10 Chapter 1 Getting Started Fig.1.6 Figure used to discuss the extensive and intensive property concepts. (b) Distinguishing Properties from Nonproperties At a given state,each property has a definite value that can be assigned without knowledge of how the system arrived at that state.The change in value of a property as the system is altered from one state to another is determined,therefore,solely by the two end states and is independent of the particular way the change of state occurred.The change is independent of the details of the process.Conversely,if the value of a quantity is independent of the process between two states,then that quan- tity is the change in a property.This provides a test for determining whether a quan- tity is a property:A quantity is a property if,and only if,its change in value between two states is independent of the process.It follows that if the value of a particular quantity depends on the details of the process,and not solely on the end states,that quantity cannot be a property. 1.3.4 Equilibrium Classical thermodynamics places primary emphasis on equilibrium states and changes equilibrium from one equilibrium state to another.Thus,the concept of equilibrium is fundamen- tal.In mechanics,equilibrium means a condition of balance maintained by an equal- ity of opposing forces.In thermodynamics,the concept is more far-reaching,including not only a balance of forces but also a balance of other influences.Each kind of influence refers to a particular aspect of thermodynamic,or complete,equilibrium. Accordingly,several types of equilibrium must exist individually to fulfill the condi- tion of complete equilibrium;among these are mechanical,thermal,phase,and chem- ical equilibrium. Criteria for these four types of equilibrium are considered in subsequent discus- sions.For the present,we may think of testing to see if a system is in thermodynamic equilibrium by the following procedure:Isolate the system from its surroundings and watch for changes in its observable properties.If there are no changes,we conclude that the system was in equilibrium at the moment it was isolated.The system can be equilibrium state said to be at an equilibrium state. When a system is isolated,it does not interact with its surroundings;however,its state can change as a consequence of spontaneous events occurring internally as its intensive properties,such as temperature and pressure,tend toward uniform values. When all such changes cease,the system is in equilibrium.At equilibrium,tempera- ture is uniform throughout the system.Also,pressure can be regarded as uniform throughout as long as the effect of gravity is not significant;otherwise,a pressure variation can exist,as in a vertical column of liquid. It is not necessary that a system undergoing a process be in equilibrium during the process.Some or all of the intervening states may be nonequilibrium states.For many such processes,we are limited to knowing the state before the process occurs and the state after the process is completed
10 Chapter 1 Getting Started 1.3.4 Equilibrium Classical thermodynamics places primary emphasis on equilibrium states and changes from one equilibrium state to another. Thus, the concept of equilibrium is fundamental. In mechanics, equilibrium means a condition of balance maintained by an equality of opposing forces. In thermodynamics, the concept is more far-reaching, including not only a balance of forces but also a balance of other influences. Each kind of influence refers to a particular aspect of thermodynamic, or complete, equilibrium. Accordingly, several types of equilibrium must exist individually to fulfill the condition of complete equilibrium; among these are mechanical, thermal, phase, and chemical equilibrium. Criteria for these four types of equilibrium are considered in subsequent discussions. For the present, we may think of testing to see if a system is in thermodynamic equilibrium by the following procedure: Isolate the system from its surroundings and watch for changes in its observable properties. If there are no changes, we conclude that the system was in equilibrium at the moment it was isolated. The system can be said to be at an equilibrium state. When a system is isolated, it does not interact with its surroundings; however, its state can change as a consequence of spontaneous events occurring internally as its intensive properties, such as temperature and pressure, tend toward uniform values. When all such changes cease, the system is in equilibrium. At equilibrium, temperature is uniform throughout the system. Also, pressure can be regarded as uniform throughout as long as the effect of gravity is not significant; otherwise, a pressure variation can exist, as in a vertical column of liquid. It is not necessary that a system undergoing a process be in equilibrium during the process. Some or all of the intervening states may be nonequilibrium states. For many such processes, we are limited to knowing the state before the process occurs and the state after the process is completed. equilibrium