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 Lecture 19 ES 202 Fluid Thermal Systems 2 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 3 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 4 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 5 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 6 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 u T P u f T v T P v f T s T P s f T h T P u f T Pv f T h f T P Psat T v f T 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 7 Quiz on Week 6 Materials Cont d P v diagram P 1 P 2 T v diagram T2 T1 Lecture 19 ES 202 Fluid Thermal Systems 8 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 9 Critical State and Reduced Coordinate Recall the phase diagrams of a general substance Solid rl in e Two phase dome po va Satura ted liq Superheated vapor ted ra tu Sa uid lin e Comp liquid Meltin g Critical Point Su tio a m bl i n Liquid po a V Critical Point on i t a ri z Vapor Base on the thermodynamic properties associated with the critical point a non dimensional reduced coordinate a group can be defined for each P T substance reduced pressure reduced temperature PR Lecture 19 Pcr ES 202 Fluid Thermal Systems TR Tcr 10 Compressibility Chart Ideal Gas Compressibility Factor Pv Z RT Ideal Gas Z 1 Good for low pressure high temperature critical point Taken from Figure 3 56 in Cengel Turner Lecture 19 ES 202 Fluid Thermal Systems 11 Revisit Ideal Gas Specific Heats In general u u du dT dv T v v T u u T v Definition of cv cv h h dh dT dP T P P T h h T P Definition of cp cp 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 du cv dT Lecture 19 dh c p dT ES 202 Fluid Thermal Systems 12 Entropy Variation in Ideal Gas Introduce the Gibbs equation for a general substance Tds du Pdv or h u Pv Tds dh vdP Interpretation q ds T int rev Tds q int rev for a simple compressible system Pdv w int rev For an ideal gas the Gibbs equation reduces to a simpler form Lecture 19 ES 202 Fluid Thermal Systems 13 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 dT dv R T v u du cv dT s ds cv or Different ways to approximate the integrals direct integration cv and cp as functions of T divide and conquer average specific heats Lecture 19 h dh c p dT dT s c p T ES 202 Fluid Thermal Systems dP R P geometrical interpretation 14