CHAPTER ONE INTRODUCTION

1.1 THE SCOPE OF THERMODYNAMICS

The word thermodynamics means heat power, or power developed from heat, rellecting its origin in the analysis of steam engines. As a fully developed modem science, thermodynamics deals with transformations of energy of all kinds from one form to another. The general restrictions within which all such transformations are observed to occur are known as the first and second laws of thermodynamics. These laws cannot be proved in the mathematical sense. Rather, their validity rests upon experience. Given mathematical expression, these laws lead to a network of equations from which a wide range of practical results and conclusions can be deduced. The universal applicability of this science is shown by the fact that it is employed alike by physicists, chemists, and engineers. The basic principles are always the same, but the applications differ. The chemical engineer must be able to cope with a wide variety of problems. Among the most important are the determination of heat and work requirements for physical and chemical processes, and the determination of equilibrium conditions for chemical reactions and for the transfer of chemical species between phases. TheQl'odynamic considerations by themselves are not sufficient to allow calculation of the rates of chemical or physical processes. Rates depend on both driving force and resistance. Although driving forces are thermodynamic vari­ ables, resistances are not. Neither can thermodynamics, a macroscopic-property formulation, reveal the microscopic (molecular) mechanisms of physical or chemical processes. On the other hand, knowledge of the microscopic behavior

1 ] INTRODUCTION 10 CHEMICAL ENGINEERING THERMODYNAMICS INTRODUCTION ~ of matter can be useful in the calculation of thermodynamic properties. Such as there are atoms in 0.012 kg of carbon-I 2. This is equivalent to the "gram mole" property values are essential to the practical application of thermodynamics; commonly used by chemists. numerical results of thermodynamic analysis are accurate only to the extent that Decimal mUltiples and fractions of SI units are designated by prefixes. Those the required data are accurate. The chemical engineer must deal with many in common use are listed in Table 1.1. Thus we have, for example, that I cm = chemical species and their mixtures, and experimental data are often unavailable. 10-2 m and I kg = 103 g. Thus one must make effective use of correlations developed from a limited data Other systems of units, such as the English engineering system, use units that base, but generalized to provide estimates in the absence of data. are related to SI units by fixed conversion factors. Thus, the foot (ft) is defined The application of thermodynamics to any real problem starts with the as 0.3048 m, the pound mass (Ibm) as 0.45359237 kg, and the pound mole (lb mol) identification of a particular body of matter as the focus of attention. This quantity as 453.59237 mol. of matter is called the system, and its thermodynamic state is defined by a few measurable macrosCopic properties. These depend on the fundamental dimensions of science, of which length, time, mass, temperature, and amount of 1.3 FORCE substance are of interest here. The SI unit of force is the newton, symbol N, derived from Newton's second law, which expresses force F as the product of mass m and acceleration a: 1.2 DIMENSIONS AND UNITS F=ma The fundamental dimensions are primitives, recognized through our sensory The newton is defined as the force which when applied to a mass of I kg produce, perceptions and not definable in terms of anything simpler. Their use, however, an acceleration of I m s -2; thus the newton is a derived unit representin~ 2 requires the definition of arbitrary scales of measure, divided into specific units I kgms- . of size. Primary units have been set by international agreement, and are codified In the English engineering system of units, force is treated as an additional as the International System of Units (abbreviated SI, for Systeme International). independent dimension along with length, time, and mass. The pound force (Ib,: The second, symbol s, is the SI unit of time, defined as the duration of is defined as that force which accelerates I pound mass 32.1740 feet per second 9,192,631,770 cycles of radiation associated with a specified transition of the per second. Newton's law must here include a dimensional proportionalit) cesium atom. The meter, symbol m, is the fundamental unit of length, defined constant if it is to be reconciled with this definition. Thus, we write as the distance light travels in a vacuum during 1/299,792,458 of a second. The I kilogram, symbol kg, is the mass of a platinum/iridium cylinder kept at the F=-ma International Bureau of Weights and Measures at Sevres, France. The unit of go temperature is the kelvin, symbol K, equal to 1/273.16 of the thermodynamic whencet temperature of the triple point of water. A more detailed discussion of tem­ perature, the characteristic dimension of thermodynamics, is given in Sec. 1.4. 1(lb,} =.!. x 1(lbm} x 32.1740(ft)(s}-2 The measure of the amount of substance is the mole, symbol mol, defined as the go amount of substance represented by as many elementary entities (e.g., molecules) and