equilibrium state (a) (b) Fig. 1.6 Figure used to discuss the extensive and intensive property concepts. Distinguishing Properties from Nonproperties At a given state, each property has a definite value that can be assigned without knowledge of how the system arrived at that state. The change in value of a property as the system is altered from one state to another is determined, therefore, solely by the two end states and is independent of the particular way the change of state occurred. The change is independent of the details of the process. Conversely, if the value of a quantity is independent of the process between two states, then that quantity is the change in a property. This provides a test for determining whether a quantity is a property: A quantity is a property if, and only if, its change in value between two states is independent of the process. It follows that if the value of a particular quantity depends on the details of the process, and not solely on the end states, that quantity cannot be a property
1.4 Measuring Mass,Length,Time,and Force 11 Measuring Mass,Length, Time,and Force When engineering calculations are performed,it is necessary to be concerned with the units of the physical quantities involved.A unit is any specified amount of a quantity by comparison with which any other quantity of the same kind is measured. For example,meters,centimeters,kilometers,feet,inches,and miles are all units of length.Seconds,minutes,and hours are alternative time units. Because physical quantities are related by definitions and laws,a relatively small number of physical quantities suffice to conceive of and measure all others.These are called primary dimensions.The others are measured in terms of the primary dimen- sions and are called secondary.For example,if length and time were regarded as primary,velocity and area would be secondary. A set of primary dimensions that suffice for applications in mechanics is mass, length,and time.Additional primary dimensions are required when additional phys- ical phenomena come under consideration.Temperature is included for thermody- namics,and electric current is introduced for applications involving electricity. Once a set of primary dimensions is adopted,a base unit for each primary dimen- base unit sion is specified.Units for all other quantities are then derived in terms of the base units.Let us illustrate these ideas by considering briefly two systems of units:SI units and English Engineering units. 1.4.1 SI Units In the present discussion we consider the SI system of units that takes mass,length, and time as primary dimensions and regards force as secondary.SI is the abbreviation for Systeme International d'Unites (International System of Units),which is the legally accepted system in most countries.The conventions of the SI are published and controlled by an international treaty organization.The Sl base units for mass, SI base units length,and time are listed in Table 1.3 and discussed in the following paragraphs.The SI base unit for temperature is the kelvin,K. The SI base unit of mass is the kilogram,kg.It is equal to the mass of a particular cylinder of platinum-iridium alloy kept by the International Bureau of Weights and Measures near Paris.The mass standard for the United States is maintained by the National Institute of Standards and Technology(NIST).The kilogram is the only base unit still defined relative to a fabricated object. The SI base unit of length is the meter (metre),m,defined as the length of the path traveled by light in a vacuum during a specified time interval.The base unit of time is the second,s.The second is defined as the duration of 9,192,631,770 cycles of the radiation associated with a specified transition of the cesium atom. The SI unit of force,called the newton,is a secondary unit,defined in terms of the base units for mass,length,and time.Newton's second law of motion states that the net force acting on a body is proportional to the product of the mass and the TABLE 1.3 Units for Mass,Length,Time,and Force English Quantity Unit Symbol Unit Symbol mass kilogram kg pound mass Ib length meter 0 foot ft time second second force newton pound force lbf (=1kg·m/s) (=32.1740b·t/s)
1.4 Measuring Mass, Length, Time, and Force 11 1.4 Measuring Mass, Length, Time, and Force When engineering calculations are performed, it is necessary to be concerned with the units of the physical quantities involved. A unit is any specified amount of a quantity by comparison with which any other quantity of the same kind is measured. For example, meters, centimeters, kilometers, feet, inches, and miles are all units of length. Seconds, minutes, and hours are alternative time units. Because physical quantities are related by definitions and laws, a relatively small number of physical quantities suffice to conceive of and measure all others. These are called primary dimensions. The others are measured in terms of the primary dimensions and are called secondary. For example, if length and time were regarded as primary, velocity and area would be secondary. A set of primary dimensions that suffice for applications in mechanics is mass, length, and time. Additional primary dimensions are required when additional physical phenomena come under consideration. Temperature is included for thermodynamics, and electric current is introduced for applications involving electricity. Once a set of primary dimensions is adopted, a base unit for each primary dimension is specified. Units for all other quantities are then derived in terms of the base units. Let us illustrate these ideas by considering briefly two systems of units: SI units and English Engineering units. 