Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Using Thermodynamic
Tables
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Saturated Liquid and
Saturated vapor
States
A4 & A5
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
The two-phase region for water
V  V f  Vg
Critical Point
p
v fg  vg  v f
Saturated Liquid
V
Saturated Vapor
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 2-30
A partial list
of Table A–4.
2-10
Enthalpy
• What does hfg represent?
– Total amount of energy to change a saturated
liquid to a saturated vapor
– Enthalpy of vaporization or latent heat of
vaporization.
Saturated Liquid-Vapor
Mixtures
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Quality...
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Liquid-vapor equilibrium
Vapor at P,T
Vapor at P,T
Liquid at P,T
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Surroundings
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Quality
x
mvapor
mliquid  mvapor
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Quality defined
p
v f  v  vg
vf v
vg
V
Quality, x, allows location of states inside
the vapor-liquid region.
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Quality
x
mvapor
mliquid  mvapor
v  v f  xv fg
v  xvg  1  x v f
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Internal energy in the vapor-liquid
region
u  u f  xu fg
u  xug  (1  x)u f
The same holds for specific enthalpy, h
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Superheated Vapor
Characterized by… p83
Table A6
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 2-40
A partial listing
of Table A–6.
2-11
Compressed Liquid
Characterized by… p84
Tables A7 or A4 & A5
Can treat as saturated
liquid at Temperature.
Exception is enthalpy
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Reference States and Values
• For energies, entropies, and enthalpies, can
only calculate changes and can’t measure.
• Must pick a zero point.
– for water, saturated liquid at 0.01°C
– for refrigerant-134a, saturated liquid at -40°C
• OK as long as you are consistent.
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
EQUATIONS OF
STATE FOR GASES:
Equation that relates the pressure, temperature, and specific
Volume of a substance.
Gas vs. vapor?
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Definition of gas...
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Fluids and gasses
A liquid will take the
shape of its container
but exhibits a free
surface.
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
A gas will fill its container
completely and does not
exhibit a free surface.
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
The ideal gas...
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
P-V-T relation for ideal gases
Bar means on a molar
basis
lim
p 0
pv
R
T
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
pv
T
T1
T2
T3
p
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
The ideal gas equation of state
pv  R T
This implies: (1) very little molecular
interaction (p  0),and (2) molecules
are point masses, i.e., zero volume.
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
The universal gas constant
Universal – p88 (2-11)
Specific – Table A-1 p824
R  RM
 8.314 kJ / km ol K
 1545ft  lbf / lbm ol R
M = Molecular weight, kg/kmol
or lbm/lbmol.
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
The ideal gas state surface
p
T
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Ideal Gas State Surface
V
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Water?
Instructor’s Visual Aids
Heat Work and Energy. A First Course in Thermodynamics
© 2002, F. A. Kulacki
Chapter 2 Module 2 Slide ‹#›
Additional Aspects for the P-V-T Surface for Water
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
FIGURE 2-49
Percentage of error
involved in assuming
steam to be an ideal
gas, and the region
where steam can be
treated as an ideal gas
with less than 1
percent error.
2-12