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

ES 202 Fluid & Thermal Systems Assignments Homework: 7-62, 7-63 in Cengel & Turner Reading assignment 7-4, 7-5 and 7-6 in Cengel & Turner ES 201 notes Lecture 19 ES 202 Fluid & Thermal Systems

ES 202 Fluid & Thermal Systems 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. Lecture 19 ES 202 Fluid & Thermal Systems

Future Quieter Airplane!! primary stream secondary (bypass) stream Sawtooth geometry (chevron) in engine exhaust nozzle is shown to reduce engine noise. Lecture 19 ES 202 Fluid & Thermal Systems

ES 202 Fluid & Thermal Systems 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 Lecture 19 ES 202 Fluid & Thermal Systems

ES 202 Fluid & Thermal Systems 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) Lecture 19 ES 202 Fluid & Thermal Systems

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 = P2 with 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 = T2 with T1 < T2) on the P-v diagram. Indicated clearly their behavior in the two-phase region and label them clearly. Lecture 19 ES 202 Fluid & Thermal Systems

Quiz on Week 6 Materials (Cont’d) T-v diagram P-v diagram P2 P1 T2 T1 Lecture 19 ES 202 Fluid & Thermal Systems

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. Lecture 19 ES 202 Fluid & Thermal Systems

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: Two-phase dome Superheated vapor Comp. liquid Saturated vapor line Saturated liquid line Critical Point Vapor Liquid Solid Sublimation Vaporization Melting Critical Point reduced pressure: reduced temperature: , Lecture 19 ES 202 Fluid & Thermal Systems

Compressibility Chart Factor: Ideal Gas Ideal Gas: Good for: low pressure high temperature critical point (Taken from Figure 3-56 in Cengel & Turner) Lecture 19 ES 202 Fluid & Thermal Systems

Revisit Ideal Gas Specific Heats In general, For an ideal gas, the specific internal energy (u) , hence, specific enthalpy (h) are functions of temperature only. For an ideal gas, the change in specific internal energy and specific enthalpy can be simplified as: Definition of cv Definition of cp , Lecture 19 ES 202 Fluid & Thermal Systems

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 Lecture 19 ES 202 Fluid & Thermal Systems

} 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 } geometrical interpretation Lecture 19 ES 202 Fluid & Thermal Systems