Table 1.1 Prefixes for SI units go = 32.1740(lbm)(ft)(lb,}-'(s}-2 The pound force is equivalent to 4.4482216 N. Fraction or Since force and mass are different concepts, a pound force and a pound ma" multiple Prelix Symbol are different quantities, and their units cannot be cancelled against one another 10-9 nano n When an equation contains both units, (Ib,) and (Ibm), the dimensional constanl 6 10- micro P. go must-also appear in the equation to make it dimensionally correct. 3 10- milli m Weight properly refers to the force of gravity on a body, and is therefon 10-2 centi c correctly expressed in newtons or in pounds force. Unfortunately, standards 01 10' kilo k 10' mega M 10' giga G t Where English units are employed, parentheses enclose the abbreviations of all units. 4 INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS INTRODUCTION 5

mass are often called "weights," and the use of a balance to compare masses is Thus a uniform tube, partially filled with mercury, alcohol, or some other called "weighing." Thus, one must discern from the context whether force or can indicate degree of "hotness" simply by the length of the fluid column. mass is meant when the word "weight" is used in a casual or informal way. Howev,er, numerical values are assigned to the various degrees of hotness by art,itr,ary definition. Example 1.1 An astrQnaut weighs 730 N in Houston, Texas, where the local acceler­ For the Celsius scale, the ice point (freezing point of water saturated with ation of gravity is 9 = 9.792 m S-2. What is the mass of the astronaut, and what does 'r at standard atmospheric pressure) is zero, and the steam point (boiling point he weigh on the moon, where 9 = 1.67 m s-21 .:~pure water at standard atmospheric pressure) is 100. We may give a thermometer SOLUTION Letting a = g, we write Newton's law as a numerical scale by immersing it in an ice bath and making a mark for zero at the fluid level, and then immersing it in boiling water and making a mark for F=mg 100 at this greater fluid level. The distance between the two marks is divided into whence 100 equal spaces called degrees. Other spaces of equal size may be marked off F 730N I below zero and above 100 to extend the range of the thermometer. m = - = = 74.55 N m- S' 9 9.792ms' All thermometers, regardless of fluid, read the same at zero and 100 if they 2 Since the newton N has the units kgms- , this result simplifies to are calibrated by the method described, but at other points the readings do not usually correspond, because fluids vary in their expansion characteristics. An m = 74.55 kg arbitrary choice could be made, and for many purposes this would be entirely This mass of the astronaut is independent of loc~tion, but his weight depends on the satisfactory. However, as will be shown, the temperature scale of the SI system, local acceleration of gravity. Thus on the moon his weight is with its kelvin unit, symbol K, is based on the ideal gas as thermometric fluid. Since the definition of this scale depends on the properties of gases, detailed Fmoon = mOmoon = 74.55 kg x 1.67 m S-2 discussion of it is delayed until Chap. 3. We note, however, that this is an absolute or scale, and depends on the concept of a lower limit of temperature. Fmoon = 124.5 kg m s-' = 124.5 N Kelvin temperatures are given the symbol T; Celsius temperatures, given the symbol t, are defined in relation to Kelvin temperatures by To work this problem in the English epgineering system of units, we convert the astronaut's weight to (lb,) and the values of 9 to (ft)(s)-'. Since 1 N is equivalent to tOC = T K - 273.15 O.2248090b,) and 1 m to 3.28084(ft), we have: The unit of Celsius temperature is the degree Celsius, nc, equal to the kelvin. Weight of astronaut in Houston = 164.1 (lb,) However, temperatures on the Celsius scale are 273.15 degrees lower than on the gHn~'nn = 32.13 and gmoon = 5.48(ft)(s)-' Kelvin scale. This means that the lower limit of temperature, called absolute zero on the Kelvin scale, occurs at - 273.l5°C. Newton's law here gives In practice it is the International Practical Temperature Scale of 1968 (IPTS-68) Fg, 164.1(lb,) x 32.174O(lb )(ft)(lb,)-'(s)-' m=- m which is used for calibration of scientific and industrial instruments.t This scale 9 32.13(ft)(s) , has been so chosen that temperatures measured on it closely approximate ideal-gas or temperatures; the differences are within the limits of present accuracy of measure­ ment. The IPTS-68 is based on assigned values of temperature for a number of m = 164.3(lb ) m reproducible equilibrium states (defining fixed points) and on standard instru­ Thus the astronaufs m!1ss in (Ibm) and weight in (lb f ) in Houston are numerically ments calibrated at these temperatures. Interpolation between the fixed-point almost the same, but on the moon this is not the case: temperatures is provided by formulas that establish the relation between readings of the standard instruments and values of the international practical temperature. F = mgmoon = (164.3)(5.48) 28 O(lb) moon g, 32.1740 ., The defining fixed points are specified phase-equilibrium states of pure sub­ stances,* a~ given in Table 1.2. 1.4 TEMPERATURE t The English-language text of the definition of IPTS-68, as agreed upon by the International Committee of Weights and Measures, is published in Metralogia, 5:35-44, 1%9; see also ibid., 12:7-17, The most common method of temperature measurement is with a liquid-in-glass 1976. thermometer. This method depends on the expansion of fluids when they are t See Sees. 2.7 and 2.8. 6 INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS INTRODUCTION 7

