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Chapter 3 Thermodynamics 1 1
Thermodynamics I
Introduction 1. Basic Concepts of Thermodynamics 2. Energy,
Energy Transfer, and General Energy Analysis 3. Properties of Pure
Substances 4. Energy Analysis of Closed Systems 5. Energy and Mass
Analysis of Control Volumes 6. The Second Law of Thermodynamics 7.
Entropy 8. Steam Power Cycle Applications Examples
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Chapter 3 EG-161: Thermodynamics 1 2
Overview Properties of Pure Substances
3-1 Pure Substance 3-2 Phases of a Pure Substance 3-3
Phase-Change Processes of Pure Substances 3-4 Property Diagrams for
Phase-Change Processes 3-5 Property Tables 3-6 The Ideal-Gas
Equation of State 3-7 Compressibility Factor
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Chapter 3 EG-161: Thermodynamics 1 3
Pure Substance A pure substance has a
fixed chemical composition throughout various processes.
Examples are: water, nitrogen, helium and carbon dioxide.
Homogeneous mixtures also qualify as pure substances (e.g.
air).
A mixture of two or more phases can still be a pure
substance.
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Chapter 3 EG-161: Thermodynamics 1 4
Phases of a Pure Substance 3 principal phases: solid, liquid
and
gas-phase. Substances may have several phases
with the principal phase (e.g. ice has 7, iron has 3, carbon has
2).
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Chapter 3 EG-161: Thermodynamics 1 5
Phase-Change Processes
Subcooled/compressed liquid
Saturated Liquid Saturated Liquid-Vapour Mixture
Saturated Vapour
Superheated Vapour
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Chapter 3 EG-161: Thermodynamics 1 6
Property Diagrams for Phase-Change Processes: T-v
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Chapter 3 EG-161: Thermodynamics 1 7
Property Diagrams for Phase-Change Processes: P-v
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Chapter 3 EG-161: Thermodynamics 1 8
Rankine Cycle - Phase Change
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Chapter 3 EG-161: Thermodynamics 1 9
Saturation Temperature and Saturation Pressure
The temperature at which water starts boiling depends on the
pressure.
If the pressure is fixed, so is the boiling temperature. During
the phase change the two phases are in equilibrium. For a pure
substance and a given pressure the phase-change
temperature is called saturation temperature Tsat. For a pure
substance and a given temperature the phase-change
pressure is called saturation pressure Psat.
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Chapter 3 EG-161: Thermodynamics 1 10
Some Consequences of Tsat and Psat Dependence
The temperature of liquid nitrogen exposed to the atmosphere
remains constant at 196C, and thus it maintains the test chamber at
196C.
In 1775, ice was made by evacuating
the air space in a water tank.
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Chapter 3 EG-161: Thermodynamics 1 11
P-v Diagram for Substance that Contracts/Expands on Freezing
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Chapter 3 EG-161: Thermodynamics 1 12
P-T or Phase Diagram
Substance Ttp (K) Ptp (kPa) Water 273.16 0.61
Nitrogen 63.18 12.6
Latent heat of sublimation/ deposition
Latent heat of vaporization/ condensation
Latent heat of fusion
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Chapter 3 EG-161: Thermodynamics 1 13
Enthalpy
Enthalpy is a combination property. In the analysis of cycles
we
frequently encounter the expression:
U+PV For simplicity reason this quantity
is termed enthalpy: H=U+PV (kJ) h=u+Pv (kJ/kg)
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Chapter 3 EG-161: Thermodynamics 1 14
Saturated Liquid and Vapour States
vf: specific volume of saturated liquid
vf vg vg: specific volume of saturated vapour
fg g f
fg g f
fg g f
fg g f
v v vu u uh h hs s s
=
=
=
=
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Chapter 3 EG-161: Thermodynamics 1 15
A rigid tank contains 50 kg of saturated liquid water at 90C.
Determine the pressure in the tank and the volume of the tank.
Saturated Liquid and Vapour States Example
Answer: P=70.18kPa V=0.0518m3
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Chapter 3 EG-161: Thermodynamics 1 16
A mass of 200g of saturated liquid water is completely vaporized
at a constant pressure of 100kPa. Determine a) the volume change
and b) the amount of energy added to the water.
Saturated Liquid and Vapour States Example
Answer: DV=0.3386m3 DE=451.6kJ
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Chapter 3 EG-161: Thermodynamics 1 17
To analyse a liquid-vapour mixture in the wet-region we need to
know the proportions of the liquid and the vapour phases.
