Pure substance Phases of a pure substance Phase change processes of pure substances Compressed liquid, Saturated liquid, Saturated vapor, Superheated vapor Saturated temperature and Satuated pressure Property diagrams for phase change processes The T-v diagram, The P-v diagram, The P-T diagram, The P-v-T diagram Property tables Enthalpy Saturated liquid, Saturated vapor, Saturated liquid vapor mixture, Superheated vapor, compressed liquid Reference state and Reference values The ideal gas equation of state Is water vapor an ideal gas?

1. PROPERTIES OF PURE
SUBSTANCES
Lecture 6
Keith Vaugh BEng (AERO) MEng
Reference text: Chapter 4 - Fundamentals of Thermal-Fluid Sciences, 3rd Edition
Yunus A. Cengel, Robert H. Turner, John M. Cimbala
McGraw-Hill, 2008
KEITH VAUGH

2. }
KEITH VAUGH

3. OBJECTIVES
Introduce the concept of a pure substance.
}
KEITH VAUGH

4. OBJECTIVES
Introduce the concept of a pure substance.
Discuss the physics of phase-change processes.
}
KEITH VAUGH

5. OBJECTIVES
Introduce the concept of a pure substance.
Discuss the physics of phase-change processes.
}
Illustrate the P-v, T-v, and P-T property
diagrams and P-v-T surfaces of pure
substances.
KEITH VAUGH

6. OBJECTIVES
Introduce the concept of a pure substance.
Discuss the physics of phase-change processes.
}
Illustrate the P-v, T-v, and P-T property
diagrams and P-v-T surfaces of pure
substances.
Demonstrate the procedures for determining
thermodynamic properties of pure substances
from tables of property data.
KEITH VAUGH

7. OBJECTIVES
Introduce the concept of a pure substance.
Discuss the physics of phase-change processes.
}
Illustrate the P-v, T-v, and P-T property
diagrams and P-v-T surfaces of pure
substances.
Demonstrate the procedures for determining
thermodynamic properties of pure substances
from tables of property data.
Describe the hypothetical substance “ideal gas”
and the ideal-gas equation of state.
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8. }
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9. Apply the ideal-gas equation of state in the solution
of typical problems.
}
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10. Apply the ideal-gas equation of state in the solution
of typical problems.
Introduce the compressibility factor, which accounts
}
for the deviation of real gases from ideal-gas
behaviour.
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11. Apply the ideal-gas equation of state in the solution
of typical problems.
Introduce the compressibility factor, which accounts
}
for the deviation of real gases from ideal-gas
behaviour.
Present some of the best-known equations of state.
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12. PURE SUBSTANCE
Pure substance
A substance that has a fixed chemical composition throughout.
Air is a mixture of several gases, but it is considered to be a
}
pure substance.
Nitrogen and gaseous air are pure A mixture of liquid and gaseous water is
substances. a pure substance, but a mixture of liquid
and gaseous air is not.
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13. KEITH VAUGH

14. The arrangement of atoms in different phases:
(a) molecules are at relatively fixed positions in a solid,
(b) groups of molecules move about each other in the liquid phase, and
(c) molecules move about at random in the gas phase.
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15. PHASE CHANGE PROCESSES
OF PURE SUBSTANCES
}
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16. PHASE CHANGE PROCESSES
OF PURE SUBSTANCES
Compressed liquid (sub-cooled liquid)
}
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17. PHASE CHANGE PROCESSES
OF PURE SUBSTANCES
Compressed liquid (sub-cooled liquid)
A substance that it is not about to vaporise. }
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18. PHASE CHANGE PROCESSES
OF PURE SUBSTANCES
Compressed liquid (sub-cooled liquid)
A substance that it is not about to vaporise.
Saturated liquid
}
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19. PHASE CHANGE PROCESSES
OF PURE SUBSTANCES
Compressed liquid (sub-cooled liquid)
A substance that it is not about to vaporise.
Saturated liquid
}
A liquid that is about to vaporise.
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20. PHASE CHANGE PROCESSES
OF PURE SUBSTANCES
Compressed liquid (sub-cooled liquid)
A substance that it is not about to vaporise.
Saturated liquid
}
A liquid that is about to vaporise.
Saturated vapour
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21. PHASE CHANGE PROCESSES
OF PURE SUBSTANCES
Compressed liquid (sub-cooled liquid)
A substance that it is not about to vaporise.
Saturated liquid
}
A liquid that is about to vaporise.
Saturated vapour
A vapour that is about to condense.
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22. PHASE CHANGE PROCESSES
OF PURE SUBSTANCES
Compressed liquid (sub-cooled liquid)
A substance that it is not about to vaporise.
Saturated liquid
}
A liquid that is about to vaporise.
Saturated vapour
A vapour that is about to condense.
Saturated liquid–vapour mixture
KEITH VAUGH