Kelvin Fahrenheit Table 1.2 Assigned values for fixed points of the IPTS-68 Celsius Rankine

Equilibrium statet 100'C -- 373.15 K -- 212('F) -- 671.67(R) --Steam poinl

Equilibrium between the solid, liquid, and vapor phases of equi­ librium hydrogen (triple point of equilibrium hydrogen) 13.81 -259.34 o'C--- 273.15 K -- 32('F) --- 491.67(R) -- Ice poinl Equilibrium between the liquid and vapor phases of equilibrium hydrogen at 33,330.6 Pa 17.042 -256.108 Equilibrium between the liquid and vapor phases of equilibrium hydrogen (boiling point of equilibrium hydrogen) 20.28 -252.87 Equilibrium between the liquid and vapor phases of neon (boiling point of neon) 27.102 -246.048 Equilibrium between the solid, liquid, and vapor phases of oxy­ gen (triple point of oxygen) 54.361 -218.789 Equilibrium between the liquid and vapor phases of oxygen (boiling point of oxygen) 90.188 -182.962 -273.15'C - 0 K --- -459.67(OF) - O( R)I----- Absolute zero Equilibrium between the solid, liquid, and vapor phases of water (triple point of water) 273.16 om Equilibrium between the liquid and vapor phases of water (boil­ ing point of water) 373.15 100.00 Equilibrium between the solid and liquid phases of zinc (freezing Fllure 1.1 Relations among temperature scales. point of zinc) 692.73 419.58 Equilibrium between the solid and liquid phases of silver (freez­ ing point of silver) 1,235.08 961.93 The Celsius degree and the kelvin represent the same temperature interva~ Equilibrium between the solid and liquid phases of gold (freezing point of gold) 1.337.58 1,064.43 as do the Fahrenheit degree and the rankine. However, I 'C (or I K) is equivalent to 1.8('F) [or 1.8(R)]. The relationships among the four temperature scales are t Except for the triple points and one equilibrium point (17.042 K), temperatures are for equi­ shown in Fig. 1.1. In thermodynamics, when temperature is referred to without librium states at l(atm). qualification, absolute temperature is implied.

