1.7 Temperature measured.At high temperatures liquids vaporize and,therefore,these temperatures also cannot be determined by a liquid-in-glass thermometer.Accordingly,several different thermometers might be required to cover a wide temperature interval.bbbb In view of the limitations of empirical means for measuring temperature,it is desir- able to have a procedure for assigning temperature values that do not depend on the properties of any particular substance or class of substances.Such a scale is called a thermodynamic temperature scale.The Kelvin scale is an absolute thermodynamic Kelvin scale temperature scale that provides a continuous definition of temperature,valid over all ranges of temperature.The unit of temperature on the Kelvin scale is the kelvin (K). The kelvin is the SI base unit for temperature.The lowest possible value of temperature on an absolute thermodynamic temperature scale is zero. To develop the Kelvin scale,it is necessary to use the conservation of energy prin- ciple and the second law of thermodynamics;therefore,further discussion is deferred to Sec.5.8 after these principles have been introduced.We note here,however,that the Kelvin scale has a zero of 0 K,and lower temperatures than this are not defined. By definition,the Rankine scale,the unit of which is the degree rankine(R),is Rankine scale proportional to the Kelvin temperature according to T(R)1.8T(K) (1.16) As evidenced by Eq.1.16.the Rankine scale is also an absolute thermodynamic scale with an absolute zero that coincides with the absolute zero of the Kelvin scale.In thermodynamic relationships,temperature is always in terms of the Kelvin or Rankine scale unless specifically stated otherwise.Still,the Celsius and Fahrenheit scales considered next are commonly encountered. 1.7.3 Celsius and Fahrenheit Scales The relationship of the Kelvin,Rankine,Celsius,and Fahrenheit scales is shown in Fig.1.14 together with values for temperature at three fixed points:the triple point, ice point,and steam point. By international agreement,temperature scales are defined by the numerical value assigned to the easily reproducible triple point of water:the state of equilibrium triple point R 0 Steam point Triple point of water 69100 Ice point- 000 9160 Absolute zero Fig.· Comparison of temperature scales
1.7 Temperature 21 measured. At high temperatures liquids vaporize and, therefore, these temperatures also cannot be determined by a liquid-in-glass thermometer. Accordingly, several different thermometers might be required to cover a wide temperature interval. b b b b b In view of the limitations of empirical means for measuring temperature, it is desirable to have a procedure for assigning temperature values that do not depend on the properties of any particular substance or class of substances. Such a scale is called a thermodynamic temperature scale. The Kelvin scale is an absolute thermodynamic temperature scale that provides a continuous definition of temperature, valid over all ranges of temperature. The unit of temperature on the Kelvin scale is the kelvin (K). The kelvin is the SI base unit for temperature. The lowest possible value of temperature on an absolute thermodynamic temperature scale is zero. To develop the Kelvin scale, it is necessary to use the conservation of energy principle and the second law of thermodynamics; therefore, further discussion is deferred to Sec. 5.8 after these principles have been introduced. We note here, however, that the Kelvin scale has a zero of 0 K, and lower temperatures than this are not defined. By definition, the Rankine scale, the unit of which is the degree rankine (8R), is proportional to the Kelvin temperature according to T1 R2 1.8T1K2 (1.16) As evidenced by Eq. 1.16, the Rankine scale is also an absolute thermodynamic scale with an absolute zero that coincides with the absolute zero of the Kelvin scale. In thermodynamic relationships, temperature is always in terms of the Kelvin or Rankine scale unless specifically stated otherwise. Still, the Celsius and Fahrenheit scales considered next are commonly encountered. 1.7.3 Celsius and Fahrenheit Scales The relationship of the Kelvin, Rankine, Celsius, and Fahrenheit scales is shown in Fig. 1.14 together with values for temperature at three fixed points: the triple point, ice point, and steam point. By international agreement, temperature scales are defined by the numerical value assigned to the easily reproducible triple point of water: the state of equilibrium Kelvin scale Rankine scale triple point Absolute zero Steam point 0.00 Kelvin 273.15 273.16 373.15 Triple point of water Ice point K –273.15 Celsius 0.00 0.01 100.0 °C 0.00 Rankine 491.67 491.69 671.67 °R –459.67 Fahrenheit 32.0 32.02 212 °F Fig. 1.14 Comparison of temperature scales