1.4.1 SI Units In the present discussion we consider the SI system of units that takes mass, length, and time as primary dimensions and regards force as secondary. SI is the abbreviation for Système International d'Unités (International System of Units), which is the legally accepted system in most countries. The conventions of the SI are published and controlled by an international treaty organization. The SI base units for mass, length, and time are listed in Table 1.3 and discussed in the following paragraphs. The SI base unit for temperature is the kelvin, K. The SI base unit of mass is the kilogram, kg. It is equal to the mass of a particular cylinder of platinum–iridium alloy kept by the International Bureau of Weights and Measures near Paris. The mass standard for the United States is maintained by the National Institute of Standards and Technology (NIST). The kilogram is the only base unit still defined relative to a fabricated object. The SI base unit of length is the meter (metre), m, defined as the length of the path traveled by light in a vacuum during a specified time interval. The base unit of time is the second, s. The second is defined as the duration of 9,192,631,770 cycles of the radiation associated with a specified transition of the cesium atom. The SI unit of force, called the newton, is a secondary unit, defined in terms of the base units for mass, length, and time. Newton’s second law of motion states that the net force acting on a body is proportional to the product of the mass and the base unit SI base units Units for Mass, Length, Time, and Force SI English Quantity Unit Symbol Unit Symbol mass kilogram kg pound mass lb length meter m foot ft time second s second s force newton N pound force lbf (5 1 kg ? m/s2 ) (5 32.1740 lb ? ft/s2 ) TABLE 1.3
12 Chapter 1 Getting Started acceleration,written F o ma.The newton is defined so that the proportionality con- stant in the expression is equal to unity.That is,Newton's second law is expressed as the equality F=ma (1.10） The newton,N,is the force required to accelerate a mass of 1 kilogram at the rate of 1 meter per second per second.With Eq.1.1 1N =(1 kg)(1 m/s2)=1kg.m/s2 (1.2） FREXAMPLE to illustrate the use of the SI units introduced thus far,let us determine the weight in newtons of an object whose mass is 1000 kg,at a place on TAKE NOTE... Earth's surface where the acceleration due to gravity equals a standard value defined Observe that in the calcula- as 9.80665 m/s2.Recalling that the weight of an object refers to the force of gravity tion of force in newtons. and is calculated using the mass of the object,m,and the local acceleration of gravity, the unit conversion factor g,with Eq.11 we get is set off by a pair of verti- F=mg cal lines.This device is used throughout the text to =(1000kg)(9.80665m/s2)=9806.65kg·m/s2 identify unit conversions. This force can be expressed in terms of the newton by using Eq.1.2 as a unit conver- sion factor.That is. IN F= 9806.65 kg·ml 1kg·m/s =9806.65N44444 Since weight is calculated in terms of the mass and the local acceleration due to gravity,the weight of an object can vary because of the variation of the acceleration TABLE 1.4 of gravity with location,but its mass remains constant. SI Unit Prefixes Factor Prefix Symbol FOREXAMPLE if the object considered previously were on the surface of a 102 planet at a point where the acceleration of gravity is one-tenth of the value used in tera 入 1 the above calculation,the mass would remain the same but the weight would be one- giga G 106 tenth of the calculated value. mega 103 kilo 令 102 6 SI units for other physical quantities are also derived in terms of the SI base units. hecto 10-2 centi Some of the derived units occur so frequently that they are given special names and 10-3 milli 而 symbols,such as the newton.SI units for quantities pertinent to thermodynamics are 10-6 micro given as they are introduced in the text.Since it is frequently necessary to work with 10-9 nano extremely large or small values when using the SI unit system,a set of standard 10-2 pico 0 prefixes is provided in Table 1.4 to simplify matters.For example,km denotes kilo- meter,that is,103 m. 1.4.2 English Engineering Units Although SI units are the worldwide standard,at the present time many segments of the engineering community in the United States regularly use other units.A large portion of America's stock of tools and industrial machines and much valuable engi- neering data utilize units other than SI units.For many years to come,engineers in the United States will have to be conversant with a variety of units. In this section we consider a system of units that is commonly used in the United English base units States,called the English Engineering system.The English base units for mass,length, and time are listed in Table 1.3 and discussed in the following paragraphs.English units for other quantities pertinent to thermodynamics are given as they are intro- duced in the text