23. PHASE CHANGE PROCESSES
OF PURE SUBSTANCES
Compressed liquid (sub-cooled liquid)
A substance that it is not about to vaporise.
Saturated liquid
}
A liquid that is about to vaporise.
Saturated vapour
A vapour that is about to condense.
Saturated liquid–vapour mixture
The state at which the liquid and vapour phases coexist in
equilibrium.
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24. PHASE CHANGE PROCESSES
OF PURE SUBSTANCES
Compressed liquid (sub-cooled liquid)
A substance that it is not about to vaporise.
Saturated liquid
}
A liquid that is about to vaporise.
Saturated vapour
A vapour that is about to condense.
Saturated liquid–vapour mixture
The state at which the liquid and vapour phases coexist in
equilibrium.
Superheated vapour
KEITH VAUGH

25. PHASE CHANGE PROCESSES
OF PURE SUBSTANCES
Compressed liquid (sub-cooled liquid)
A substance that it is not about to vaporise.
Saturated liquid
}
A liquid that is about to vaporise.
Saturated vapour
A vapour that is about to condense.
Saturated liquid–vapour mixture
The state at which the liquid and vapour phases coexist in
equilibrium.
Superheated vapour
A vapour that is not about to condense (i.e., not a saturated vapour).
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26. KEITH VAUGH

27. At 1 atm and
20°C, water
exists in the
liquid phase
(compressed
liquid).
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28. At 1 atm and At 1 atm pressure
20°C, water and 100°C, water
exists in the exists as a liquid
liquid phase that is ready to
(compressed vaporise
liquid). (saturated
liquid).
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29. At 1 atm and At 1 atm pressure As more heat is
20°C, water and 100°C, water transferred, part
exists in the exists as a liquid of the saturated
liquid phase that is ready to liquid vaporises
(compressed vaporise (saturated
liquid). (saturated liquid–vapour
liquid). mixture).
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30. At 1 atm and At 1 atm pressure As more heat is At 1 atm pressure,
20°C, water and 100°C, water transferred, part the temperature
exists in the exists as a liquid of the saturated remains constant at
liquid phase that is ready to liquid vaporises 100°C until the last
(compressed vaporise (saturated drop of liquid is
liquid). (saturated liquid–vapour vaporised
liquid). mixture). (saturated vapour).
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31. At 1 atm and At 1 atm pressure As more heat is At 1 atm pressure, As more heat is
20°C, water and 100°C, water transferred, part the temperature transferred, the
exists in the exists as a liquid of the saturated remains constant at temperature of the
liquid phase that is ready to liquid vaporises 100°C until the last vapour starts to rise
(compressed vaporise (saturated drop of liquid is (superheated
liquid). (saturated liquid–vapour vaporised vapour).
liquid). mixture). (saturated vapour).
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32. KEITH VAUGH

33. If the entire process between state 1
and 5 described in the figure is
reversed by cooling the water while
maintaining the pressure at the same
value, the water will go back to state 1,
retracing the same path, and in so
doing, the amount of heat released will
exactly match the amount of heat
added during the heating process.
T-v diagram for the heating process of
water at constant pressure.
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34. SATURATED TEMPERATURE
AND SATURATED PRESSURE
The temperature at which water starts boiling depends
on the pressure; therefore, if the pressure is fixed, so is
the boiling temperature.
}
Water boils at 100°C at 1 atm pressure.
Saturation temperature Tsat
The temperature at which a pure substance changes
phase at a given pressure.
Saturation pressure Psat
The pressure at which a pure substance changes phase at
a given temperature.
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35. The liquid–vapour saturation curve of a
pure substance (numerical values are
for water).
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36. KEITH VAUGH