Example 1.2 Table 1.3 lists the specific volumes of water , mercury, hydrogen at I(atm), The standard instrument used from -259.34 to 630.74'C is the platinum­ and hydrogen at l00(atm) for a number oftemperatures on the International Practical resistance thermometer, and from 630.74 to 1064.43'C the platinum-IO percent Temperature Scale. Assume that each substance is the fluid in a thermometer cali­ rhodium/ platinum thermocouple is used. Above 1064.43'C the temperature is brated at the ice and steam points as suggested at the beginning of this sectidn. To defined by Planck's radiation law. determine how good these thermometers are, calculate what each reads at the true In addition to the Kelvin and Celsius scales two others are in use by temperatures for which data are given. engineers in the United States: the Rankine scale and the Fahrenheit scale. The Rankine scale is directly related to the Kelvin scale by SOLUTION In calibrating a thermometer as specified, one assumes that each degree is represented by a fixed scale length. This is equivalent to the assumption that each T(R) = 1.8T K degree of temperature change is accompanied by a fixed change in volume or specific and is an absolute scale. The Fahrenheit scale is related to the Rankine scale by an equation analogous Table 1.3 Specifie volumes in em' g-' to the relation between the Celsius and Kelvin scales.

t('F) = T(R) - 459.67 I/'e Water Mercury H,I(alm) H,IOO(atm) .... Thus the lower limit of temperature on the Fahrenheit scale is -459.67('F). The -100 7,053 76.03 relation between the Fahrenheit and Celsius scales is given by 0 1.00013 0.073554 11,125 118.36 50 1.01207 0.074223 13,161 139.18 t('F) = 1.8t'C + 32 100 1.04343 0.074894 15,197 159.71 200 1.1590 0.076250 19,266 200.72 This gives the ice point as 32('F) and the normal boiling point of water as 212('F). 8 INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS INTRODUCTION'

Table 1.4 Temperature readings for thermometers or per mole, and is therefore independent of the total amount of material considered. Density, p is the reciprocal of specific or molar volume. f/OC Water Mercury H2 t(atrn) H2 1OO(atm)

-100 -100.0 -102.3 1.6 PRESSURE 0 0 0 0 0 50 27.6 49.9 50.0 50.4 The pressure P of a fluid on a surface is defined as the normal force exerted by 100 100 100 100 100 the fluid per unit area of the surface. If force is measured in N and area in m' 200 367 201.2 199.9 199.2 the unit is the newton per square meter or N m-', called the pascal, symbol Pa: the basic SI unit of pressure. In the English engineering system the most common unit is the pound force per square inch (psi). volume of the thermometric fluid used. For water, the change in specific volume when The primary standard for the measurement of pressure derives from its t increases from 0 to 100°C is definition. A known force is balanced by a fluid pressure acting on a known area; 1.04343 - 1.00013 = 0.0433 em' whence P = F / A. The apparatus providing this direct pressure measurement is the dead-weight gauge. A simple design is shown in Fig. 1.2. The piston is carefully If it is assumed that this volume change divides equally among the 100°C. then the 3 1 fitted to the cylinder so that the clearance is small. Weights are placed on the volume change per degree is 0.000433 cm °C- • When this assumption is not valid. the thermometer gives readings in disagreement with the International Practical pan until the pressure of the oil, which tends to make the piston rise, is just Temperature Scale. balanced by the force of gravity on the piston and all that it supports. With the The change in specific volume of water between 0 and 50°C is force of gravity given by Newton's law, the pressure of the oil is 1.01207 - 1.00013 = 0.01194 em' p=F=mg 3 A A If each degree on the water thermometer represents 0.000433 cm , the number of these degrees represented by a volume change of 0.01194 em' is 0.0\194/0.000433, or 27.6(degrees). Thus the water thermometer reads 27.6(degrees) when the actual r------Weight temperature is 50°C. 3 At 200~C. the specific volume of water is 1.1590 cm , and the change between 0 and 2oo·C'is 1.1590 - 1.00013 = 0.1589 em'. Thus the water thermometer reads DllI'----- Pan 0.1589/0.000433, or 367(degrees), when the true temperature is 2OO·C. Table 1.4 gives all the results obtained by similar calculations. ------Piston Each thermometer reads the true Celsius temperature at 0 and 100 because each was calibrated at these points. At other points, however, the readings may differ from the true values of the temperature. Water is seen to be a singularly poor thermometric fluid. Mercury, on the other hand, is good, which accounts for its widespread use in thermometers. Hydrogen at l(atm) makes a very good thermometric fluid, but is not practical for general use. Hydrogen at lOO(atm) is no more practical and is less satisfactory.