12 Chapter 1 Getting Started acceleration, written F ~ ma. The newton is defined so that the proportionality constant in the expression is equal to unity. That is, Newton's second law is expressed as the equality F ma (1.1) The newton, N, is the force required to accelerate a mass of 1 kilogram at the rate of 1 meter per second per second. With Eq. 1.1 1 N 11 kg211 m/s 2 2 1 kg m/s 2 (1.2) to illustrate the use of the SI units introduced thus far, let us determine the weight in newtons of an object whose mass is 1000 kg, at a place on Earth’s surface where the acceleration due to gravity equals a standard value defined as 9.80665 m/s2 . Recalling that the weight of an object refers to the force of gravity and is calculated using the mass of the object, m, and the local acceleration of gravity, g, with Eq. 1.1 we get F mg 11000 kg219.80665 m/s 2 2 9806.65 kg m/s 2 This force can be expressed in terms of the newton by using Eq. 1.2 as a unit conversion factor. That is, F a9806.65 kg m s 2 b ` 1 N 1 kg m/s 2 ` 9806.65 N b b b b b Since weight is calculated in terms of the mass and the local acceleration due to gravity, the weight of an object can vary because of the variation of the acceleration of gravity with location, but its mass remains constant. if the object considered previously were on the surface of a planet at a point where the acceleration of gravity is one-tenth of the value used in the above calculation, the mass would remain the same but the weight would be onetenth of the calculated value. b b b b b SI units for other physical quantities are also derived in terms of the SI base units. Some of the derived units occur so frequently that they are given special names and symbols, such as the newton. SI units for quantities pertinent to thermodynamics are given as they are introduced in the text. Since it is frequently necessary to work with extremely large or small values when using the SI unit system, a set of standard prefixes is provided in Table 1.4 to simplify matters. For example, km denotes kilometer, that is, 103 m. 1.4.2 English Engineering Units Although SI units are the worldwide standard, at the present time many segments of the engineering community in the United States regularly use other units. A large portion of America’s stock of tools and industrial machines and much valuable engineering data utilize units other than SI units. For many years to come, engineers in the United States will have to be conversant with a variety of units. In this section we consider a system of units that is commonly used in the United States, called the English Engineering system. The English base units for mass, length, and time are listed in Table 1.3 and discussed in the following paragraphs. English units for other quantities pertinent to thermodynamics are given as they are introduced in the text. English base units TAKE NOTE... Observe that in the calculation of force in newtons, the unit conversion factor is set off by a pair of vertical lines. This device is used throughout the text to identify unit conversions. SI Unit Prefixes Factor Prefix Symbol 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 1022 centi c 1023 milli m 1026 micro 1029 nano n 10212 pico p TABLE 1.4
1.5 Specific Volume 13 The base unit for length is the foot,ft,defined in terms of the meter as 1ft=0.3048m (13) The inch,in.,is defined in terms of the foot: 12in.1ft One inch equals 2.54 cm.Although units such as the minute and the hour are often used in engineering,it is convenient to select the second as the English Engineering base unit for time. The English Engineering base unit of mass is the pound mass,Ib,defined in terms of the kilogram as 11b=0.45359237kg (1.4) The symbol lbm also may be used to denote the pound mass. Once base units have been specified for mass,length,and time in the English Engineering system of units,a force unit can be defined,as for the newton,using Newton's second law written as Eq.1.1.From this viewpoint,the English unit of force, the pound force,lbf,is the force required to accelerate one pound mass at 32.1740 ft/s2, which is the standard acceleration of gravity.Substituting values into Eq.1.1, 11bf=(11b)(32.1740ft/s2)=32.17401b·ft/s2 (1.5) With this approach force is regarded as secondary. The pound force,Ibf,is not equal to the pound mass,Ib,introduced previously. Force and mass are fundamentally different,as are their units.The double use of the word "pound can be confusing,so care must be taken to avoid error. FREXAMPLE to show the use of these units in a