Chapter 1 Getting Started among steam,ice,and liquid water (Sec.3.2).As a matter of convenience,the temperature at this standard fixed point is defined as 273.16 kelvins,abbreviated as 273.16 K.This makes the temperature interval from the ice point(273.15 K)to the steam point equal to 100 K and thus in agreement with the Celsius scale,which assigns 100 degrees to the same interval. Celsius scale The Celsius temperature scale uses the unit degree Celsius (C),which has the same magnitude as the kelvin.Thus,temperature differences are identical on both scales. However,the zero point on the Celsius scale is shifted to 273.15 K,as shown by the following relationship between the Celsius temperature and the Kelvin temperature: T(C)T(K)273.15 (1.17) From this it can be concluded that on the Celsius scale the triple point of water is 0.01C and that 0 K corresponds to -273.15C.These values are shown on Fig.1.14. Fahrenheit scale A degree of the same size as that on the Rankine scale is used in the Fahrenheit scale,but the zero point is shifted according to the relation T(F)T(R) 459.67 (1.18) TAKE NOTE... When making engineering Substituting Eqs.1.17 and 1.18 into Eq.1.16,we get calculations,it's usually okay to round off the last T(F) 1.8T(C)32 (1.19) numbers in Egs.1.17 and 1.18to273and460, This equation shows that the Fahrenheit temperature of the ice point (0C)is 32F respectively.This is fre- and of the steam point (100C)is 212F.The 100 Celsius or Kelvin degrees between quently done in this book. the ice point and steam point correspond to 180 Fahrenheit or Rankine degrees,as shown in Fig.1.14. BIOCONNECTIONS Cryobiology,the science of life at low temperatures, comprises the study of biological materials and systems(proteins,cells,tissues, and organs)at temperatures ranging from the cryogenic(below about 120 K)to the hypothermic(low body temperature).Applications include freeze-drying phar- maceuticals,cryosurgery for removing unhealthy tissue,study of cold-adaptation of animals and plants,and long-term storage of cells and tissues(called cryopreservation). Cryobiology has challenging engineering aspects owing to the need for refrigerators capa- ble of achieving the low temperatures required by researchers.Freezers to support research requiring cryogenic temperatures in the low-gravity environment of the International Space Station,shown in Table 1.1,are illustrative.Such freezers must be extremely compact and miserly in power use.Further,they must pose no hazards.On-board research requiring a freezer might include the growth of near-perfect protein crystals,important for understand- ing the structure and function of proteins and ultimately in the design of new drugs. 1.8 Engineering Design and Analysis The word engineer traces its roots to the Latin ingeniare,relating to invention.Today invention remains a key engineering function having many aspects ranging from developing new devices to addressing complex social issues using technology.In pur- suit of many such activities,engineers are called upon to design and analyze devices intended to meet human needs.Design and analysis are considered in this section. The state of equilibrium between ice and air-saturated water at a pressure of 1 atm. The state of equilibrium between steam and liquid water at a pressure of 1 atm
22 Chapter 1 Getting Started among steam, ice, and liquid water (Sec. 3.2). As a matter of convenience, the temperature at this standard fixed point is defined as 273.16 kelvins, abbreviated as 273.16 K. This makes the temperature interval from the ice point1 (273.15 K) to the steam point2 equal to 100 K and thus in agreement with the Celsius scale, which assigns 100 degrees to the same interval. The Celsius temperature scale uses the unit degree Celsius (8C), which has the same magnitude as the kelvin. Thus, temperature differences are identical on both scales. However, the zero point on the Celsius scale is shifted to 273.15 K, as shown by the following relationship between the Celsius temperature and the Kelvin temperature: T1 C2 T1K2 273.15 (1.17) From this it can be concluded that on the Celsius scale the triple point of water is 0.018C and that 0 K corresponds to −273.158C. These values are shown on Fig. 1.14. A degree of the same size as that on the Rankine scale is used in the Fahrenheit scale, but the zero point is shifted according to the relation T1 F2 T1 R2 459.67 (1.18) Substituting Eqs. 1.17 and 1.18 into Eq. 1.16, we get T1 F2 1.8T1 C2 32 (1.19) This equation shows that the Fahrenheit temperature of the ice point (08C) is 328F and of the steam point (1008C) is 2128F. The 100 Celsius or Kelvin degrees between the ice point and steam point correspond to 180 Fahrenheit or Rankine degrees, as shown in Fig. 1.14. Celsius scale Fahrenheit scale 1 The state of equilibrium between ice and air-saturated water at a pressure of 1 atm. 2 The state of equilibrium between steam and liquid water at a pressure of 1 atm. Cryobiology, the science of life at low temperatures, comprises the study of biological materials and systems (proteins, cells, tissues, and organs) at temperatures ranging from the cryogenic (below about 120 K) to the hypothermic (low body temperature). Applications include freeze-drying pharmaceuticals, cryosurgery for removing unhealthy tissue, study of cold-adaptation of animals and plants, and long-term storage of cells and tissues (called cryopreservation). Cryobiology has challenging engineering aspects owing to the need for refrigerators capable of achieving the low temperatures required by researchers. Freezers to support research requiring cryogenic temperatures in the low-gravity environment of the International Space