1.S DEFINED QUANTITIES; VOLUME

We have seen that in the international system of units force is defined through ";~~ ...... ~ To pressure Newton's law. Convenience dictates the introduction of a number of other defined ! source quantities. Some, like volume, are so common as to require almost no discussion. Others, requiring detailed explanation, are treated in the following sections. Volume V is a quantity representing the product of three lengths. The volume of a substance, like its mass, depends on the amount of material considered. Specific or molar volume, on the other hand, is defined as volume per unit mass Fipre 1.1 Dead-weight gauge. 10 INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS INTRODUCTION 1l where m is the mass of the piston, pan, and weights, 9 is the local acceleration or of gravity, and A is the cross-sectional area of the piston. Gauges in common use, such as Bourdon gauges, are calibrated by comparison with dead-weight P = 867.4kPa gauges. Since a vertical column of a given fluid under the influence of gravity exerts Example 1.4 At 27°C a manometer filled with mercury reads 60.5 em. The local a pressure at its base in direct proportion to its height, pressure is also expressed acceleration of gravity is 9.784 m S-2. To what pressure does this height of mercury correspond? as the equivalent height of a fluid column. This is the basis for the use of manometers for pressure measurement. Conversion of height to force per unit SOLUTION From the equation in the preceding text, area follows from Newton's law applied to the force of gravity acting on the mass of fluid in the column. The mass m is given by P = hpg At 27·C the density of mercury is 13.53 g em-'. Then m =Ahp P = 60.5 em x 13.53 g em-' x 9.784 m S-2 where A is the cross-sectional area of the column, h is its height, and p is the = 8,009 g m S-2 cm-2 fluid density. Therefore or F mg Ahpg P=-=-=--=hpg A A A or The pressure to which a fluid height corresponds depends on the density of the P = 80.09 kPa = 0.8009 bar ftuid, which depends on its identity and temperature, and on the local ;lcceleration of gravity. Thus the torr is the pressure equivalent of I millimeter ..J,finercury at O·C in a standard gravitational field and is equal to 133.322 Pa. 1.7 WORK Another unit of pressure is the standard atmosphere (atm), the approximate average pressure exerted by the earth's atmosphere at sea level, defined as Work W is done whenever a force acts through a distance. The quantity of work 101,325 Pa, 101.325 kPa, or 0.101325 MPa. The bar, an SI unit equal to 10' Pa, done is defined by the equation is roughly the size of the atmosphere. dW= Fdl (1.1) Most pressure gauges give readings which are the difference between the pressure of interest and the pressure of the surrounding atmosphere. These where F is the component of the force acting in the direction of the displacement readings are known as gauge pressures, and can be converted to absolute pressures dt This equation must be integrated if the work for a finite process is required. by addition of the barometric pressure. Absolute pressures must be used in In engineering thermodynamics an important type of work is that which thermodynamic calculations. accompanies a change in volume of a ftuid. Consider the compression or expansion of a ftuid in a cylinder caused by the movement of a piston. The force Example 1.3 A dead-weight gauge with a l-cm-diameter piston is used to measure exerted by the piston on the ftuid is equal to the product of the piston area and pressures very accurately. In a particular instance a mass of 6.14 kg (including piston the pressure of the ftuid. The displacement of the piston is equal to the volume anQ pan) brings it into balance. If the local acceleqltion of gravity is 9.82 m S-2, what change of the ftuid divided by the area of the piston. Equation (1.1) therefore is the gauge pressure being measured? If the barometric pressure is 748(torr), what becomes is the absolute pressure? V dW=PAd­ SOLUTION The force exerted by gravity on the piston, pan, and weights is A F = mg = (6.14)(9.82) = 60.295 N or, since A is constant, .... F 60.295 -2 dW= PdV (1.2) Gauge pressure = A = (1/4)( ,,)(1)2 = 76.77 N em Integrating, The absolute pressure is therefore v, P = 76.77 + (748)(0.013332) = 86.74 N em-2 W= PdV (1.3) Iv, 12 INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS INTRODUCTION 13

