低溫熱流學 part i: thermodynamics 授課教師:施陽正 博士 97 年 9 月
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低溫熱流學Part I: Thermodynamics
授課教師:施陽正 博士97年 9月
1CHAPTERCHAPTER
Introduction and
Overview
I. Introduction and Overview
1. Introduction to Thermal-Fluid Sciences
2. Thermodynamics
3. Heat Transfer
4. Fluid Mechanics
5. A Note on Dimensions and Units
6. Closed and Open System
7. Properties of a System
8. Solving Engineering Problems
9. Problem Solving Technique
10. Conservation of Mass Principle
1. Introduction to Thermal-Fluid Sciences
The physical sciences that deal with energy and the transfer, transport, and conversion of energy are usually referred to as thermal-fluid sciences or thermal sciences.
Thermal-fluid sciences:
Thermodynamics
Fluid mechanics
Heat transfer
1. Introduction to Thermal-Fluid Sciences
Application Areas of Thermal-Fluid Sciences
1. Introduction to Thermal-Fluid Sciences
1. Introduction to Thermal-Fluid Sciences
2. Thermodynamics
Thermodynamics can be defined as the science of energy.
First law of thermodynamics
Second law of thermodynamics
2. Thermodynamics
2. Thermodynamics
2. Thermodynamics
3. Heat Transfer
Energy exists in various forms. Heat is the form of energy that can be transferred from on system to another as a result of temperature difference.
The science that deals with the determination of the rates of such energy transfer is heat transfer.
Heat is transferred by three mechanisms:
Conduction
Convection
Radiation
3. Heat Transfer
3. Heat Transfer
3. Heat Transfer
3. Heat Transfer
4. Fluid Mechanics
Fluid mechanics is defined as the science that deals with the behavior of fluids at rest (fluid statics) or in motion (fluid dynamics).
4. Fluid Mechanics
4. Fluid Mechanics
4. Fluid Mechanics
4. Fluid Mechanics
5. A Note on Dimensions and Units
5. A Note on Dimensions and Units
5. A Note on Dimensions and Units
5. A Note on Dimensions and Units
or
onAcceleratiMassForce ))((maF )11(
5. A Note on Dimensions and Units
5. A Note on Dimensions and Units
5. A Note on Dimensions and Units
)21( mgW )(N
5. A Note on Dimensions and Units
5. A Note on Dimensions and Units
5. A Note on Dimensions and Units
Dimensional Homogeneity
5. A Note on Dimensions and Units
5. A Note on Dimensions and Units
6. Closed and Open System
6. Closed and Open System
6. Closed and Open System
6. Closed and Open System
6. Closed and Open System
6. Closed and Open System
7. Properties of a System
)31( )/( 3mkgV
m
)41( OH
s
2
7. Properties of a System
7. Properties of a System
)51(
1
m
V)/( 3 kgm
7. Properties of a System
8. Solving Engineering Problems
9. Problem Solving Technique
Step1: Problem Statement
Step2: Schematic
Step3: Assumptions
Step4: Physical Laws
Step5: Properties
Step6: Calculations
Step7: Reasoning,Verification,and Discussion
9. Problem Solving Technique
9. Problem Solving Technique
9. Problem Solving Technique
A Remark on Significant Digits
10. Conservation of Mass Principle
10. Conservation of Mass Principle
10. Conservation of Mass Principle
Mass and Volume Flow Rates
)71( dAmd n
)81(
AndAm )/( skg
10. Conservation of Mass Principle
10. Conservation of Mass Principle
Am m
)/( skg )91(
)101( AdAV mA
n
)111(
V
Vm
10. Conservation of Mass Principle
Conservation of Mass Principle
system ewithin th
massin changNet
system theleaving
mass Total
system theEntering
mass Total
10. Conservation of Mass Principle
)121( systemoutin mmm
)131(
)141(
)/( skgdtdmmm systemoutin /
systemei mmmm )( 12
10. Conservation of Mass Principle
)151( dtdmmm systemei /
)161( V
CVA
enA
in dVdt
ddAdA
ei
)()()(
10. Conservation of Mass Principle
10. Conservation of Mass Principle
10. Conservation of Mass Principle
Mass Balance for Steady-Flow Processes
unit timeper CV
leaving mass Total
unit timeper CV
entering mass Total
10. Conservation of Mass Principle
10. Conservation of Mass Principle
17)-(1 (kg/s) :FlowSteady ei mm
18)-(1 A A :stream) (single FlowSteady 22211121 mm
10. Conservation of Mass Principle
Special Case:Incompressible Flow ( =constant)
19)-(1 /s)(m :Flow ibleIncompressSteady 3ei VV
20)-(1 A A 221121 VV
Steady Incompressibe Flow
(single stream):