37. Latent heat
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38. Latent heat
The amount of energy absorbed or released during a phase-change process.
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39. Latent heat
The amount of energy absorbed or released during a phase-change process.
Latent heat of fusion
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40. Latent heat
The amount of energy absorbed or released during a phase-change process.
Latent heat of fusion
The amount of energy absorbed during melting. It is equivalent to the amount of
energy released during freezing.
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41. Latent heat
The amount of energy absorbed or released during a phase-change process.
Latent heat of fusion
The amount of energy absorbed during melting. It is equivalent to the amount of
energy released during freezing.
Latent heat of vaporisation
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42. Latent heat
The amount of energy absorbed or released during a phase-change process.
Latent heat of fusion
The amount of energy absorbed during melting. It is equivalent to the amount of
energy released during freezing.
Latent heat of vaporisation
The amount of energy absorbed during vaporisation and it is equivalent to the
energy released during condensation.
KEITH VAUGH

43. Latent heat
The amount of energy absorbed or released during a phase-change process.
Latent heat of fusion
The amount of energy absorbed during melting. It is equivalent to the amount of
energy released during freezing.
Latent heat of vaporisation
The amount of energy absorbed during vaporisation and it is equivalent to the
energy released during condensation.
The magnitudes of the latent heats depend on the temperature or pressure at which
the phase change occurs.
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44. Latent heat
The amount of energy absorbed or released during a phase-change process.
Latent heat of fusion
The amount of energy absorbed during melting. It is equivalent to the amount of
energy released during freezing.
Latent heat of vaporisation
The amount of energy absorbed during vaporisation and it is equivalent to the
energy released during condensation.
The magnitudes of the latent heats depend on the temperature or pressure at which
the phase change occurs.
At 1 atm pressure, the latent heat of fusion of water is 333.7 kJ/kg and the latent
heat of vaporisation is 2256.5 kJ/kg.
KEITH VAUGH

45. Latent heat
The amount of energy absorbed or released during a phase-change process.
Latent heat of fusion
The amount of energy absorbed during melting. It is equivalent to the amount of
energy released during freezing.
Latent heat of vaporisation
The amount of energy absorbed during vaporisation and it is equivalent to the
energy released during condensation.
The magnitudes of the latent heats depend on the temperature or pressure at which
the phase change occurs.
At 1 atm pressure, the latent heat of fusion of water is 333.7 kJ/kg and the latent
heat of vaporisation is 2256.5 kJ/kg.
The atmospheric pressure, and thus the boiling temperature of water, decreases
with elevation.
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46. Some Consequences of Tsat and
Psat Dependence
The variation of the temperature of
fruits and vegetables with pressure
during vacuum cooling from 25°C
to 0°C.
KEITH VAUGH

47. Some Consequences of Tsat and
Psat Dependence
The variation of the temperature of
fruits and vegetables with pressure
during vacuum cooling from 25°C
to 0°C.
KEITH VAUGH

48. Some Consequences of Tsat and
Psat Dependence
The variation of the temperature of In 1775, ice was made by
fruits and vegetables with pressure evacuating the air space
during vacuum cooling from 25°C in a water tank.
to 0°C.
KEITH VAUGH

49. PROPERTY DIAGRAMS FOR
PHASE-CHANGE PROCESSES
The variations of properties during phase-change
processes are best studied and understood with the help
of property diagrams such as the T-v, P-v, and P-T
diagrams for pure substances.
}
Recall
T-v diagram for the heating
process of water at constant
pressure.
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50. KEITH VAUGH

51. T-v diagram for a pure substance
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52. T-v diagram for a pure substance
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53. T-v diagram for a pure substance
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54. T-v diagram for a pure substance
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55. T-v diagram for a pure substance
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56. T-v diagram for a pure substance
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57. T-v diagram for a pure substance
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58. T-v diagram for a pure substance
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59. T-v diagram for a pure substance
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60. KEITH VAUGH

61. Critical point
The point at which the saturated
liquid and saturated vapour states
are identical.
At supercritical pressures (P > Pcr), there is
no distinct phase-change (boiling) process.
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62. KEITH VAUGH

63. T-v diagram of constant-pressure
phase-change processes of a pure
substance at various pressures
(numerical values are for water).
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64. KEITH VAUGH

65. P-v diagram of a pure substance
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66. The pressure in a P-v diagram of a pure substance
piston–cylinder device
can be reduced by
reducing the weight of
the piston.
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67. Extending the diagrams to
include the Solid Phase
}
P-v diagram of a substance that contracts on freezing
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68. KEITH VAUGH

