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ES 202 Fluid and Thermal Systems Lecture 19: Models Versus General Substances (1/27/2003)

ES 202 Fluid and Thermal Systems Lecture 19: Models Versus General Substances (1/27/2003). Assignments. Homework: 7-62, 7-63 in Cengel & Turner Reading assignment 7-4, 7-5 and 7-6 in Cengel & Turner ES 201 notes. Announcements. Homework due today at 5 pm in my office

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ES 202 Fluid and Thermal Systems Lecture 19: Models Versus General Substances (1/27/2003)

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  1. ES 202Fluid and Thermal SystemsLecture 19:Models Versus General Substances (1/27/2003)

  2. Assignments • Homework: • 7-62, 7-63 in Cengel & Turner • Reading assignment • 7-4, 7-5 and 7-6 in Cengel & Turner • ES 201 notes ES 202 Fluid & Thermal Systems

  3. Announcements • Homework due today at 5 pm in my office • Check the revised course syllabus on the course web page again. There are more changes. ES 202 Fluid & Thermal Systems

  4. Future Quieter Airplane!! primary stream secondary (bypass) stream Sawtooth geometry (chevron) in engine exhaust nozzle is shown to reduce engine noise. ES 202 Fluid & Thermal Systems

  5. Road Map of Lecture 19 • Quiz on Week 6 materials • Real gas versus ideal gas • notion of reduced coordinate • definition of compressibility factor • Z-chart • Ideal gas model • change in specific internal energy and specific enthalpy • change in specific entropy • Gibbs equation and its interpretation • variation of specific heats ES 202 Fluid & Thermal Systems

  6. Quiz on Week 6 Materials • Indicate in the following cases whether the given information is sufficient or insufficient in fully determining the thermodynamic state of the substance: • pressure and temperature in compressed liquid (YES) • pressure and temperature in superheated vapor (YES) • pressure and temperature in saturated mixture (NO) • pressure and temperature in saturated vapor (YES) • pressure and specific volume in saturated liquid (YES) • pressure and specific entropy in saturated mixture (YES) • temperature and specific enthalpy in superheated vapor (YES) • quality and temperature in saturated mixture (YES) • Given the following limited data from a property table of water at a pressure of 2 MPa: • h = 3023.5 kJ/kg at T = 300 deg C • h = 3137.0 kJ/kg at T = 350 deg C What is h at T = 330 deg C and P = 2 MPa? (h = 3091.6 kJ/kg) ES 202 Fluid & Thermal Systems

  7. Quiz on Week 6 Materials (Cont’d) • According to the Compressed Liquid Approximation, how are the following thermodynamic properties approximated in the compressed liquid region: • Sketch two constant pressure curves (P = P1, P = P2with P1 < P2) on the T-v diagram. Indicated clearly their behavior in the two-phase region and label them clearly. • Sketch two constant temperature curves (T = T1, T = T2with T1 < T2) on the P-v diagram. Indicated clearly their behavior in the two-phase region and label them clearly. ES 202 Fluid & Thermal Systems

  8. P2 P1 T2 T1 Quiz on Week 6 Materials (Cont’d) P-v diagram T-v diagram ES 202 Fluid & Thermal Systems

  9. Real Gas Versus Ideal Gas • Recall ideal gas as a simplified (yet powerful) model for real gas behavior • Its original derivation assumes negligible mutual interaction between gas molecules. Hence, it is expected to work well for gases under low pressure. • But, the next logical question will be: “How low is low?” or “Against what standard is low pressure measured with respect to?” • To answer this question, we need to recall the phase diagrams of a general substance. ES 202 Fluid & Thermal Systems

  10. Critical Point Comp. liquid Liquid Critical Point Superheated vapor Melting Solid Vaporization Saturated vapor line Saturated liquid line Two-phase dome Vapor Sublimation reduced temperature: reduced pressure: Critical State and Reduced Coordinate • Recall the phase diagrams of a general substance: • Base on the thermodynamic properties associated with the critical point, a non-dimensional reduced coordinate (a p group) can be defined for each substance: , ES 202 Fluid & Thermal Systems

  11. Compressibility Factor: Ideal Gas: Compressibility Chart Ideal Gas • Good for: • low pressure • high temperature critical point (Taken from Figure 3-56 in Cengel & Turner) ES 202 Fluid & Thermal Systems

  12. Revisit Ideal Gas Specific Heats • In general, • For an ideal gas, the specific internal energy(u) , hence, specific enthalpy(h) are functions of temperatureonly. • For an ideal gas, the change in specific internal energy and specific enthalpy can be simplified as: Definition of cv Definition of cp , ES 202 Fluid & Thermal Systems

  13. Entropy Variation in Ideal Gas • Introduce the Gibbs equation for a general substance: • Interpretation: • for a simple compressible system, • For an ideal gas, the Gibbs equation reduces to a simpler form. or ES 202 Fluid & Thermal Systems

  14. } geometrical interpretation Variation in Specific Heats • In general, the specific heats (cv, cp) are NOT true constants. They vary (increase) slightly with temperature even for ideal gases. • Afterall, it is the change in properties that matters (their absolute values depend on the chosen reference state.) • For an ideal gas with finite temperature change: • Different ways to approximate the integrals: • direct integration (cv and cp as functions of T) • divide and conquer • “average” specific heats , or ES 202 Fluid & Thermal Systems

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