10. Conservation of Mass Principle
2CHAPTERCHAPTER
Basic Concepts of Thermodynamics
I. Basic Concepts of Thermodynamics
1. Introduction 前言.
2. Dimensions and Units 單位與因次
3. Closed and Open Systems 密閉系統或開放系統
4. Forms of Energy 能量的形式
5. Properties of a system 性質
6. State and Equilibrium 狀態與平衡
7. Processes and Cycles 過程與循環
8. State Postulate 狀態假說
9. Pressure and Temperature 壓力與溫度
1. Introduction
Thermodynamics is the science of energy and entropy.
The first law of thermodynamics is simply an expression of the conservation of energy principle, and it asserts that energy is a thermodynamic property.
The second law of thermodynamics asserts that energy has quality as well as quantity, and actual processes occur in the direction of decreasing quality of energy.
2. Dimensions and Units
Dimension
Primary dimensions --mass m, length L, time t, temperature T.
Secondary dimensions -- energy E, volume V
Units
English system
International system (SI)
2. Dimensions and Units
Dimension SI Unit IP Unit
Length, L m ft
Time, t sec sec
Mass, m kg lbmEnergy, E Joule Btu
Power, W Waltt Btu/hr
Dimension SI Unit IP Unit
density, kg/m3 lbm/ft3
velocity, v m/sec ft/sec
2. Dimensions and Units
Multiple Prefix
1012 tera, T109 giga, G106 mega, M
103 kilo, k
10-2 centi, c10-3 milli, m10-6 micro, 10-9 nano, n10-12 pico, p
3. Closed and Open Systems
A thermodynamic system, or simply a system, is defined as a quantity of matter or a region in space chosen for study.
The mass or region outside the system is called the surroundings.
The real or imaginary surface that separates the system from its surrounding is called the boundary.
3. Closed and Open Systems
A system of fixed mass is called a closed system, or control mass. -- Energy, not mass, crosses closed-system
boundaries.
3. Closed and Open Systems
A system that involves mass transfer across its boundaries is called an open system, or control volume.– Mass and energy cross control volume boundaries.
3. Closed and Open Systems
An isolated system is a general system of fixed mass where no heat or work may cross the boundaries.
The thermodynamic relations that are applicable to closed and open systems are different. Therefore, it is extremely important that we recognize the type of system we have before we start analyzing it.
4. Forms of Energy
Energy – Stored energy and Transient energy
Stored energy (儲能 )
Internal energy (內能 )
Potential energy (位能 )
Kinetic energy (動能 )
Chemical energy (化學能 )
Nuclear (atomic) energy (核能或原子能 )
Transient energy (轉移能或暫態能 )
Heat (熱 )
Work (功 )
5. Properties of a System
Any macroscopic characteristic of a system is called a property.
Pressure, P
Temperature, T
Volume, V
Mass, m
Density,
Energy, E; Enthalpy, H; Entropy, S
5. Properties of a System
The mass-dependent properties of a system are called extensive properties (uppercase letters) and the others, intensive properties (lowercase letters) .
5. Properties of a System
Extensive properties per unit mass are called specific properties.
Specific volume, v=V/m
Specific total energy, e=E/m
Specific internal energy, u=U/m
Specific enthalpy, h=H/m
Specific entropy, s=S/m
6. State and Equilibrium
6. State and Equilibrium
A system is said to be in thermodynamic equilibrium if it maintains thermal, mechanical, phase and chemical equilibrium.
Thermal equilibrium – the temperature is the same throughout the entire system.
Mechanical equilibrium – there is no change in pressure at any point of the system with time.
Phase equilibrium – the mass of each phase reaches an equilibrium level and stays there.
Chemical equilibrium – the chemical composition does not change with time.
6. State and Equilibrium
State Postulate
The state of a simple compressible system is completely specified by two independent, intensive properties.