Station, shown in Table 1.1, are illustrative. Such freezers must be extremely compact and miserly in power use. Further, they must pose no hazards. On-board research requiring a freezer might include the growth of near-perfect protein crystals, important for understanding the structure and function of proteins and ultimately in the design of new drugs. BIOCONNECTIONS 1.8 Engineering Design and Analysis The word engineer traces its roots to the Latin ingeniare, relating to invention. Today invention remains a key engineering function having many aspects ranging from developing new devices to addressing complex social issues using technology. In pursuit of many such activities, engineers are called upon to design and analyze devices intended to meet human needs. Design and analysis are considered in this section. TAKE NOTE... When making engineering calculations, it’s usually okay to round off the last numbers in Eqs. 1.17 and 1.18 to 273 and 460, respectively. This is frequently done in this book
1.8 Engineering Design and Analysis 1.8.1 Design Engineering design is a decision-making process in which principles drawn from engi- neering and other fields such as economics and statistics are applied,usually itera- tively,to devise a system,system component,or process.Fundamental elements of design include the establishment of objectives,synthesis,analysis,construction,testing, evaluation,and redesign (as necessary).Designs typically are subject to a variety of constraints related to economics,safety,environmental impact,and so on. design constraints Design projects usually originate from the recognition of a need or an opportunity that is only partially understood initially.Thus,before seeking solutions it is important to define the design objectives.Early steps in engineering design include developing quantitative performance specifications and identifying alternative workable designs that meet the specifications.Among the workable designs are generally one or more that are "best"according to some criteria:lowest cost,highest efficiency.smallest size. lightest weight,and so on.Other important factors in the selection of a final design include reliability.manufacturability,maintainability,and marketplace considerations Accordingly,a compromise must be sought among competing criteria,and there may be alternative design solutions that are feasible.3 1.8.2 Analysis Design requires synthesis:selecting and putting together components to form a coor- dinated whole.However,as each individual component can vary in size,performance, cost.and so on.it is generally necessary to subject each to considerable study or analysis before a final selection can be made. FREXAMPLE a proposed design for a fire-protection system might entail an overhead piping network together with numerous sprinkler heads.Once an overall configuration has been determined,detailed engineering analysis is necessary to spec- ify the number and type of the spray heads,the piping material,and the pipe diam- eters of the various branches of the network.The analysis also must aim to ensure all components form a smoothly working whole while meeting relevant cost con- straints and applicable codes and standards.b Engineers frequently do analysis,whether explicitly as part of a design process or for some other purpose.Analyses involving systems of the kind considered in this book use,directly or indirectly,one or more of three basic laws.These laws,which are independent of the particular substance or substances under consideration,are 1.the conservation of mass principle 2.the conservation of energy principle 3.the second law of thermodynamics In addition,relationships among the properties of the particular substance or sub- stances considered are usually necessary (Chaps.3,6,11-14).Newton's second law of motion (Chaps.1,2,9),relations such as Fourier's conduction model (Chap.2),and principles of engineering economics (Chap.7)also may play a part. The first steps in a thermodynamic analysis are defining the system and identifying relevant interactions with the surroundings.Attention then turns to the pertinent physical laws and relationships that allow the behavior of the system to be described in terms of an engineering model.The objective in modeling is to obtain a simplified engineering model representation of system behavior that is sufficiently faithful for the purpose of the 3For further discussion,see A.Bejan,G.Tsatsaronis,and M.J.Moran,Thermal Design and Optimization, John Wiley Sons,New York,1996.Chap.1
