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Properties of Pure Substances
Ability to acquire and explain the basic
concepts in thermodynamics
Course Learning OutcomesThe student should be able to:
• Define saturated liquid, saturated vapor, saturated liquid-vapor mixture,
compressed liquid, superheated vapor, critical points, and triple point.
• Sketch a P-v, T-v, and P-T diagrams and identify the phase regions of pure
substances on the diagrams.substances on the diagrams.
• Obtain thermodynamic properties of pure substances from property tables.
• Show the state of pure substance on a P-v and T-v diagram with respect to
saturation lines.
• Show the isobaric, isochoric and isothermal processes on a P-v and T-v
diagram with respect to saturation lines.
• Solve problems related to properties and processes of pure substance
2.1 Pure substance
2.2 Equilibrium phases of pure substance
2.3 Phase change processes of pure substance2.3 Phase change processes of pure substance
2.4 Property diagrams for phase change processes
2.5 Property tables
2.6 The ideal gas equation of state
2.1 Pure Substance� Pure substance - A substance that has a fixed chemical
composition throughout
� Examples of pure substances:
1. Water (solid, liquid, and vapor phases)
2. Mixture of liquid water and water vapor
3. CO2
4. N2
5. Mixtures of gases, such as air, as long as there is no
change of phase
6. He
� Air is a mixture of several gases, but it is considered to be a
pure substance.
Nitrogen and gaseous air are pure substances.
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A mixture of liquid and gaseous water is a pure substance, but a
mixture of liquid and gaseous air is not.
2.2 Equilibrium phases of pure substance
Phase is identified as having a distinct molecular arrangement that is
homogeneous throughout and separated from the others by easily
identifiable boundary surfaces.
The arrangement of atoms in different phases:
(a) solid phase - molecules are at relatively fixed positions
(b) liquid phase - groups of molecules move about each other in the
molecules
(c) gas phase - move about at random
Equilibrium phases of pure substance
Phase equilibrium: Phase equilibrium: Phase equilibrium: Phase equilibrium: If a system involves two phases and when the mass of each phase reaches an equilibrium level and stays there.
State PostulateState PostulateState PostulateState Postulate
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State PostulateState PostulateState PostulateState PostulateThe state postulate for a simple, pure substance states that the equilibrium state can be determined by specifying any two independent intensive properties.
2.3 Phase-change processes of pure
substance
Saturated vapor
Saturated liquid
- Water exists in
the liquid phase
- compressed
liquid or
subcooled liquid:
A substance that
it is not about to
vaporize.
- Water exists as a
liquid that is ready
to vaporize
- saturated liquid:
A liquid that is
about to vaporize..
- As more heat is
transferred, part of
the saturated liquid
vaporizes
-saturated liquid-
vapor mixture
- At 1 atm
pressure, the
temperature
remains constant
at 100°C until the
last drop of liquid
is vaporized
- saturated vapor
- As more heat is
transferred, the
temperature of
the vapor starts
to rise
- superheated
vapor
If the entire process between state 1 and 5 described in the figure is reversed by cooling the water (maintain 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 amount of heat released amount of heat released amount of heat released (during the cooling process) will exactly match the amount of (during the cooling process) will exactly match the amount of (during the cooling process) will exactly match the amount of (during the cooling process) will exactly match the amount of heat addedheat addedheat addedheat added during the heating process.
T-v diagram for the heating process of water at constant pressure
• Saturation temperature Saturation temperature Saturation temperature Saturation temperature TTTTsatsatsatsat: The temperature at which a pure substance changes phase at a given pressure.
• Saturation pressure Saturation pressure Saturation pressure Saturation pressure PPPPsatsatsatsat: The pressure at which a pure substance changes phase at a given temperature.
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Example: For water (pure substance)
At a pressure of 101.325 kPa, Tsat is 99.97°C.
At a temperature of 99.97°C, Psat is 101.325 kPa.
• 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.
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The liquid-vapor saturation curve of a pure substance
(water). Cengel 6th Ed pg 116
Example 2.1Example 2.1Example 2.1Example 2.1
Determine the saturation pressure, Psat for water at temperature of
i) 25°Cii) 225°C.