7. Processes and Cycles
Any change that a system undergoes from one equilibrium state to another is called a process. (Fig.1-26)
When a process proceeds in such a manner that the system remains infinitesimally close to an equilibrium state at all times, it is called a quasi-static, or quasi-equilibrium, process. (Fig. 1-29)
Quasi-equilibrium
7. Processes and Cycles
7. Processes and Cycles
Process Property held constant
isobaric pressure
isothermal temperature
isochoric volume
isentropic entropy (see Chapter 6) Constant Pressure Process
WaterF
System Boundary
7. Processes and Cycles
A process with identical end states is called a cycle. (Fig.1-30)
ProcessB
ProcessA
1
2P
V
9. Pressure and Temperature
P P Pgage abs atm
P P Pvac atm abs
P P Pabs atm gage
9. Pressure and Temperature
P gh kPa ( )
9. Pressure and Temperature
T K T = C + 273.15
T R T = F + 459.69
9. Pressure and Temperature
Two bodies are in thermal equilibrium when they have reached the same temperature.
Zeroth law of thermodynamics (熱力學第零定律 )
If two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other.
3CHAPTERCHAPTER
Properties of Pure Substances
II. Properties of Pure Substances
1. Pure substance 純物質
2. Phase of a pure substance 純物質之相
3. Phase change processes of pure substances 純物質之相變化
4. Property diagrams for phase change processes 相變過程之性質圖
5. Vapor Pressure and Phase Equilibrium 蒸氣壓與相平衡
6. Property Tables 熱力性質表
II. Properties of Pure Substances
7. The ideal-gas equation of state 理想氣體狀態方程式
8. Compressibility factor – a measure of deviation from ideal-gas behavior 壓縮因子
9. Other Equations of State 其他氣體狀態方程式
10. Internal Energy, Enthalpy, and Specific Heats of Ideal Gases
內能、焓與比熱
1. Pure Substance
A pure substance has a homogeneous and invariable chemical composition and may exist in more than one phase. -- Water, nitrogen, helium, and carbon dioxide.
A pure substance does not have to be of a single chemical element or compound. A mixture of various chemical elements or compounds also qualifies as a pure substance as long as the mixture is homogeneous. -- Air
A mixture of two or more phases of a pure substance is still a pure substance. – a mixture of ice and liquid water.
2. Phase of a Pure Substance
Pure substance have three principal phases – solid, liquid, and gas.
3. Phase Change Processes of Pure Substances
Compressed liquid and saturated liquid.
Saturated vapor and superheated vapor.
Saturation temperature and saturation pressure.
3. Phase Change Processes of Pure Substances
4. Property Diagrams for Phase Change Processes
The T-v diagram
4. Property Diagrams for Phase Change Processes
The T-v diagram
4. Property Diagrams for Phase Change Processes
The P-v diagram
4. Property Diagrams for Phase Change Processes
The P-T diagram
P-v-T Surface of a substance that contracts on freezing
P-v-T Surface of a substance that expands on freezing
5. Vapor Pressure and Phase Equilibrium
vaatm PPP
Tsatv PP @
5. Vapor Pressure and Phase Equilibrium
6. Property Tables
Enthalpy – a combination property
H U PV
h u Pv
6. Property Tables
1a. Saturated Liquid and Saturated Vapor States
vf = specific volume of saturated liquid
vg = specific volume of saturated vapor
vfg = difference between vg and vf,
vfg = vg - vf
6. Property Tables
Example 2-1
A rigid tank contains 50 kg of saturated liquid water at 90 . Determine the pressure in the tank and the volume ℃of the tank.
Example 2-2
A mass of 200 g 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.
6. Property Tables
1b. Saturated Liquid-Vapor Mixture
Quality x is defined as
xmass
mass
m
m msaturated vapor
total
g
f g
6. Property Tables
1b. Saturated Liquid-Vapor Mixture
v v x v vf g f ( )
y y x y y
y x yf g f
f fg
( )
y may be replaced by any of the variables v, u, h, or s.
xy y
yf
fg
6. Property Tables
2. Superheated Vapor
6. Property Tables
3. Compressed Liquid
y y f T @
y may be replaced by any of the variables v, u, h, or s.
7. Ideal-Gas Equation of State
Pv RTPressure
[kPa]
Specific volume[m3/kg]
Temperature[ , K℃ ]
Gas constant[kJ/(kg K)]
or kPa.m3/(kg K)
RR
Mu
7. Ideal-Gas Equation of State
Universal gas constant[ , K℃ ]
Molar mass[g/(gmol)]
or [kg/(kmol)]
7. Ideal-Gas Equation of State
Pv RT
PV
mRT
PV mRT
7. Ideal-Gas Equation of State
Example 2-3
Determine the mass of the air in a room whose dimensions are 4mx5mx6m at 100kPa and 25 C.
