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Chapter 1 - Basic concepts
Chapter 1 - Basic concepts
01.2 Molecular Nature of Temperature, Pressure, and Energy
01.2 Molecular Nature of Temperature, Pressure, and Energy
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Molecular Nature of Kinetic Energy and Temperature (3:34)
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.
Molecular Nature of U: Thermal Energy
Molecular Nature of Internal Energy: Thermal Energy
This introduction to "thermal energy" elaborates on the ideal gas definition of temperature, which derives from the way that PV is related to kinetic energy. This PV relation can be easily understood in terms of an ultrasimplified model of ideal gas pressure. (uakron, 6min). Noting empirically from the ideal gas law that PV=nRT, we are led to the derivation of Eqn. 1.1 (uakron, 5min, same as above). This result suggests counter-intuitive implications about the the ways that solid, liquid, and gas molecular velocities must be related. When applying Eqn. 1.1, you must be careful to keep your units straight, as illustrated in this sample calculation of molecular temperature for Xenon (Mw=131g/mol) (uakron, 5min). On a closely related note, we could perform a sample calculation of molecular pressure for Xenon using Eqn. 1.21.
Comprehension Questions:
1. If two phases are in equilibrium (e.g. a vapor with a solid), then their temperatures are equal and the rate at which molecules leave the solid equals the rate at which molecules enter the solid. Which molecules are moving faster, solid or vapor? For simplicity, assume that the vapor is xenon and the solid is xenon. Hint: think about the exchange of momentum when the vapor molecules collide with the solid.
2. Compute the average (root mean square) velocity (m/s) of molecules at room temperature and pressure and compare to their speeds of sound. You can search the internet to find the speed of sound.
a. Argon
b. Xenon
3. Three xenon atoms are moving with (x,y,z) velocities in m/s of (300,-450,100), (-100,300,-50), (-200,-150,-50). Estimate the temperature (K) of this fluid.
4. Estimate the pressure of the xenon atoms in Q3 above in a vessel that is 4nm3 in size.
Molecular Nature of U: Configurational Energy
Molecular Nature of Internal Energy: Configurational Energy. (uakron.edu, 19min) Making the connection between "u" and "U" requires the concept configuring the molecules such that their potentials overlap. Then it is a simple matter (conceptually) to count the number of overlaps that occur and multiply by the energy of the overlap to get the "configurational energy." Adding the configurational energy to the translational (and vibrational) energy (Uig, discussed above), gives the total "U."
Comprehension Questions:
For 1-4, assume 100 molecules are held in a cylinder with solid walls. A piston in the cylinder can move to adjust the density.
1. Suppose the range of the potential (λ) was increased. Would the configurational energy increase, decrease, or stay the same?
2. Suppose the density was decreased. Would the configurational energy increase, decrease, or stay the same?
3. Suppose the temperature was increased at constant density. Would the configurational energy increase, decrease, or stay the same?
4. Suppose the temperature was increased at constant density. Would the configurational energy characterized by (U-Uig)/RT increase, decrease, or stay the same?
5. Molecules A and B can be represented by the square-well potential. For molecule A, σ = 0.2 nm and ε = 30e-22 J. For molecule B, σ = 0.35 nm and ε = 20e-22 J. Sketch the potential models for the two molecules on the same pair of axes clearly indicating σ's and ε's of each species. Start your x-axis at zero and scale your drawing properly. Make molecule A a solid line and B a dashed line. Which molecule would you expect to have the higher boiling temperature? (Hint: check out Figure 1.2.)
6. Sketch the potential and the force between two molecules vs. dimensionless distance, r/σ, according to the Lennard-Jones potential. Considering the value of r/σ when the force is equal to zero, is it greater, equal, or less than unity?
