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

2. 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

3. 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

4. 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

5. 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

6. 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 = kJ/kg at T = 300 deg C
h = kJ/kg at T = 350 deg C
What is h at T = 330 deg C and P = 2 MPa? (h = kJ/kg)
Lecture 19
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 = 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

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

10. 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

11. 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

12. 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

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
Lecture 19
ES 202 Fluid & Thermal Systems

14. } 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