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Begin With the End in Mind : Class Learning Objectives

Begin With the End in Mind : Class Learning Objectives. Demonstrate Knowledge LoL for: the ‘ General Equation of State ’ used to represent the P - v - T Surface ; the Ideal Gas Equation of State and the van der Waals Equation of State;

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Begin With the End in Mind : Class Learning Objectives

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  1. Begin With the End in Mind :Class Learning Objectives Demonstrate Knowledge LoL for: • the ‘GeneralEquation of State’ used torepresentthe P - v - TSurface; • the IdealGas Equation of State and the vanderWaals Equation of State; • using Gibbs’ Phase Rule to locate ‘states of matter’ on the P - v - T Surface; • including ‘Thermodynamic Property Constraints’ in a Model Analysis; • the VaporPressureEquation constraint.

  2. Class 7 - Thermodynamic Property Constraints • Part 1 - Contact Before Work 5 min • Part 2 - The Equation of State20 min • Part 3 - The P - vview of the EOS25 min • Break 10 min • Part 4 - The P - Tview of the EOS 20 min • Part 5 - Gibbs Phase Rule 10 min • Part 6 - EOS and Model Analysis 15 min • Part 7 - Clarification 5 min

  3. Equation of State (20 min) Each sub-team of two persons, use a blank sheet of paper or a page from your Academic Journal to: • Define a 'pure substance'; include three common examples. • Define a 'phase' and list the 4 phases of matter that are known to exist in 1998; include a common example of each phase. • What is the generalmathematicalequation that describes the equation of state, or EOS, for a puresubstance in a singlephase at equilibrium (p. 737)? N.B. This general equation defines a3 dimensionalSURFACE !

  4. Equation of State (cont.) • What two, specificEquationsofState will be used in ECE 340 (p. 737)? • What are the two, inherentlyintensive, thermodynamic state VARIABLES(Table 8.2, p. 741)? • List 10 other thermodynamic property 'FUNCTIONS' and twotransport property 'FUNCTIONS' of T and P (p. 737); we define these as FUNCTIONS of the thermodynamic state VARIABLES, T and P.

  5. Pure Component Properties P V V?

  6. P T Pure Component Properties

  7. The ‘P - v’ and ‘P - T’ Views (45 min) 7 Sketch the P- v (Figure 8.1, p. 739) andP- T (Figure 8.2, p. 740) diagrams; on BOTH diagrams, highlight or delineate the following: 7A the NORMALboilingpoint, or NBP,i.e., at P = 1ATM (FYI, some pure substances do not have an NBP, e.g., CO2) 7B the ISOTHERM associated with the normal boiling point temperature,i.e., the line where T = Tnbp

  8. The ‘P - v’ and ‘P - T’ Views (cont.) 7C the SOLID, LIQUID, and GASregions;N.B. these regions are PROJECTED asAREAS in a PLANEin a two dimensional representation or view. 7DDefinesaturated liquid and saturated vapor; highlight or delineate the phaseboundary between a saturatedvapor and a saturatedliquid; N.B. Also note that the 'phase envelope' is empty, i.e., the three dimensional surface does NOT include the phase envelope or 'dome' under the phase boundary.

  9. The ‘P - v’ and ‘P - T’ Views (cont.) 7E the CRITICALPOINT; state the physical significance of the critical point 7F the CRITICALISOTHERM 7G the CRITICALREGION; N.B. this region is PROJECTED as the AREA in a PLANEin a two dimensional representation or view. 7H another ISOTHERMbetween the NBP isotherm and the critical isotherm on the P - v diagram.

  10. Break Be back with your team, ready to work, in 10minutes : rememberourECE 340 Class Code of Cooperation !

  11. The ‘P - v’ and ‘P - T’ Views (cont.) 7I the NORMALfreezingpoint at P = 1 ATM 7J the TRIPLE point where saturatedvapor, liquid and solid coexist.