Molecular Nature of U: Etomica
Molecular Nature of Energy, Temperature, and Pressure By Etomica(uakron.edu, 17min). We can use a free website (Etomica.org) to visualize the ways that molecules interact, resulting in the average properties that we see at the macroscopic level. The oversimplified nature of the ideal gas model becomes really obvious and the improvement of the hard sphere model is easily understood. Including both attractive and repulsive forces, as in the square well potential model, leads to more surprising behavior. The two effects may cancel and make the Z factor (Z=PV/RT) look like an ideal gas even though it is not. Also, the adiabatic transformation between potential energy and kinetic energy leads to spikes in temperature as molecules enter each other's attractive wells. In certain cases, you might see molecules get stuck in each others' wells. This is effectively "bonding." This bonding is limited at very low density because it requires a third interaction to occur during the collision in order to stay bonded. This requirement lies at the fundamental basis of what is known as "unimolecular reaction," a fairly advanced concept that is easily understood by watching the video. Note: if the etomica applet causes problems with your browser, check the instructions in section 7.10 to download all the apps and run locally. We use the apps for homework in Chapter 7, so it's money in the bank.
Comprehension Questions:
1. What is the average temperature (K) illustrated in the screencast? Is it higher or lower than the initial temperature? Explain.
2. What is the average pressure (bar) illustrated in the screencast?
3. Go to the etomica.org website and perform your own simulation with the piston-cylinder applet starting with 100 molecules and assuming the square well poential model. You can run the simulation in fast mode, but let the molecules collide for 2500 ps. Then report the average value of T,P,U,Z. (Hint: compute Z from its definition, and be careful with units.)
Intermolecular Potential Energy (msu.edu) (7:11)
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?
01.3 Molecular Nature of Entropy
01.3 Molecular Nature of Entropy
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Molecular Nature of S: A Brief Intro to Entropy
Molecular Nature of Entropy (uakron.edu, 5min) Entropy is often related to chaos or disorder, but it has a specific, mathematical definition in thermodynamics. There is nothing metaphysical about it. This very brief presentation introduces the conceptual basis of how the arrangements of molecules between boxes can be related to the flow of work energy, or lack thereof, depending on how the process is conducted. This conceptual basis is expanded in Section 4.2 to permit quantitative calculations of entropy changes based on molecular configurations.
01.4 Basic Concepts
01.4 Basic Concepts
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Molecular Nature of U and PV=RT (msu.edu) (5:04)
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.
01.5 Real Fluids and Tabulated Properties
01.5 Real Fluids and Tabulated Properties
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P-V and P-T diagrams: Boundaries for S, L, V
P-V and P-T diagrams (LearnChemE.com) (5:52) Describes distinctions and trends between solid, vapor, liquid, gas.
Single and Double Interpolation using Steam Tables
Steam Tables (LearnChemE.com) (5:59) calculate enthalpy of steam by interpolation
SteamTables:DoubleInterpolation
Double interpolation (uakron, 8min) is exactly what it sounds like: to find a steam property when neither the pressure nor temperature are among the tabulated values, you need to interpolate twice. We interpolate first on pressure, then on temperature. It is a bit tedious, but straightforward.
Comprehension Questions:
1. Describe how you would use double interpolation to obtain H if given T=275 C and P=0.45MPa.
2. Describe how you would use double interpolation to obtain H if given T=275 C and V=0.555m3/kg.
e-SteamTables:SteamXls
When you use a spreadsheet like Steam.xlsx(uakron, 15min), interpolation can be greatly expedited. It is recommended that you enable the solver before applying Steam.xls.
Comprehension Questions:
1. Compute H if given T=275 C and P=0.45MPa.
2. Compute H if given T=275 C and V=0.555m3/kg.
3. Which would be more practical for solving a project, double interpolation or steam.xlsx?
Steam Quality Calculation
Steam quality given temperature and volume (LearnChemE.com, 9min) Steam quality is the fraction of H2O that exists as vapor. Its computation can be accomplished by knowing one of the saturation properties (T or P) and one of the tabulated properties (V,U,H,S). This kind of calculation is sometimes known as the "lever rule" or "inverse lever rule" because the given property acts like the fulcrum on a lever, specifying whether the liquid or vapor property receives the heavier weight. e.g. if the given property is closer to the saturated vapor value, then the vapor value receives a hevierer weight.
Comprehension Questions:
1. Compute the enthalpy (kJ/kg) at 100 C and a quality (q) of 33%.
2. Compute the entropy (kJ/kg-C) at 200 C and a quality of 90%.
01.6 Summary
01.6 Summary
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Chapter 1 Objectives in Review
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
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.