69. P-v diagram of a substance that
expands on freezing (such as
water)
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70. P-v diagram of a substance that At triple-point pressure
expands on freezing (such as and temperature, a
water) substance exists in three
phases of equilibrium
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71. Sublimation: Passing from the solid
phase directly into the vapour phase.
P-T diagram of pure substance
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72. Sublimation: Passing from the solid
phase directly into the vapour phase.
P-T diagram of pure substance
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73. Sublimation: Passing from the solid
phase directly into the vapour phase.
P-T diagram of pure substance At low pressures (below the
triple-point value), solids
evaporate without melting
first (sublimation)
KEITH VAUGH

74. The P-v-T surfaces present a great deal of information at once, but in a
thermodynamic analysis it is more convenient to work with two-dimensional
diagrams, such as the P-v and T-v diagrams.
P-v-T surface of a substance that
contracts on freezing
KEITH VAUGH

75. The P-v-T surfaces present a great deal of information at once, but in a
thermodynamic analysis it is more convenient to work with two-dimensional
diagrams, such as the P-v and T-v diagrams.
P-v-T surface of a substance that
contracts on freezing
KEITH VAUGH

76. The P-v-T surfaces present a great deal of information at once, but in a
thermodynamic analysis it is more convenient to work with two-dimensional
diagrams, such as the P-v and T-v diagrams.
P-v-T surface of a substance that P-v-T surface of a substance that
contracts on freezing expands on freezing (like water)
KEITH VAUGH

77. PROPERTY TABLES
For most substances, the relationships among
thermodynamic properties are too complex to be
expressed by simple equations.
}
Properties are frequently presented in the form of
tables.
Some thermodynamic properties can be measured
easily, but others cannot and are calculated by using
the relations between them and measurable
properties.
The results of these measurements and calculations
are presented in tables in a convenient format.
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78. The combination u+Pv is
frequently encountered in the
analysis of control volumes
KEITH VAUGH

79. The combination u+Pv is
frequently encountered in the
analysis of control volumes
Enthalpy—A Combination Property
h = u + Pv ( kg)
kJ
H = U + PV ( kJ )
KEITH VAUGH

80. The combination u+Pv is
frequently encountered in the
analysis of control volumes
Enthalpy—A Combination Property
h = u + Pv ( kg)
kJ
H = U + PV ( kJ )
The product pressure × volume
has energy units
KEITH VAUGH

81. Saturated liquid and saturated vapour states
A partial list of Table A-4 page 994
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82. Saturated liquid and saturated vapour states
v f = specific volume of saturated liquid
vg = specific volume of saturated vapor
v fg = difference between v f and vg
(that is v fg = vg − v f )
A partial list of Table A-4 page 994
KEITH VAUGH

83. Saturated liquid and saturated vapour states
v f = specific volume of saturated liquid
vg = specific volume of saturated vapor
v fg = difference between v f and vg
(that is v fg = vg − v f )
Enthalpy of vaporisation, hfg (Latent
heat of vaporisation)
The amount of energy needed to
vaporise a unit mass of saturated liquid
at a given temperature or pressure.
A partial list of Table A-4 page 994
Table A–4: Saturation properties of water under temperature, page 994
Table A–5: Saturation properties of water under pressure, page 996
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84. P-v diagram of saturated liquid and
saturated vapour states of water
KEITH VAUGH

85. P-v diagram of saturated liquid and
saturated vapour states of water
KEITH VAUGH

86. P-v diagram of saturated liquid and T-v diagram of saturated liquid and
saturated vapour states of water saturated vapour states of water
KEITH VAUGH

87. Saturated liquid - vapour mixture
The relative amounts of liquid and
vapour phases in a saturated mixture
are specified by the quality x.
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88. Saturated liquid - vapour mixture
mvapor The ratio of the mass of
Quality, x = vapour to the total mass
mtotal of the mixture
The relative amounts of liquid and
vapour phases in a saturated mixture
are specified by the quality x.
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89. Saturated liquid - vapour mixture
mvapor The ratio of the mass of
Quality, x = vapour to the total mass
mtotal of the mixture
mtotal = mliquid + mvapor = m f + mg
The relative amounts of liquid and
vapour phases in a saturated mixture
are specified by the quality x.
KEITH VAUGH