Is Water Vapor an Ideal Gas ?
%100
%
table
idealtable
v
vv
err
Z is called compressibility factor (壓縮性因子 )
For ideal gas: Z = 1
ideal
actual
v
v
PRT
vZ
ZRTPvRT
PvZ
/
Tr: reduced temperature
Pr: reduced pressure
TT
TP
P
PRcr
Rcr
and
8. Other Equations of State Van der Waals Equation of State
Beattie-Bridgeman Equation of State
Benedict-Webb-Rubin Equation of State
8. Other Equations of State
%100
%
table
equationtable
v
vv
err
9. Specific Heats9. Specific Heats
The specific heat is defined as the energy required to raise the temperature of a unit mass of a substance by one degree.
Specific heat at constant volume: Cv
Specific heat at constant pressure: Cp
10. Internal Energy, Enthalpy, and Specific Heats of Ideal Gases
10. Internal Energy, Enthalpy, and Specific Heats of Ideal Gases
For an ideal gas
)(
)(
Thh
Tuu
dTTCdhT
hC
dTTCduT
uC
pp
p
vv
v
)(
)(
10. Internal Energy, Enthalpy, and Specific Heats of Ideal Gases
10. Internal Energy, Enthalpy, and Specific Heats of Ideal Gases
Fig. 3-56
Ideal-gas Cp for
some gases.
Table A-2 (p.845)
10. Internal Energy, Enthalpy, and Specific Heats of Ideal Gases
10. Internal Energy, Enthalpy, and Specific Heats of Ideal Gases
For small temperature intervals, specific heat may be assumed to vary linearly with temperature.
10. Internal Energy, Enthalpy, and Specific Heats of Ideal Gases
10. Internal Energy, Enthalpy, and Specific Heats of Ideal Gases
Specific-heat relations of ideal gases.
specific heat ratio,
CkR
kC
R
kP V
1 1
and
10. Internal Energy, Enthalpy, and Specific Heats of Ideal Gases
10. Internal Energy, Enthalpy, and Specific Heats of Ideal Gases
Example 3-16
A piston-cylinder device initially contains air at 150kPa and 27C. At this state, the piston is resting on a pair of stops, and the enclosed volume is 400L. The mass of the piston is such that a 350 kPa pressure is required to move it. The air is now heated until its volume has doubled. Determine (a)the final temperature, (b)the work done b
y the air, and (c)the total heat added.
10. Internal Energy, Enthalpy, and Specific Heats of Solids and Liquids10. Internal Energy, Enthalpy, and
Specific Heats of Solids and Liquids
For incompressible substances (liquids and solids), both the constant-pressure and constant-volume specific heats are identical and denoted by C:
dTTCdu )(
10. Internal Energy, Enthalpy, and Specific Heats of Solids and Liquids10. Internal Energy, Enthalpy, and
Specific Heats of Solids and Liquids
dTTCdu )(
4CHAPTERCHAPTER
Energy Transfer by Heat, Work,
and Mass
IV. Energy Transfer by Heat, Work, and Mass
1. Heat Transfer
2. Energy Transfer by Work
3. Mechanical Forms of Work
4. Nonmechanical Forms of Work
5. Flow Work and the Energy of a Flowing Fluid
1. Heat Transfer
Energy can cross the boundary of a closed system in two distinct forms: heat and work.
Heat is defined as the form of energy that is transferred between two systems (or a system and its surroundings) by virtue of a temperature difference.
Several phrases which are in common use today such as: heat flow, heat addition, heat rejection, heat removal , heat gain, heat loss, heat storage, heat generation, electrical heating, resistance heating, heat of reaction, specific heat, sensible heat, latent heat, waste heat, body heat, are not consistent with the strict thermodynamic meaning of the term heat, which limits its use to the transfer of thermal energy during a process.
In thermodynamics the term heat simply means heat transfer.
A process during which there is no heat transfer is called an adiabatic process.
Heat has energy units, kJ or Btu.
The amount of heat transferred during the process between two states is denoted by Q12 or just Q.
Heat transfer per unit mass of a system is denoted q and is determined from
[kJ/kg] m
The heat transfer rate (the amount of heat transferred per unit time) is denoted
The amount of heat transfer during a process is determined by
When heat transfer rate remains constant during a process, then.