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Determine the saturation temperature, Tsat for water at pressure of
i) 1.23 kPaii) 500 kPa.
� Latent heatLatent heatLatent heatLatent heat: The amount of energy absorbed or released during a phase-change process.
� Latent heat of fusionLatent heat of fusionLatent heat of fusionLatent heat of fusion: The amount of energy absorbed during melting (equivalent to the amount of energy released during freezing). released during freezing).
� Latent heat of vaporization: Latent heat of vaporization: Latent heat of vaporization: Latent heat of vaporization: The amount of energy absorbed during vaporization (equivalent to the energy released during condensation)
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� 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 vaporization is 2256.5 kJ/kg.
� Atmospheric pressure and boiling temperature of water decrease with water decrease with increases of elevation.
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The variations of properties during phase-change processes are best studied using property diagrams for
pure substances.
T-v Diagram
P-vDiagram
P-TDiagram
The T-v Diagram
17T-v diagram of constant-pressure phase-change processes of water (pure
substance) at various pressures. Cengel 6th Ed pg 119.
At supercritical pressures (P >Pcr), there is no a distinct phase-change process.
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Critical pointCritical pointCritical pointCritical point: The point at which the saturated liquidsaturated liquidsaturated liquidsaturated liquid and saturated vaporsaturated vaporsaturated vaporsaturated vaporstates are identical
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The P-v Diagram
20P-v diagram of a pure substance.
The pressure in a piston-cylinder
device can be reduced by
reducing the weight of the
piston.
At triple-point pressure and
temperature, a substance exists in
three phases in equilibrium.
For water, Ttp = 0.01°C Ptp = 0.6117
kPa
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P-v diagram of a substance that contracts on freezing.
P-v diagram of a substance that expands on freezing (such as
water).
Phase Diagram
The P-T Diagram
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P < Ptp: Sublimation (Evaporation directly without melting first)
P > Ptp: Melting -> Evaporation
P > Ptp
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Sublimation
P < Ptp
2.5 Property Tables
• For most substances, the relationships among thermodynamic properties
are too complex to be expressed by simple equations.
• Therefore, 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. measurable properties.
• The results of these measurements and calculations are presented in
tables in a convenient format.
Table A–4: Saturation properties of water under temperature. Pg 916-917
Table A–5: Saturation properties of water under pressure. Pg 918-919
Table A–6: Superheated properties of water. Pg 920-923
Table A–7: Compressed liquid water. Pg 924
Enthalpy - A Combination Property
The product pressure × volume has
energy units.or
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The combination u + Pv is frequently encountered in
the analysis of control volumes.
Saturated Liquid and Saturated Vapor States
Table A–4: Saturation properties of water under temperature. Pg 916
Table A–5: Saturation properties of water under pressure. Pg 918
A partial list of Table A–4.
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Enthalpy of vaporization, hfg (Latent heat of
vaporization): The amount of energy needed
to vaporize a unit mass of saturated liquid at a
given temperature or pressure.
The subscript fgfgfgfg used in Tables A–4 and A–5 refers to the difference between the saturated vapor value and the saturated liquid value region. That is,
u u ufg g f= −
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h h h
s s s
fg g f
fg g f
= −
= −
A rigid tank contains 50 kg of saturated liquid water at 90°C. Determine the pressure in the tank and the volume of the tank.
Example Example Example Example 3.23.23.23.2
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A piston-cylinder device contains 0.06 m3 of saturated water vapor at 350 kPa pressure. Determine the temperature and the mass of the vapor inside the cylinder.
Example Example Example Example 3.23.23.23.2
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A mass of 200 g of saturated liquid water is completely vaporized at a constant pressure of 100 kPa. Determinea) The volume changeb) The amount of energy transferred to the water
Example Example Example Example 3.33.33.33.3
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• During vaporization process, a substance exists as part liquid and part vapor � mixture of saturated liquid and saturated vapor
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The relative amounts of liquid and vapor phases in a saturated mixture are specified by the quality xquality xquality xquality x.
vapor g gmass m mx
mass m m m= = =
+
• Quality, Quality, Quality, Quality, x : The ratio of the mass of vapor to the total mass of the mixture.