90. Saturated liquid - vapour mixture
mvapor The ratio of the mass of
Quality, x = vapour to the total mass
mtotal of the mixture
mtotal = mliquid + mvapor = m f + mg
Temperature and pressure are depended
properties for a mixture
The relative amounts of liquid and
vapour phases in a saturated mixture
are specified by the quality x.
KEITH VAUGH

91. Saturated liquid - vapour mixture
mvapor The ratio of the mass of
Quality, x = vapour to the total mass
mtotal of the mixture
mtotal = mliquid + mvapor = m f + mg
Temperature and pressure are depended
properties for a mixture
The relative amounts of liquid and A two-phase system can be
vapour phases in a saturated mixture treated as a homogenous
are specified by the quality x. mixture for convenience
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92. KEITH VAUGH

93. Quality is related to the horizontal
distances on P-v and T-v diagrams
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94. vavg = v f + xv fg ( kg)
m3
Quality is related to the horizontal
distances on P-v and T-v diagrams
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95. vavg = v f + xv fg ( kg)
m3
mg
x=
mt
Quality is related to the horizontal
distances on P-v and T-v diagrams
KEITH VAUGH

96. vavg = v f + xv fg ( kg)
m3
mg vavg − v f
x= x=
mt v fg
Quality is related to the horizontal
distances on P-v and T-v diagrams
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97. vavg = v f + xv fg ( kg)
m3
mg vavg − v f
x= x=
mt v fg
uavg = u f + xu fg ( kg)
kJ
havg = h f + xh fg ( kg)
kJ
Quality is related to the horizontal
distances on P-v and T-v diagrams
KEITH VAUGH

98. vavg = v f + xv fg ( kg)
m3
mg vavg − v f
x= x=
mt v fg
uavg = u f + xu fg ( kg)
kJ
havg = h f + xh fg ( kg)
kJ
y → v,u, or h
yavg = y f + xy fg
Quality is related to the horizontal y f ≤ yavg ≤ yg
distances on P-v and T-v diagrams
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99. vavg = v f + xv fg ( kg)
m3
mg vavg − v f
x= x=
mt v fg
uavg = u f + xu fg ( kg)
kJ
havg = h f + xh fg ( kg)
kJ
y → v,u, or h
yavg = y f + xy fg
The v value of a saturated liquid–vapour y f ≤ yavg ≤ yg
mixture lies between the vf and vg values
at the specified T or P.
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100. Superheated Vapour
In the region to the right of the saturated
vapor line and at temperatures above the
critical point temperature, a substance
exists as superheated vapour.
In this region, temperature and pressure
are independent properties.
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101. Superheated Vapour
In the region to the right of the saturated
}
vapor line and at temperatures above the
critical point temperature, a substance
exists as superheated vapour.
In this region, temperature and pressure
are independent properties.
A partial listing of Table A-6
page 998
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102. Superheated Vapour
In the region to the right of the saturated
}
vapor line and at temperatures above the
critical point temperature, a substance
exists as superheated vapour.
In this region, temperature and pressure
are independent properties.
Compared to saturated vapour, superheated A partial listing of Table A-6
vapour is characterised by page 998
Lower pressures ( P < Psat at a given T )
Higher temperatures (T < Tsat at a given P )
(
Higher specific volumes v < vg at a given P or T )
Higher specific energies ( u < u at a given P or T )
g
Higher enthalpies ( h < h at a given P or T )
g
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103. Compressed Liquid
Compressed liquid is characterised by
Higher pressures ( P > Psat at a given T )
Lower temperatures (T < Tsat at a given P )
(
Lower specific volumes v < vg at a given P or T )
Lower specific energies ( u < u at a given P or T )
g
Lower enthalpies ( h < h at a given P or T )
g
KEITH VAUGH

104. Compressed Liquid
Compressed liquid is characterised by
Higher pressures ( P > Psat at a given T )
Lower temperatures (T < Tsat at a given P )
(
Lower specific volumes v < vg at a given P or T )
Lower specific energies ( u < u at a given P or T )
g
Lower enthalpies ( h < h at a given P or T )
g
The compressed liquid properties depend on
temperatures more so that they do on pressure
Given: P and T
v ≅ v f @T
A compressed liquid may be u ≅ u f @T
approximated as a saturated
liquid at a given temperature h ≅ h f @T
KEITH VAUGH

