ES 202 Fluid and Thermal Systems Lecture 19 Models Versus General Substances 1 27 2003 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 2 1 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 3 Critical State and Reduced Coordinate Recall the phase diagrams of a general substance Two phase dome line Solid e in rl po va Satura ted liq uid ted ra tu Sa Superheated vapor S n tio ma i l ub Meltin g Critical Point Comp liquid Liquid r po Va iz Critical Point on ati Vapor Base on the thermodynamic properties associated with the critical point a non dimensional reduced coordinate a group can be defined for each substance P reduced temperature T T reduced pressure P R R Pcr Tcr Lecture 19 ES 202 Fluid Thermal Systems 4 2 Compressibility Chart Ideal Gas Compressibility Factor Z Pv 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 5 Revisit Ideal Gas Specific Heats In general u u du dT dv T v 1 2 v T 3 u u T v Definition of cv cv h h dh dT dP T P 1 2 P T 3 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 6 3 Entropy Variation in Ideal Gas Introduce the Gibbs equation for a general substance Tds du Pdv h u Pv Tds dh vdP or Interpretation q ds T int rev Tds q int rev Pdv w int rev for a simple compressible system For an ideal gas the Gibbs equation reduces to a simpler form Lecture 19 ES 202 Fluid Thermal Systems 7 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 u du s ds c v c dT v dT dv R T v h dh c p dT or s c p dT dP R T P Different ways to approximate the integrals direct integration cv and cp as functions of T divide and conquer average specific heats Lecture 19 ES 202 Fluid Thermal Systems geometrical interpretation 8 4
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