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

1 CHAPTER Introduction and Overview

I. Introduction and Overview Introduction to Thermal-Fluid Sciences Thermodynamics Heat Transfer Fluid Mechanics A Note on Dimensions and Units Closed and Open System Properties of a System Solving Engineering Problems Problem Solving Technique 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

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

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

7. Properties of a System

7. Properties of a System

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

10. Conservation of Mass Principle

10. Conservation of Mass Principle

10. Conservation of Mass Principle

10. Conservation of Mass Principle

10. Conservation of Mass Principle

10. Conservation of Mass Principle

10. Conservation of Mass Principle

10. Conservation of Mass Principle Mass Balance for Steady-Flow Processes

10. Conservation of Mass Principle

10. Conservation of Mass Principle

10. Conservation of Mass Principle Special Case:Incompressible Flow ( =constant) Steady Incompressibe Flow (single stream):

10. Conservation of Mass Principle

2 CHAPTER Basic Concepts of Thermodynamics

I. Basic Concepts of Thermodynamics Introduction 前言. Dimensions and Units 單位與因次 Closed and Open Systems 密閉系統或開放系統 Forms of Energy 能量的形式 Properties of a system 性質 State and Equilibrium 狀態與平衡 Processes and Cycles 過程與循環 State Postulate 狀態假說 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 Mass, m kg lbm Energy, E Joule Btu Power, W Waltt Btu/hr Dimension SI Unit IP Unit density, r kg/m3 lbm/ft3 velocity, v m/sec ft/sec

2. Dimensions and Units Multiple Prefix 1012 tera, T 109 giga, G 106 mega, M 103 kilo, k 10-2 centi, c 10-3 milli, m 10-6 micro, m 10-9 nano, n 10-12 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 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, r 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 Water F System Boundary

7. Processes and Cycles A process with identical end states is called a cycle. (Fig.1-30) Process B A 1 2 P V

9. Pressure and Temperature

9. Pressure and Temperature

9. Pressure and Temperature

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.

3 CHAPTER Properties of Pure Substances

II. Properties of Pure Substances Phase of a pure substance 純物質之相 Phase change processes of pure substances 純物質之相變化 Property diagrams for phase change processes 相變過程之性質圖 Vapor Pressure and Phase Equilibrium 蒸氣壓與相平衡 Property Tables 熱力性質表

II. Properties of Pure Substances The ideal-gas equation of state 理想氣體狀態方程式 Compressibility factor – a measure of deviation from ideal-gas behavior 壓縮因子 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

5. Vapor Pressure and Phase Equilibrium

6. Property Tables Enthalpy – a combination property

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 Example 2-2 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

6. Property Tables 1b. Saturated Liquid-Vapor Mixture y may be replaced by any of the variables v, u, h, or s.

6. Property Tables 2. Superheated Vapor

6. Property Tables 3. Compressed Liquid y may be replaced by any of the variables v, u, h, or s.

7. Ideal-Gas Equation of State Specific volume [m3/kg] Temperature [℃, K] Pressure [kPa] Gas constant [kJ/(kg K)] or kPa.m3/(kg K)

7. Ideal-Gas Equation of State Universal gas constant [℃, K] Molar mass [g/(gmol)] or [kg/(kmol)]

7. Ideal-Gas Equation of State

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 ?

Z is called compressibility factor (壓縮性因子) For ideal gas: Z = 1

Tr: reduced temperature Pr: reduced pressure

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

9. 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 For an ideal gas

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

10. Internal Energy, Enthalpy, and Specific Heats of Ideal Gases Specific-heat relations of ideal gases. specific heat ratio,

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 by the air, and (c)the total heat added.

10. 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:

10. Internal Energy, Enthalpy, and Specific Heats of Solids and Liquids

4 CHAPTER Energy Transfer by Heat, Work, and Mass

Energy Transfer by Heat, Work, and Mass Heat Transfer Energy Transfer by Work Mechanical Forms of Work Nonmechanical Forms of Work 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

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.

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

(+) (–)

Work and heat are interactions between a system and its surroundings, and there are many similarities between the two: Both are recognized at the boundaries of the system as they cross them. – Both heat and work are boundary phenomena. Systems possess energy, but not heat transfer or work. – Heat and work are transient phenomena. Both are associated with a process, not a state. Unlike properties, heat or work has no meaning at a state. 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 (d) point functions – exact differentials (d)

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

Moving Boundary Work

Example 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. Determine the boundary work done during this process.

Example 4-7 Boundary Work during an Isothermal Process A 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 = constant)

Spring Work

4. Nonmechanical Forms of Work Electrical work: (kJ)

5. Flow Work and the Energy of a Flowing Fluid

Total Energy of a Flowing Fluid

Energy Transport by Mass

5 CHAPTER The First Law of Thermodynamics

The First Law of Thermodynamics Energy Balance for Closed Systems Energy Balance for Steady-Flow Systems Some Steady-Flow Engineering Devices Energy Balance for Unsteady-Flow Processes

1. 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 Balance

Energy Balance

Energy Balance

2. 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

Net work done in all form Net change in total energy of system Net heat transfer across system boundaries

For a stationary closed systems

For a cyclic process

Various forms of the first-law relation for closed systems.

Examples 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 Systems Mass balance for steady-flow systems:

Energy balance for steady-flow systems:

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 Diffuser

Example 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 Compressors

Example 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 5-14 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. Compare the magnitudes of Dh, Dke, and Dpe. Determine the work done per unit mass of hot gases. Calculate the mass flow rate of the steam.

Throttling Valves

The temperature of an ideal gas does not change during a throttling(h =constant) process since h = h (T)

Joule-Thomson Coefficient

Example 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 Chamber

Heat Exchanger The heat transfer associated with a heat exchanger may be zero or nonzero depending on how the system is selected

Pipe and Duct Flow .