  12. T > Tcand P > Pc Liquid Region Critical Region Compressedor Subcooled CriticalPoint Solid Region Saturated Liquid/Vapor Envelope P ? T = constant ? GasRegion NFP NBP 1 ATM TripleLine ? Saturated Solid/Liquid Envelope V V? Pure Component Properties ?

  13. Pure Component Properties CriticalRegion Saturated Solid Liquid Line Fusion CriticalPoint P Liquid Region Solid Region 1 ATM NFP NBP Gas Region TriplePoint Saturated Liquid/Vapor Line Vaporization T

  14. Two Phase Mixtures (cont.) • How are the AVERAGE properties of a twophasemixture (e.g., a mixture of a saturatedvapor and a saturatedliquid) DETERMINED or CALCULATED (pp. 744 - 745)? • How are the properties of a two phase mixture (e.g., a mixture of a saturated vapor and a saturated liquid) REPRESENTED on the P - v diagram; what is the 'inverse lever rule'?(pp. 744 - 745)? 10What is a 'VAPORPRESSURE'equation(pp. 743 and 765)? How is it represented on both the P - v and P - T diagrams?

  15. Inverse Lever Rule x varies from 0 to 1 Saturated Liquid/Vapor Envelope P vSL vSV GasRegion x 1 - x vavg = x vSV + (1 - x) vSL V vavg

  16. Gibbs Phase Rule (10 min) 11State and explain Gibbs Phase Rule; summarize Gibbs Phase Rule for a pure substance and determine the 'degrees of freedom' or 'what must be specified' for each of the points, curves, or regions delineated on the P - v and P - T diagrams in question 7 above; 12 Review the use of the general representation for Thermodynamic Property Constraints in the Model Analysis of the LNG process on p. 557.

  17. Model Analysis 1. Model Variables (all symbols!) From the Sketch … From Equation 1 ... From Equation 2, etc. …. 2. Analysis Variables (all symbols!) - Equations _______ Remaining Unknowns - Data (from ‘MotherNature’) - Specifications (from ‘Humans’) - Parameters (shared!) - Initial Conditions (time <= 0) - Independent Variables (e.g., time) _______ Design Variables; Solvable ?

  18. . . Q?= 0 . CM Q?= 0 . z Q?= 0 x y System Boundary QP . Compressor Precooler WC 3 2 Cooler 4 7 Expansion Device Adiabatic Flash Separator 5

  19. The System = Gas EquationsTotal Mass Conservation

  20. The System = Gas EquationsTotal Energy Conservation

  21. The System = Gas EquationsTotal Mass Conservation andTotal Energy Conservation

  22. LNG Model Analysis

  23. ‘Flow Work’ PLUSthe Work Associatedwith the Expansionor Contraction of the Fluid Mechanical Energy AccountingSteady State - SISO KineticEnergy PotentialEnergy ShaftWork Irreversible Conversionof Mechanical Energy

  24. Mechanical Energy AccountingSteady State - SISO (Alternate)(10 min)

  25. Work Associatedwith the Expansionor Contraction of the Fluid Mechanical Energy AccountingSteady State - SISO (Alternate) Pressure Energy, ‘Pv’ Energy, or ‘Flow Work’ KineticEnergy PotentialEnergy ShaftWork Irreversible Conversionof Mechanical Energy

  26. Heuristic for Finding Additional Model Equations

  27. Mass Flow Acrossthe System BoundaryNote the minus sign! Note the minus sign Entropy Generatedin the SurroundingsNEW !!! Entropy AccountingSurroundings Mass Flow Acrossthe System Boundary Heat Flow Acrossthe System Boundary EntropyAccumulatedin theSurroundings a ‘Constraint’

  28. System + Surroundings

  29. Entropy Accounting ModelFor a Single Process or Path

  30. 0 0 Entropy Accounting ModelFor an Isentropic Process or Path

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