The new property is called quality x:
where
Saturated Liquid-Vapour Mixtures Quality x
1
vapour
total
liquid
total
mx
mm
xm
=
=
: mass fraction of vapour
: mass fraction of liquid (or simply moisture)
total liquid vapour f gm m m m m= + = +
(
using 1
or1 )
f g
f g gf f g
f g f fg
g
V V Vm m m m
mv m v m v x xm m m
v x v xv v v xv
= +
= + = =
= + =
=
+
and
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Chapter 3 EG-161: Thermodynamics 1 18
Saturated Liquid-Vapour Mixtures Quality x
f
fg
f fg
f fg
f fg
f fg
v vx
vv v xv
u u xuh h xhs s xs
=
= +
= +
= +
= +
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Chapter 3 EG-161: Thermodynamics 1 19
Saturated Liquid-Vapour Mixtures Example
Answer: P=70.18kPa V=4.73m3
A rigid tank contains 10 kg of saturated liquid water at 90C. If
8 kg of the water is in the liquid phase and the rest is in the
vapour phase, determine a) the pressure in the tank, and b) the
volume of the tank.
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Chapter 3 EG-161: Thermodynamics 1 20
Saturated Liquid-Vapour Mixtures Example
Answer: T=Tsat@kPa=-15.60C x=0.158 h=62.7kJ/kg mg=0.632kg and
Vg=0.0777m3
An 80 L vessel contains 4 kg of refrigerant 134-a at a pressure
of 160kPa. Determine a) the temperature of refrigerant, b) the
quality, c) the enthalpy of the refrigerant, and d) the volume
occupied by the vapour phase.
1
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Chapter 3 EG-161: Thermodynamics 1 21
Compressed Liquid A compressed liquid is to be approximated as
saturated liquid at
the given temperature. The properties depend more on the
temperature than they do
on the pressure.
Example: Determine the internal energy of compressed liquid
water at 80C and 5 MPa: From compressed liquid table:
u=333.72kJ/kg From saturation table:
u334.86kJ/kg Error: 0.34%
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Chapter 3 EG-161: Thermodynamics 1 22
Superheated Vapour Pressure and
Temperature are no longer dependent variables.
Super-heated vapour is a single-phase substance.
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Chapter 3 EG-161: Thermodynamics 1 23
Determine the temperature of water at a state of P=0.5MPa
and h=2890kJ/kg.
Answer:
At 0.5MPa saturated vapour: hg=2748.7kJ/kg. Therefore we have
super- heated vapour. Linear interpolation from tables gives:
T=216.4C
Superheated Vapour Example
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Chapter 3 EG-161: Thermodynamics 1 24
THE 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 behavior of a gas quite accurately within some
properly selected region.
R: gas constant M: molar mass (kg/kmol) Ru: universal gas
constant
Ideal gas equation of state P: absolute pressure T: absolute
temperature in Kelvin
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Chapter 3 EG-161: Thermodynamics 1 25
THE IDEAL-GAS EQUATION OF STATE
Different substances have different gas constants.
Various expressions of ideal gas equation
Ideal gas equation at two states for a fixed mass
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Chapter 3 EG-161: Thermodynamics 1 26
Compressibility Factor The compressibility factor Z is a
correction factor and is a
measure of the deviation from ideal-gas behaviour. Z is defined
as:
ideal
actual
vvZ
ZRTPvRTPvZ
=
=
=
or
Thermodynamics IOverview Properties of Pure SubstancesPure
SubstancePhases of a Pure SubstancePhase-Change ProcessesProperty
Diagrams for Phase-Change Processes: T-vProperty Diagrams for
Phase-Change Processes: P-vRankine Cycle - Phase Change Saturation
Temperature and Saturation PressureSome Consequences of Tsat and
Psat DependenceP-v Diagram for Substance that Contracts/Expands on
FreezingP-T or Phase DiagramEnthalpySaturated Liquid and Vapour
StatesSaturated Liquid and Vapour StatesExampleSaturated Liquid and
Vapour StatesExampleSaturated Liquid-Vapour MixturesQuality
xSaturated Liquid-Vapour MixturesQuality xSaturated Liquid-Vapour
MixturesExampleSaturated Liquid-Vapour MixturesExampleCompressed
LiquidSuperheated VapourSuperheated VapourExampleTHE IDEAL-GAS
EQUATION OF STATETHE IDEAL-GAS EQUATION OF STATECompressibility
Factor