the density.
1. Suppose the range of the potential (λ) was increased. Would the configurational energy increase, decrease, or stay the same?
2. Suppose the density was decreased. Would the configurational energy increase, decrease, or stay the same?
3. Suppose the temperature was increased at constant density. Would the configurational energy increase, decrease, or stay the same?
4. Suppose the temperature was increased at constant density. Would the configurational energy characterized by (U-U^ig)/RT  increase, decrease, or stay the same?
5. Molecules A and B can be represented by the square-well potential. For molecule A, σ = 0.2 nm and ε = 30e-22 J. For molecule B, σ = 0.35 nm and ε = 20e-22 J.  Sketch the potential models for the two molecules on the same pair of axes clearly indicating σ's and ε's of each species. Start your x-axis at zero and scale your drawing properly.  Make molecule A a solid line and B a dashed line. Which molecule would you expect to have the higher boiling temperature? (Hint: check out Figure 1.2.)
6. Sketch the potential and the force between two molecules vs. dimensionless distance, r/σ, according to the Lennard-Jones potential. Considering the value of r/σ when the force is equal to zero, is it greater, equal, or less than unity?

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.

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.

Thermodynamic pathways of EOS's for arbitrary reference states (uakron.edu, 20min) The development of a thermodynamic pathway from an arbitrary reference state to a given state condition is independent of the thermodynamic model. It depends only on (1a) identifying the condition of the reference state (e.g. ideal gas, real vapor, or liquid) (1b) transforming from the reference state to the ideal gas, if necessary (2) transforming from the ideal gas at the condition of the reference state to the ideal gas at the given state condition (3a) identifying the condition at the given state (3b) transforming from the ideal gas at the given state to the real fluid at the given state. The methodology is illustrated for two thermodynamic models: the P^sat/H_^vap model of Figure 2.6c,Eqs 2.45,47 vs. the PR EOS. The screencast is a bit long, but it covers 16 sample calculations (8 for H and 8 for S) and comparisons between PREOS vs P^sat/H_^vap. You might like to refer back to Sections 2.10 and 3.6 to review the P^sat/H_^vap model and the elemental reference state. Push pause before each sample calculation and check whether you can predict the next answer.

Comprehension Questions:

1. Compute "H" by hand for propane at 80C and 3 MPa relative to a reference at 230K and 1bar, assuming Cp^ig/R = 8.85 and the PR EOS. You may use PREOS.xlsx to compute H-Hig, but you must show your hand calculations for each step (1a-3b). Compare your answer to the result tabulated in PREOS.xlsx.
2. Compute "S" by hand for propane at 80C and 3 MPa relative to a reference at 230K and 1bar, assuming Cp^ig/R = 8.85 and the PR EOS. You may use PREOS.xlsx to compute S-Sig, but you must show your hand calculations for each step (1a-3b). Compare your answer to the result tabulated in PREOS.xlsx.
3. Compute "H" by hand for propane at 80C and 3 MPa relative to a reference at 230K and 1bar, assuming Cp^ig/R = 8.85 and the P^sat/H_^vap model. Show your hand calculations for each step (1a-3b). Compare your answer to the result tabulated in PREOS.xlsx.
4. Compute "S" by hand for propane at 80C and 3 MPa relative to a reference at 230K and 1bar, assuming Cp^ig/R = 8.85 and the P^sat/H_^vap model. Show your hand calculations for each step (1a-3b). Compare your answer to the result tabulated in PREOS.xlsx.