single calculation,let us deter- mine the weight of an object whose mass is 1000 lb at a location where the local acceleration of gravity is 32.0 ft/s2.By inserting values into Eq.1.1 and using Eq.1.5 as a unit conversion factor,we get F=mg=(10001b)32.0 994.591bf 32.17401b·ft/s This calculation illustrates that the pound force is a unit of force distinct from the pound mass,a unit of mass. Specific Volume Three measurable intensive properties that are particularly important in engineering thermodynamics are specific volume,pressure,and temperature.Specific volume is considered in this section.Pressure and temperature are considered in Secs.1.6 and 1.7,respectively. From the macroscopic perspective,the description of matter is simplified by con- sidering it to be distributed continuously throughout a region.The correctness of this idealization,known as the continuum hypothesis,is inferred from the fact that for an extremely large class of phenomena of engineering interest the resulting description of the behavior of matter is in agreement with measured data. When substances can be treated as continua,it is possible to speak of their inten- sive thermodynamic properties "at a point."Thus,at any instant the density p at a point is defined as p=() (1.6) where V'is the smallest volume for which a definite value of the ratio exists.The Ext Int Properties A.3-Tabs b c volume V'contains enough particles for statistical averages to be significant.It is the ●
1.5 Specific Volume 13 The base unit for length is the foot, ft, defined in terms of the meter as 1 ft 0.3048 m (1.3) The inch, in., is defined in terms of the foot: 12 in. 1 ft One inch equals 2.54 cm. Although units such as the minute and the hour are often used in engineering, it is convenient to select the second as the English Engineering base unit for time. The English Engineering base unit of mass is the pound mass, lb, defined in terms of the kilogram as 1 lb 0.45359237 kg (1.4) The symbol lbm also may be used to denote the pound mass. Once base units have been specified for mass, length, and time in the English Engineering system of units, a force unit can be defined, as for the newton, using Newton’s second law written as Eq. 1.1. From this viewpoint, the English unit of force, the pound force, lbf, is the force required to accelerate one pound mass at 32.1740 ft/s2 , which is the standard acceleration of gravity. Substituting values into Eq. 1.1, 1 lbf 11 lb2132.1740 ft/s 2 2 32.1740 lb ft/s 2 (1.5) With this approach force is regarded as secondary. The pound force, lbf, is not equal to the pound mass, lb, introduced previously. Force and mass are fundamentally different, as are their units. The double use of the word “pound” can be confusing, so care must be taken to avoid error. to show the use of these units in a single calculation, let us determine the weight of an object whose mass is 1000 lb at a location where the local acceleration of gravity is 32.0 ft/s2 . By inserting values into Eq. 1.1 and using Eq. 1.5 as a unit conversion factor, we get F mg 11000 lb2a32.0 ft s 2 b ` 1 lbf 32.1740 lb ft/s 2 ` 994.59 lbf This calculation illustrates that the pound force is a unit of force distinct from the pound mass, a unit of mass. b b b b b 1.5 Specific Volume Three measurable intensive properties that are particularly important in engineering thermodynamics are specific volume, pressure, and temperature. Specific volume is considered in this section. Pressure and temperature are considered in Secs. 1.6 and 1.7, respectively. From the macroscopic perspective, the description of matter is simplified by considering it to be distributed continuously throughout a region. The correctness of this idealization, known as the continuum hypothesis, is inferred from the fact that for an extremely large class of phenomena of engineering interest the resulting description of the behavior of matter is in agreement with measured data. When substances can be treated as continua, it is possible to speak of their intensive thermodynamic properties “at a point.” Thus, at any instant the density at a point is defined as r lim VSV¿ a m V b (1.6) where V9 is the smallest volume for which a definite value of the ratio exists. The volume V9 contains enough particles for statistical averages to be significant. It is the Ext_Int_Properties A.3 – Tabs b & c