1.8 Engineering Design and Analysis 23 1.8.1 Design Engineering design is a decision-making process in which principles drawn from engineering and other fields such as economics and statistics are applied, usually iteratively, to devise a system, system component, or process. Fundamental elements of design include the establishment of objectives, synthesis, analysis, construction, testing, evaluation, and redesign (as necessary). Designs typically are subject to a variety of constraints related to economics, safety, environmental impact, and so on. Design projects usually originate from the recognition of a need or an opportunity that is only partially understood initially. Thus, before seeking solutions it is important to define the design objectives. Early steps in engineering design include developing quantitative performance specifications and identifying alternative workable designs that meet the specifications. Among the workable designs are generally one or more that are “best” according to some criteria: lowest cost, highest efficiency, smallest size, lightest weight, and so on. Other important factors in the selection of a final design include reliability, manufacturability, maintainability, and marketplace considerations. Accordingly, a compromise must be sought among competing criteria, and there may be alternative design solutions that are feasible.3 1.8.2 Analysis Design requires synthesis: selecting and putting together components to form a coordinated whole. However, as each individual component can vary in size, performance, cost, and so on, it is generally necessary to subject each to considerable study or analysis before a final selection can be made. a proposed design for a fire-protection system might entail an overhead piping network together with numerous sprinkler heads. Once an overall configuration has been determined, detailed engineering analysis is necessary to specify the number and type of the spray heads, the piping material, and the pipe diameters of the various branches of the network. The analysis also must aim to ensure all components form a smoothly working whole while meeting relevant cost constraints and applicable codes and standards. b b b b b Engineers frequently do analysis, whether explicitly as part of a design process or for some other purpose. Analyses involving systems of the kind considered in this book use, directly or indirectly, one or more of three basic laws. These laws, which are independent of the particular substance or substances under consideration, are 1. the conservation of mass principle 2. the conservation of energy principle 3. the second law of thermodynamics In addition, relationships among the properties of the particular substance or substances considered are usually necessary (Chaps. 3, 6, 11–14). Newton’s second law of motion (Chaps. 1, 2, 9), relations such as Fourier's conduction model (Chap. 2), and principles of engineering economics (Chap. 7) also may play a part. The first steps in a thermodynamic analysis are defining the system and identifying relevant interactions with the surroundings. Attention then turns to the pertinent physical laws and relationships that allow the behavior of the system to be described in terms of an engineering model. The objective in modeling is to obtain a simplified representation of system behavior that is sufficiently faithful for the purpose of the design constraints engineering model 3 For further discussion, see A. Bejan, G. Tsatsaronis, and M. J. Moran, Thermal Design and Optimization, John Wiley & Sons, New York, 1996, Chap. 1
Chapter 1 Getting Started analysis,even if many aspects exhibited by the actual system are ignored.For example, idealizations often used in mechanics to simplify an analysis and arrive at a manage- able model include the assumptions of point masses,frictionless pulleys,and rigid beams.Satisfactory modeling takes experience and is a part of the art of engineering. Engineering analysis is most effective when it is done systematically.This is con- sidered next. 1.9 Methodology for Solving Thermodynamics Problems A major goal of this textbook is to help you learn how to solve engineering problems that involve thermodynamic principles.To this end.numerous solved examples and end- of-chapter problems are provided.It is extremely important for you to study the exam- ples and solve problems,for mastery of the fundamentals comes only through practice. To maximize the results of your efforts,it is necessary to develop a systematic approach. You must think carefully about your solutions and avoid the temptation of starting prob- lems in the middle by selecting some seemingly appropriate equation,substituting in numbers,and quickly "punching up"a result on your calculator.Such a haphazard problem-solving approach can lead to difficulties as problems become more complicated. Accordingly,it is strongly recommended that problem solutions be organized using the following five steps,which are employed in the solved examples of this text. 1 Known:State briefly in your own words what is known.This requires that you read the problem carefully and think about it. Find:State concisely in your own words what is to be determined. 3 Schematic and Given Data:Draw a sketch of the system to be considered.Decide whether a closed system or control volume is appropriate for the analysis,and then carefully identify the boundary.Label the diagram with relevant information from the problem statement. Record all property values you are given or anticipate may be required for subsequent calculations.Sketch appropriate property diagrams(see Sec.3.2),locating key state points and indicating,if possible,the processes executed by the system. The importance of good sketches of the system and property diagrams cannot be overemphasized.They are often instrumental in enabling you to think clearly about the problem. Engineering Model:To form a record of how you model the problem,list all simplifying assumptions and idealizations made to reduce it to one that is manageable.Sometimes this information also can be noted on the sketches of the previous step.The development of an appropriate model is a key aspect of successful problem solving. 