低溫熱流學 Part I: Thermodynamics 授課教師：施陽正博士 97 年 9 月

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


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


Application Areas of 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





or

onAcceleratiMassForce ))((maF )11(




)21( mgW )(N




Dimensional Homogeneity










)31( )/( 3mkgV

m

)41( OH

s

2



)51(

1

m

V)/( 3 kgm


8. Solving Engineering Problems


Step1: Problem Statement

Step2: Schematic

Step3: Assumptions

Step4: Physical Laws

Step5: Properties

Step6: Calculations

Step7: Reasoning,Verification,and Discussion




A Remark on Significant Digits




Mass and Volume Flow Rates

)71( dAmd n

)81(

AndAm )/( skg



Am m

)/( skg )91(

)101( AdAV mA

n

)111(

V

Vm


Conservation of Mass Principle

system ewithin th

massin changNet

system theleaving

mass Total

system theEntering

mass Total


)121( systemoutin mmm

)131(

)141(

)/( skgdtdmmm systemoutin /

systemei mmmm )( 12


)151( dtdmmm systemei /

)161( V

CVA

enA

in dVdt

ddAdA

ei

)()()(




Mass Balance for Steady-Flow Processes

unit timeper CV

leaving mass Total

unit timeper CV

entering mass Total



17)-(1 (kg/s) :FlowSteady ei mm

18)-(1 A A :stream) (single FlowSteady 22211121 mm


Special Case:Incompressible Flow ( =constant)

19)-(1 /s)(m :Flow ibleIncompressSteady 3ei VV

20)-(1 A A 221121 VV

Steady Incompressibe Flow

(single stream):


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)


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


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.


A system of fixed mass is called a closed system, or control mass. -- Energy, not mass, crosses closed-system

boundaries.


A system that involves mass transfer across its boundaries is called an open system, or control volume.– Mass and energy cross control volume boundaries.


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 )


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


The mass-dependent properties of a system are called extensive properties (uppercase letters) and the others, intensive properties (lowercase letters) .


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


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.


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



Process Property held constant

isobaric pressure

isothermal temperature

isochoric volume

isentropic entropy (see Chapter 6) Constant Pressure Process

WaterF

System Boundary


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


P gh kPa ( )


T K T = C + 273.15

T R T = F + 459.69


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


The T-v diagram


The P-v diagram


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


Universal gas constant[ , K℃ ]

Molar mass[g/(gmol)]

or [kg/(kmol)]


Pv RT

PV

mRT

PV mRT


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



For an ideal gas

)(

)(

Thh

Tuu

dTTCdhT

hC

dTTCduT

uC

pp

p

vv

v

)(

)(



Fig. 3-56

Ideal-gas Cp for

some gases.

Table A-2 (p.845)



For small temperature intervals, specific heat may be assumed to vary linearly with temperature.



Specific-heat relations of ideal gases.

specific heat ratio,

CkR

kC

R

kP V

1 1

and



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

Qq

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.


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)



(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



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


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


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.


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


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

.

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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

低溫熱流學 Part I: Thermodynamics 授課教師：施陽正博士 97 年 9 月