[kW]or [kJ/s] Q
[kJ] 2
1dtQQ
t
t
[kJ] tQQ
The sign for heat is as follows: heat transfer to a system is positive, and heat transfer from a system is negative.
Modes of heat transfer
Heat can be transferred in three different ways: conduction (傳導 ), convection (對流 ), and radiation (輻射 ).
2. Energy Transfer by Work
Work, like heat, is an energy interaction between a system and its surroundings.
If the energy crossing the boundary of a closed system is not heat, it must be work.
Work is the energy transfer associated with a force acting through a distance.
Work is also a form of energy and has energy units such as kJ.
The work done during a process between states 1 and 2 is denoted W12, or simply W.
The work done per unit mass of a system is defined as
The work done per unit time is called power
[kJ/kg] m
Ww
[kW]or [kJ/s] W
(+)
(–)
(+)
(–)
Work and heat are interactions between a system and its surroundings, and there are many similarities between the two:
i. Both are recognized at the boundaries of the system as they cross them. – Both heat and work are boundary phenomena.
ii. Systems possess energy, but not heat transfer or work. – Heat and work are transient phenomena.
iii. Both are associated with a process, not a state. Unlike properties, heat or work has no meaning at a state.
iv. Both are path functions (I.e., their magnitudes depend on the path followed during a process as well as the end states.)
path functions – inexact differentials ()
point functions – exact differentials (d)
2
1
12 VVVdV
)(not 2
1
12 WWW
Example 4-1
Burning of a Candle in an Insulated Room
A candle is burning in a well-insulated room. Taking the room (the air plus the candle) as the system, determine (a) if there is any heat transfer during this burning process and (b) if there is any change in the internal energy of the system.
Example 4-2
Heating of a Potato in an Oven
A potato that is initially at room temperature (25C) is being baked in an oven which is maintained at 200C. Is there any heat transfer during this baking process?
Example 4-3
Heating of an Oven by Work Transfer
A well-insulated electric oven is being heated through its heating element. If the entire oven, including the heating element, is taken to be the system, determine whether this is a heat or work interaction?
Example 4-4
Heating of an Oven by Heat Transfer
Answer the question in Example 3-4 if the system is taken as only the air in the oven without the heating element?
3. Mechanical Forms of Work
Moving boundary work: (kJ)
› Shaft work: (kJ)
› Spring work: (kJ)
Moving Boundary Work
PdVPAds
FdsW
2
1
(kJ) PdVWb
2
1
2
1
PdVAdAArea
Moving Boundary Work
2
1
2
1
PdVAdAArea
Example 3-7Example 3-7
Boundary Work during a Constant-Volume Process
A rigid tank contains air at 500 kPa and 150C. As a result of heat transfer to the surroundings, the temperature and pressure inside the tank drop to 65C and 400 kPa, respectively. Determi
ne the boundary work done during this process.
Example 4-7Example 4-7
Boundary Work during an Isothermal ProcessA piston-cylinder device initially contains 0.4 m3 of air at 100kPa and 80C. The air is now compressed to 0.1 m3 in such a way that the temperature inside the cylinder remains constant. Determine the work done during this process.
Polytropic process ( 多變過程 ) (Pvn = constan
t)
WPV PV
nn kJb
2 2 1 1
11( ) ( )
Spring Work
4. Nonmechanical Forms of Work
› Electrical work: (kJ)
5. Flow Work and the Energy of a Flowing Fluid
5. Flow Work and the Energy of a Flowing Fluid
(kJ/kg) Pvw flow
(kJ) PVPALFLW
PAF
flow
Flow work
gzV
upekeue 2
2
Total Energy of a Flowing Fluid
)( pekeuPvePv
gzV
hpekeh 2
2
Energy Transport by Mass
(kW) )2
(
(kJ) )2
(
2
2
gzV
hmmE
gzV
hmmE
mass
mass
5CHAPTERCHAPTER
The First Law of Thermodynamics
V. The First Law of Thermodynamics
1. The First Law of Thermodynamics
2. Energy Balance for Closed Systems
3. Energy Balance for Steady-Flow Systems
4. Some Steady-Flow Engineering Devices
5. Energy Balance for Unsteady-Flow Processes
1. The First Law of Thermodynamics1. The First Law of Thermodynamics
Energy can be neither created nor destroyed.