6 Analysis:Using your assumptions and idealizations,reduce the appropriate governing equations and relation- ships to forms that will produce the desired results. It is advisable to work with equations as long as possible before substituting numerical data.When the equa- tions are reduced to final forms,consider them to determine what additional data may be required.Identify the tables,charts,or property equations that provide the required values.Additional property diagram sketches may be helpful at this point to clarify states and processes. When all equations and data are in hand,substitute numerical values into the equations.Carefully check that a consistent and appropriate set of units is being employed.Then perform the needed calculations. Finally,consider whether the magnitudes of the numerical values are reasonable and the algebraic signs associated with the numerical values are correct
24 Chapter 1 Getting Started analysis, even if many aspects exhibited by the actual system are ignored. For example, idealizations often used in mechanics to simplify an analysis and arrive at a manageable model include the assumptions of point masses, frictionless pulleys, and rigid beams. Satisfactory modeling takes experience and is a part of the art of engineering. Engineering analysis is most effective when it is done systematically. This is considered next. 1.9 Methodology for Solving Thermodynamics Problems A major goal of this textbook is to help you learn how to solve engineering problems that involve thermodynamic principles. To this end, numerous solved examples and endof-chapter problems are provided. It is extremely important for you to study the examples and solve problems, for mastery of the fundamentals comes only through practice. To maximize the results of your efforts, it is necessary to develop a systematic approach. You must think carefully about your solutions and avoid the temptation of starting problems in the middle by selecting some seemingly appropriate equation, substituting in numbers, and quickly “punching up” a result on your calculator. Such a haphazard problem-solving approach can lead to difficulties as problems become more complicated. Accordingly, it is strongly recommended that problem solutions be organized using the following five steps, which are employed in the solved examples of this text. ❶ Known: State briefly in your own words what is known. This requires that you read the problem carefully and think about it. ❷ Find: State concisely in your own words what is to be determined. ❸ Schematic and Given Data: Draw a sketch of the system to be considered. Decide whether a closed system or control volume is appropriate for the analysis, and then carefully identify the boundary. Label the diagram with relevant information from the problem statement. Record all property values you are given or anticipate may be required for subsequent calculations. Sketch appropriate property diagrams (see Sec. 3.2), locating key state points and indicating, if possible, the processes executed by the system. The importance of good sketches of the system and property diagrams cannot be overemphasized. They are often instrumental in enabling you to think clearly about the problem. ❹ Engineering Model: To form a record of how you model the problem, list all simplifying assumptions and idealizations made to reduce it to one that is manageable. Sometimes this information also can be noted on the sketches of the previous step. The development of an appropriate model is a key aspect of successful problem solving. ❺ Analysis: Using your assumptions and idealizations, reduce the appropriate governing equations and relationships to forms that will produce the desired results. It is advisable to work with equations as long as possible before substituting numerical data. When the equations are reduced to final forms, consider them to determine what additional data may be required. Identify the tables, charts, or property equations that provide the required values. Additional property diagram sketches may be helpful at this point to clarify states and processes. When all equations and data are in hand, substitute numerical values into the equations. Carefully check that a consistent and appropriate set of units is being employed. Then perform the needed calculations. Finally, consider whether the magnitudes of the numerical values are reasonable and the algebraic signs associated with the numerical values are correct. c c c c