105. Compressed Liquid
Compressed liquid is characterised by
Higher pressures ( P > Psat at a given T )
Lower temperatures (T < Tsat at a given P )
(
Lower specific volumes v < vg at a given P or T )
Lower specific energies ( u < u at a given P or T )
g
Lower enthalpies ( h < h at a given P or T )
g
The compressed liquid properties depend on
temperatures more so that they do on pressure
Given: P and T A more accurate relation for h
v ≅ v f @T h ≅ h f @T + v f @T ( P − Psat @T )
A compressed liquid may be u ≅ u f @T
approximated as a saturated
liquid at a given temperature h ≅ h f @T
KEITH VAUGH

106. REFERENCE STATE AND
REFERENCE VALUES
}
KEITH VAUGH

107. REFERENCE STATE AND
REFERENCE VALUES
The values of u, h, and s cannot be measured
directly, and they are calculated from measurable
properties using the relations between properties.
}
KEITH VAUGH

108. REFERENCE STATE AND
REFERENCE VALUES
The values of u, h, and s cannot be measured
directly, and they are calculated from measurable
properties using the relations between properties.
}
KEITH VAUGH

109. REFERENCE STATE AND
REFERENCE VALUES
The values of u, h, and s cannot be measured
directly, and they are calculated from measurable
properties using the relations between properties.
}
However, those relations give the changes in
properties, not the values of properties at specified
states.
KEITH VAUGH

110. REFERENCE STATE AND
REFERENCE VALUES
The values of u, h, and s cannot be measured
directly, and they are calculated from measurable
properties using the relations between properties.
}
However, those relations give the changes in
properties, not the values of properties at specified
states.
KEITH VAUGH

111. REFERENCE STATE AND
REFERENCE VALUES
The values of u, h, and s cannot be measured
directly, and they are calculated from measurable
properties using the relations between properties.
}
However, those relations give the changes in
properties, not the values of properties at specified
states.
Therefore, we need to choose a convenient
reference state and assign a value of zero for a
convenient property or properties at that state.
KEITH VAUGH

112. REFERENCE STATE AND
REFERENCE VALUES
The values of u, h, and s cannot be measured
directly, and they are calculated from measurable
properties using the relations between properties.
}
However, those relations give the changes in
properties, not the values of properties at specified
states.
Therefore, we need to choose a convenient
reference state and assign a value of zero for a
convenient property or properties at that state.
KEITH VAUGH

113. REFERENCE STATE AND
REFERENCE VALUES
The values of u, h, and s cannot be measured
directly, and they are calculated from measurable
properties using the relations between properties.
}
However, those relations give the changes in
properties, not the values of properties at specified
states.
Therefore, we need to choose a convenient
reference state and assign a value of zero for a
convenient property or properties at that state.
The reference state for water is 0.01°C and for
R-134a is -40°C in tables.
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114. {
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115. {
KEITH VAUGH

116. { Some properties may have negative values as a
result of the reference state chosen.
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117. { Some properties may have negative values as a
result of the reference state chosen.
KEITH VAUGH

118. { Some properties may have negative values as a
result of the reference state chosen.
Sometimes different tables list different values
for some properties at the same state as a result of
using a different reference state.
KEITH VAUGH

119. { Some properties may have negative values as a
result of the reference state chosen.
Sometimes different tables list different values
for some properties at the same state as a result of
using a different reference state.
KEITH VAUGH

120. { Some properties may have negative values as a
result of the reference state chosen.
Sometimes different tables list different values
for some properties at the same state as a result of
using a different reference state.
However, In thermodynamics we are concerned
with the changes in properties, and the reference
state chosen is of no consequence in calculations.
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121. Refer to pages, 1003 and 1006
KEITH VAUGH

122. IDEAL GAS EQUATION
OF STATE
Equation of state
Any equation that relates the pressure, temperature, and
specific volume of a substance.
}
The simplest and best-known equation of state for substances
in the gas phase is the ideal-gas equation of state. This
equation predicts the P-v-T behaviour of a gas quite
accurately within some properly selected region.
KEITH VAUGH

123. IDEAL GAS EQUATION
OF STATE
Equation of state
Any equation that relates the pressure, temperature, and
specific volume of a substance.
}
The simplest and best-known equation of state for substances
in the gas phase is the ideal-gas equation of state. This
equation predicts the P-v-T behaviour of a gas quite
accurately within some properly selected region.
⎛ T ⎞ Ideal Gas
P = R ⎜ ⎟ → Pv = RT
⎝ v ⎠ equ. of state
KEITH VAUGH