• Quality is between 0 and 1 Quality is between 0 and 1 Quality is between 0 and 1 Quality is between 0 and 1 ���� 0: sat. liquid, 1: sat. vapor.0: sat. liquid, 1: sat. vapor.0: sat. liquid, 1: sat. vapor.0: sat. liquid, 1: sat. vapor.
total t f g
xmass m m m
= = =+
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We note
, ,
f g
f g
t avg f f f g g g
V V V
m m m
V m v V m v V m v
= +
= +
= = =
Substituting mf = mt – mg, dividing (1) by mt
and substituting mg/mt = x yields A two-phase system can be treated as a
t
(1)f f g gmv m v m v= +mtvavg
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(1 )avg f gv x v xv= − +
and substituting mg/mt = x yields
avg f fgv v xv= +
avg f
fg
v vx
v
−=
A two-phase system can be treated as a
homogeneous mixture for convenience.
where vfg = vg - vf
Then
y v, u, or h.• The previous relationships can be summarized in a
single equation as:
• This application is called the Lever Rule
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The v value of a saturated liquid–vapor
mixture lies between the vf and vg values at
the specified T or P.
avg f
fg
v vx
v
−=
Example 3.4
A rigid tank contains 10 kg of water at 90°C. If 8 kg of the water is in the liquid
form and the rest is in the vapor form, determine:
a) The pressure in the tank
b) The volume of the tank
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Example Example Example Example 3.53.53.53.5
An 80-L vessel contains 4 kg of refrigerant-134a at a pressure of 160 kPa. Determine:
a) The temperatureb) The qualityc) The enthalpy of the refrigerantd) The occupied by the vapor phase
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Table ATable ATable ATable A––––6666: Superheated properties of water. Pg 920
• In the region to the right of the saturated vapor line and at temperatures above the critical point temperature, a substance exists as superheated vapor.
• In this region, temperature and pressure are independent properties.
ExerciseExerciseExerciseExerciseExerciseExerciseExerciseExercise
Identify:a) Saturated vapor lineb) Critical pointc) Superheated vapor region!
What is the phase of this region?
P or T
v
Compared to saturated vapor, superheated vapor is characterized by
A partial listing of Table A–6.
At a specified P, superheated vapor exists
at a higher h than the saturated vapor.
Example Example Example Example 3.63.63.63.6
Determine the internal energy of water at 200 kPa and 300°C.
Example Example Example Example 3.73.73.73.7Example Example Example Example 3.73.73.73.7
Determine the temperature of water at a state of P=0.5 MPa and h=2890 kJ/kg.
Table ATable ATable ATable A––––7777: Compressed liquid water. Pg 924
Compressed liquid is characterized by
At a given P and T, a pure substance will exist as a compressed liquid if
y y y y →→→→ v, u, or h
•A more accurate relation for h
• A compressed liquid may be approximated as a saturated liquid may be approximated as a saturated liquid may be approximated as a saturated liquid may be approximated as a saturated liquid
• The compressed liquid properties depend on temperature much more strongly than they do on pressure.
• A compressed liquid may be approximated as a saturated liquid may be approximated as a saturated liquid may be approximated as a saturated liquid may be approximated as a saturated liquid at the given temperature.at the given temperature.at the given temperature.at the given temperature.
Example 3.8Example 3.8Example 3.8Example 3.8
Determine the internal energy of compressed liquid water at 80°C and 5 Mpa using
a) Data from the compressed liquid tableb) Data from saturated-liquid data
What is the error involved in the second case?
2.6 The ideal gas equation of state
• Equation of state: Any equation that relates the pressure, temperature, and
specific volume of a substance.
Ideal gas equation of
state
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R: gas constant
M: molar mass (kg/kmol)
Ru: universal gas constant
Different substances have different gas
constants.
Mass = Molar mass × Mole number
Various expressions of ideal gas equation
Ideal gas equation at two states for a fixed mass
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Properties per unit mole are denoted with a bar on the top.
Determine the mass of the air in a room whose
dimensions are 4 m x 5 m x 6 m at 100 kPa and
25°C.