1.9 Methodology for Solving Thermodynamics Problems The problem solution format used in this text is intended to guide your thinking, not substitute for it.Accordingly,you are cautioned to avoid the rote application of these five steps,for this alone would provide few benefits.Indeed,as a particular solution evolves you may have to return to an earlier step and revise it in light of a better understanding of the problem.For example,it might be necessary to add or delete an assumption,revise a sketch,determine additional property data,and so on. The solved examples provided in the book are frequently annotated with various comments intended to assist learning,including commenting on what was learned, identifying key aspects of the solution,and discussing how better results might be obtained by relaxing certain assumptions. In some of the earlier examples and end-of-chapter problems,the solution format may seem unnecessary or unwieldy.However,as the problems become more compli- cated you will see that it reduces errors,saves time,and provides a deeper understand- ing of the problem at hand. The example to follow illustrates the use of this solution methodology together with important system concepts introduced previously,including identification of interactions occurring at the boundary. EXAMPLE 1.1 c Using the Solution Methodology and System Concepts A wind turbine-electric generator is mounted atop a tower.As wind blows steadily across the turbine blades, electricity is generated.The electrical output of the generator is fed to a storage battery. (a)Considering only the wind turbine-electric generator as the system,identify locations on the system boundary where the system interacts with the surroundings.Describe changes occurring within the system with time. (b)Repeat for a system that includes only the storage battery. SOLUTION Known:A wind turbine-electric generator provides electricity to a storage battery. Find:For a system consisting of(a)the wind turbine-electric generator,(b)the storage battery,identify locations where the system interacts with its surroundings,and describe changes occurring within the system with time. Schematic and Given Data: Part (a) Engineering Model: 1.In part (a),the system is the control volume shown by the dashed line on the figure. Air flow Turbine-generator 2.In part(b),the system is the closed system shown by the dashed line on the figure 3.The wind is steady. Electric Part (b) current How Storage battery Thermal interaction Fig.E. Analysis: (a)In this case,the wind turbine is studied as a control volume with air flowing across the boundary.Another principal interaction between the system and surroundings is the electric current passing through the wires. From the macroscopic perspective,such an interaction is not considered a mass transfer,however.With a
1.9 Methodology for Solving Thermodynamics Problems 25 The problem solution format used in this text is intended to guide your thinking, not substitute for it. Accordingly, you are cautioned to avoid the rote application of these five steps, for this alone would provide few benefits. Indeed, as a particular solution evolves you may have to return to an earlier step and revise it in light of a better understanding of the problem. For example, it might be necessary to add or delete an assumption, revise a sketch, determine additional property data, and so on. The solved examples provided in the book are frequently annotated with various comments intended to assist learning, including commenting on what was learned, identifying key aspects of the solution, and discussing how better results might be obtained by relaxing certain assumptions. In some of the earlier examples and end-of-chapter problems, the solution format may seem unnecessary or unwieldy. However, as the problems become more complicated you will see that it reduces errors, saves time, and provides a deeper understanding of the problem at hand. The example to follow illustrates the use of this solution methodology together with important system concepts introduced previously, including identification of interactions occurring at the boundary. Using the Solution Methodology and System Concepts A wind turbine–electric generator is mounted atop a tower. As wind blows steadily across the turbine blades, electricity is generated. The electrical output of the generator is fed to a storage battery. (a) Considering only the wind turbine–electric generator as the system, identify locations on the system boundary where the system interacts with the surroundings. Describe changes occurring within the system with time. (b) Repeat for a system that includes only the storage battery. SOLUTION Known: A wind turbine–electric generator provides electricity to a storage battery. Find: For a system consisting of (a) the wind turbine–electric generator, (b) the storage battery, identify locations where the system interacts with its surroundings, and describe changes occurring within the system with time. Schematic and Given Data: Analysis: (a) In this case, the wind turbine is studied as a control volume with air flowing across the boundary. Another principal interaction between the system and surroundings is the electric current passing through the wires. From the macroscopic perspective, such an interaction is not considered a mass transfer, however. With a c c c c EXAMPLE 1.1 c Engineering Model: 1. In part (a), the system is the control volume shown by the dashed line on the figure. 2. In part (b), the system is the closed system shown by the dashed line on the figure. 3. The wind is steady. Storage battery Thermal interaction Air flow Part (a) Part (b) Turbine–generator Electric current flow Fig. E1.1