124. IDEAL GAS EQUATION
OF STATE
Equation of state
Any equation that relates the pressure, temperature, and
specific volume of a substance.
}
The simplest and best-known equation of state for substances
in the gas phase is the ideal-gas equation of state. This
equation predicts the P-v-T behaviour of a gas quite
accurately within some properly selected region.
⎛ T ⎞ Ideal Gas
P = R ⎜ ⎟ → Pv = RT
⎝ v ⎠ equ. of state
R: gas constant
Ru
R=
M ( kJ
kg
3
⋅ K or kPa ⋅ m kg ⋅ K ) M: molar mass (kg/kmol)
Ru: universal gas constant
KEITH VAUGH

125. Mass = Molar mass × Mole number
m = MN ( kg )
KEITH VAUGH

126. Mass = Molar mass × Mole number
m = MN ( kg )
V = mv → PV = mRT Various
expressions of
mR = ( MN ) R = NRu → PV = NRuT
ideal gas
V = Nv → Pv = RuT equation
Properties per unit
mole are denoted with
a bar on the top.
KEITH VAUGH

127. Mass = Molar mass × Mole number
m = MN ( kg )
V = mv → PV = mRT Various
expressions of
mR = ( MN ) R = NRu → PV = NRuT
ideal gas
V = Nv → Pv = RuT equation
Properties per unit
mole are denoted with
Ideal gas equation at two states for a fixed mass a bar on the top.
P1V1 P2V2
=
T1 T2
KEITH VAUGH

128. Mass = Molar mass × Mole number
m = MN ( kg )
V = mv → PV = mRT Various
expressions of
mR = ( MN ) R = NRu → PV = NRuT
ideal gas
V = Nv → Pv = RuT equation
Properties per unit
mole are denoted with
Ideal gas equation at two states for a fixed mass a bar on the top.
P1V1 P2V2
=
T1 T2
Real gases behave as an ideal gas at low densities
(i.e., low pressure, high temperature).
KEITH VAUGH

129. Is water vapour an Ideal Gas?
KEITH VAUGH

130. Is water vapour an Ideal Gas?
At pressures below 10 kPa, water vapour
can be treated as an ideal gas, regardless
of its temperature, with negligible error
(less than 0.1 percent).
KEITH VAUGH

131. Is water vapour an Ideal Gas?
At pressures below 10 kPa, water vapour
can be treated as an ideal gas, regardless
of its temperature, with negligible error
(less than 0.1 percent).
At higher pressures, however, the ideal
gas assumption yields unacceptable
errors, particularly in the vicinity of the
critical point and the saturated vapour
line.
KEITH VAUGH

132. Is water vapour an Ideal Gas?
At pressures below 10 kPa, water vapour
can be treated as an ideal gas, regardless
of its temperature, with negligible error
(less than 0.1 percent).
At higher pressures, however, the ideal
gas assumption yields unacceptable
errors, particularly in the vicinity of the
critical point and the saturated vapour
line.
KEITH VAUGH

133. Is water vapour an Ideal Gas?
At pressures below 10 kPa, water vapour
can be treated as an ideal gas, regardless
of its temperature, with negligible error
(less than 0.1 percent).
At higher pressures, however, the ideal
gas assumption yields unacceptable
errors, particularly in the vicinity of the
critical point and the saturated vapour
line.
In air-conditioning applications, the
water vapour in the air can be treated as
an ideal gas. Why?
In steam power plant applications,
however, the pressures involved are
usually very high; therefore, ideal-gas
relations should not be used.
KEITH VAUGH

134. Pure substance
Phases of a pure substance
Phase change processes of pure substances
 Compressed liquid, Saturated liquid, Saturated vapour, Superheated vapour
 Saturated temperature and Saturated pressure
Property diagrams for phase change processes
 The T-v diagram, The P-v diagram, The P-T diagram, The P-v-T diagram
Property tables
 Enthalpy
 Saturated liquid, Saturated vapour, Saturated liquid vapour mixture, Superheated
vapour, compressed liquid
 Reference state and Reference values
The ideal gas equation of state
 Is water vapour an ideal gas?
KEITH VAUGH