First law of thermodynamics, or the conservation of energy principle, is based on experimental observations.
During an interaction between a system and its surroundings, the amount of energy gained by the system must be exactly equal to the amount of energy lost by the surroundings.
Energy BalanceEnergy Balance
Energy BalanceEnergy Balance
Energy BalanceEnergy Balance
2. Energy Balance for Closed Systems2. Energy Balance for Closed Systems
The first law of thermodynamics, or the conservation of energy principle for a closed system or a fixed mass, may be expressed as follows:
or
(kJ) ,, systemoutnetinnet EWQ
(kJ) EWQ
(kJ) EWQ
Net heat transfer across system
boundaries
outin QQ
Net work done in all form
inout WW
Net change in total energy of system
PEKEU
EE
12
For a stationary closed systems
PEKEUWQ
For a cyclic process
0 WQ
Various forms of the first-law relation for closed systems.
ExamplesExamples
Example 5-1: Cooling of a Hot Fluid in a Tank
Example 5-2: Electric Heating of a Gas at Constant Pressure
Example 5-3: Unrestrained Expansion of Water into an Evacuated Tank
Example 5-4: Heating of a Gas in a Tank by Stirring
Example 5-5: Heating of a Gas by a Resistance Heater
Example 5-6: Heating of a Gas at Constant Pressure
Example 5-7: Cooling of an Iron Block by Water
3. Energy Balance for Steady-Flow Systems3. Energy Balance for Steady-Flow Systems
Mass balance for steady-flow systems:
dt
dmmm CV
i eei
i eei mm
Energy balance for steady-flow systems:
dt
dEEE CVoutin
outin EE
i
ii
iiee
ee
e gzV
hmgzV
hmWQ )2
()2
(22
)2
()2
(22
ee
ee
eoutouti
ii
iiinin gzV
hmWQgzV
hmWQ
4. Some Steady-Flow Engineering Devices
Nozzles and Diffusers
Turbines and Compressors
Throttling Valves
Mixture Chambers
Heat Exchangers
Pipe and Duct Flow
(Fig. 4-25)
Nozzle and DiffuserNozzle and Diffuser
0Q
0W
0ke0pe
Example 5-11Example 5-11
Deceleration of Air in a Diffuser
Air at 10C and 80kPa enters the diffuser of a jet engine steadily with a velocity of 200m/s. The inlet area of the diffuser is 0.4 m2. The air leaves the diffuser with a velocity that is very small compared with the inlet velocity. Determine (a) the mass flow rate of the air and (b) the temperature of the air leaving the diffuser.
Turbines and CompressorsTurbines and Compressors
0Q
0W
0ke0pe
Example 5-13Example 5-13
Compressing Air by a Compressor
Air at 100kPa and 280K is compressed steadily to 600kPa and 400K. The mass-flow rate of the air is 0.02 kg/s, and a heat loss of 16kJ/kg occurs during the process. Assuming the changes in kinetic and potential energies are negligible, determine the necessary power input to the compressor.
Example 5-14Example 5-14
Power Generation by a Steam Turbine
The power output of an adiabatic gas turbine is 5MW, and the inlet and the exit conditions of the hot gases are as indicated in Fig.4-30. The gases can be treated as air.
(a) Compare the magnitudes of h, ke, and pe.
(b) Determine the work done per unit mass of hot gases.
(c) Calculate the mass flow rate of the steam.
Throttling ValvesThrottling Valves
0Q
0W
0ke0pe
constant energy flow energy internal222111
21
vpuvpu
hh
The temperature of an ideal gas does not change during a throttling(h =constant) process since h = h (T)
Joule-Thomson CoefficientJoule-Thomson Coefficient
hP
T
tCoefficienThomson -Joule
0 0
decreases T 0
constant remains T 0
increases T 0
Example 5-15Example 5-15
Expansion of R-134a in a Refrigerator
R-134a enters the capillary tube of a refrigerator as saturated liquid at 0.8MPa and is throttled to a pressure of 0.12MPa. Part of the refrigerant evaporates during this process and the refrigerant exists as a saturated liquid-vapor mixture at the final state. Determine the temperature drop of the refrigerant during this process.
Mixing ChamberMixing Chamber
0Q
0W
0ke0pe
Heat ExchangerHeat Exchanger
The heat transfer associated with a heat exchanger may be zero or nonzero depending on how the system is selected
Pipe and Duct FlowPipe and Duct Flow
.