14 Chapter 1 Getting Started smallest volume for which the matter can be considered a continuum and is normally small enough that it can be considered a "point."With density defined by Eq.1.6, density can be described mathematically as a continuous function of position and time. The density,or local mass per unit volume,is an intensive property that may vary from point to point within a system.Thus,the mass associated with a particular vol- ume V is determined in principle by integration m (1.7) and not simply as the product of density and volume. specific volume The specific volume v is defined as the reciprocal of the density,v=1/p.It is the volume per unit mass.Like density,specific volume is an intensive property and may vary from point to point.SI units for density and specific volume are kg/m3 and m/kg,respectively.They are also often expressed,respectively,as g/cm'and cm'/g.English units used for density and specific volume in this text are Ib/ft3 and ft/lb,respectively. In certain applications it is convenient to express properties such as specific vol- ume on a molar basis rather than on a mass basis.A mole is an amount of a given substance numerically equal to its molecular weight.In this book we express the molar basis amount of substance on a molar basis in terms of the kilomole (kmol)or the pound mole (Ibmol),as appropriate.In each case we use 171 1= M 1.8) The number of kilomoles of a substance,n,is obtained by dividing the mass,m,in kilograms by the molecular weight,M,in kg/kmol.Similarly,the number of pound moles,n,is obtained by dividing the mass,m,in pound mass by the molecular weight, M,in Ib/lbmol.When m is in grams,Eq.1.8 gives n in gram moles,or mol for short. Recall from chemistry that the number of molecules in a gram mole,called Avogadro's number,is 6.022 X 1023.Appendix Tables A-1 and A-1E provide molecular weights for several substances. To signal that a property is on a molar basis,a bar is used over its symbol.Thus, signifies the volume per kmol or Ibmol,as appropriate.In this text,the units used for are m'/kmol and ft'/lbmol.With Eq.1.8,the relationship between v and v is =Mv (1.9) where M is the molecular weight in kg/kmol or lb/lbmol,as appropriate. 1.6 Pressure Next,we introduce the concept of pressure from the continuum viewpoint.Let us begin by considering a small area,A,passing through a point in a fluid at rest.The fluid on one side of the area exerts a compressive force on it that is normal to the area,Fommal.An equal but oppositely directed force is exerted on the area by the fluid on the other side.For a fluid at rest,no other forces than these act on the area.The pressure pressure,p,at the specified point is defined as the limit p lim ormal (1.10) Ext_Int_Properties where A'is the area at the "point"in the same limiting sense as used in the defini- A.3 Tab d 。tion of density
14 Chapter 1 Getting Started smallest volume for which the matter can be considered a continuum and is normally small enough that it can be considered a “point.” With density defined by Eq. 1.6, density can be described mathematically as a continuous function of position and time. The density, or local mass per unit volume, is an intensive property that may vary from point to point within a system. Thus, the mass associated with a particular volume V is determined in principle by integration m V rdV (1.7) and not simply as the product of density and volume. The specific volume is defined as the reciprocal of the density, 5 1/. It is the volume per unit mass. Like density, specific volume is an intensive property and may vary from point to point. SI units for density and specific volume are kg/m3 and m3 /kg, respectively. They are also often expressed, respectively, as g/cm3 and cm3 /g. English units used for density and specific volume in this text are lb/ft3 and ft3 /lb, respectively. In certain applications it is convenient to express properties such as specific volume on a molar basis rather than on a mass basis. A mole is an amount of a given substance numerically equal to its molecular weight. In this book we express the amount of substance on a molar basis in terms of the kilomole (kmol) or the pound mole (lbmol), as appropriate. In each case we use n m M (1.8) The number of kilomoles of a substance, n, is obtained by dividing the mass, m, in kilograms by the molecular weight, M, in kg/kmol. Similarly, the number of pound moles, n, is obtained by dividing the mass, m, in pound mass by the molecular weight, M, in lb/lbmol. When m is in grams, Eq. 1.8 gives n in gram moles, or mol for short. Recall from chemistry that the number of molecules in a gram mole, called Avogadro’s number, is 6.022 3 1023. Appendix Tables A-1 and A-1E provide molecular weights for several substances. To signal that a property is on a molar basis, a bar is used over its symbol. Thus, y signifies the volume per kmol or lbmol, as appropriate. In this text, the units used for y are m3 /kmol and ft3 /lbmol. With Eq. 1.8, the relationship between y and y is y My (1.9) where M is the molecular weight in kg/kmol or lb/lbmol, as appropriate. specific volume molar basis 1.6 Pressure Next, we introduce the concept of pressure from the continuum viewpoint. Let us begin by considering a small area, A, passing through a point in a fluid at rest. The fluid on one side of the area exerts a compressive force on it that is normal to the area, Fnormal. An equal but oppositely directed force is exerted on the area by the fluid on the other side. For a fluid at rest, no other forces than these act on the area. The pressure, p, at the specified point is defined as the limit p lim ASA¿ a Fnormal A b (1.10) where A9 is the area at the “point” in the same limiting sense as used in the definition of density. pressure Ext_Int_Properties A.3 – Tab d