with Newton's second law becomes

dW = madl

By definition the acceleration is a = du/ dt, where u is the velocity of the body. Thus p du dW= m-dl dt which may be written dl dW= m-du dt Since the definition of velocity is u = dl/ dt, the expression for work becomes v Figure 1.3 PV diagram. dW= mudu This equation may now be integrated for a finite change in velocity from u, to u,: Equation (1.3) is an expression for the work done as a result of a finite compression or expllnsion process. t This kind of work can be represented as an W=m "' udu=m (u'2_~ u') area on a pressure-vs.-volume (PV) diagram, such as is shown in Fig. 1.3. In this fUl 2 2 case a gas having an initial volume V, at pressure P, is compressed to volume or V, at pressure P, along the path shown from I to 2. This path relates the pressure at any point during the process to the volume. The work required for the process W = m2u~ _ m;i = a( mn (1.4) is given by Eq. (1.3) and is represented on Fig. 1.3 by the area under the curve. The SI unit of work is the newton-meter or joule, symbol J. In the English Each of the quantities !mu' in Eq. (1.4) is a kinetic energy, a term introduced engineering system the unit often used is the foot-pound force (ft Ib,). by Lord Kelvint in 1856. Thus, by definition, (1.5) 1.8 ENERGY Equation (1.4) shows that the work done on a body in accelerating it from an initial velocity u, to a final velocity u, is equal to the change in kinetic energy The general principle of conservation of energy was established about 1850. The of the body. Conversely, if a moving body is decelerated by the action of a germ of this principle as it applies to mechanics was implicit in the work of resisting force, the work done by the body is equal to its change in kinetic energy. Galileo (1564-1642) and Isaac Newton (1642-1726). Indeed, it follows almost In the SI system of units with mass in kg and velocity in m s -', kinetic energy automatically from Newton's second law of motion once work is defined as the EK has the units of kg m' s-'. Since the newton is the composite unit kg m s-', product of force and displacement. No such concept existed until 1826, when it EK is measured in newton-meters or joules. In accord with Eq. (1.4), this is the was introduced by the French mathematician J. V. Poncelet at the suggestion of unit of work. G. G. Coriolis, a French engineer. The word force (or the Latin vis) was used In the English engineering system, kinetic energy is expressed as !mu'/ goo not only in the sense described by NeWton in his laws of motion, but also was where g, has the value 32.1740 and the units (Ibm )(ft)(lbf )-'(s)-'. Thus the unit applied to the quantities we now define as work and potential and kinetic energy. of kinetic energy in this system is This ambiguity precluded for some time the development of any general principle E - mu' _ (Ib )(ft),(s)-' _ fi of mechanics beyond Newton's laws of motion. m K - 2g, - (lb )(ft)(Ib,) '(s) 2 - ( t Ib,) Several useful relationships follow from the definition of work as a quantita­ m tive and unambiguous physical entity. If a body of mass m is acted upon by the Dimensional cd'nsistency here requires the inclusion of gc. force F during a differential interval of time dt, the displacement of the body is dL The work done by the force F is given by Eq. (1.1), which when combined t Lord Kelvin, or William Thomson (1824-1907), was an English physicist who, along with the German physicist Rudolf Clausius (1822-1888). laid the foundations for the modem science of t However. see Sec. 2.9 for limitations on its application. thermodynamics. INTROOUCTION 15 14 INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS

If a body of mass m is raised from an initial elevation z, to a final elevation In the English engineering system, potential energy is expressed as mzg / go' Thus the unit of potential energy in this system is z an upward force at least equal to the weight of the body must be exerted on itand this force must move through the distance z, - Z,. Since the weight of the E _ mzg _ (Ibm)(ft)(ft)(s)-' (ft Ib,) b~dy is the force of gravity on it, the minimum force required is given by Newton's p - g, - (lbm)(ft)(lb,) '(s) , law as Again, g, must be included for dimensional consistency. F=ma=mg In any examination of physical processes, an attempt is made to find or to define quantities which remain constant regardless of the changes which occur, where 9 is the local acceleration of gravity. The minimum work required to raise One such quantity, early recognized in the development of mechanics, is mass. the body is the product of this force and the change in elevation: The great utility of the law of conservation of mass as a general principle in science suggests that further principles of conservation should be of comparable value. Thus the development of the concept of energy logically led to the principle of its conservation in mechanical processes. If a body is given energy when it is or elevated, then the body should conserve or retain this energy until it performs W = mz,g - mz,g = Il(mzg) (1.6) the work of which it is capable. An elevated body, allowed to fall freely, should gain in kinetic energy what it loses in potential energy so that its capacity for We see from Eq. (1.6) that the work done on the body in raising it is equal to doing work remains unchanged. For a freely falling body, we should be able to the change in the quantity mzg. Conversely, if the body is lowered against a write: resisting force equal to its weight, the work done by the body is equal to the change in the quantity mzg. Equation (1.6) is similar in form to Eq. (1.4), and both show that the work done is equal to the change in a quantity which describes or the condition of the body in relation to its surroundings. In each case the work mu~ mui performed can be recovered by carrying out the reverse process and returning 2-2+ mz,g - mz,g = 0 the body to its initial condition. This observation leads naturally to the thought that, if the work done on a body in accelerating it or in elevating it can be The validity of this equation has been confirmed by countless experiments. Success subsequently recovered, then the body by virtue of its velocity or elevation must in application to freely falling bodies led to the generalization of the principle contain the ability or capacity to do this work. This concept proved so useful in of energy conservation to apply to all purely mechanical processes, Ample experi­ rigid-body mechanics that the capacity of a body for doing work was given the mental evidence to justify this generalization was readily obtained. name energy, a word derived from the Greek and meaning "in work." Hence the Other forms of mechanical energy besides kinetic and gravitational potential work of accelerating a body is said to produce a change in its kinetic energy, or energy are possible. The most obvious is potential energy of configuration. When a spring is compressed, work is done by an external force. Since the spring can later perform this work against a resisting force, the spring possesses capacity W = IlEK = Il -2-mu') ( for doing work. This is potential energy of configuration. Energy of the same form exists in a stretched rubber band or in a bar of metal deformed in the elastic and the work done on a body in elevating it is said to produce a change in its region. potential energy, or To increase the generality of the principle of conservation of energy in W = IlEp = Il(mzg) mechanics, we look upon work itself as a form of energy. This is clearly permis­ sible, because both kinetic- and potential-energy changes are equal to the work Thus potential energy is defined as done in producing them [Eqs. ( 1.4) and (1.6)]. However, work is energy in transit and is never re!\l!.rded as residing in a body. When work is done and does not Ep = mzg (1.7) appear simultaneously as work elsewhere, it is converted into another form of energy. This term was first proposed in 1853 by the Scottish engineer Willia,m Rankine (1820-1872), In the SI system of units with mass in kg, elevation in m, and the The body or assemblage on which attention is focused is called the system. acceleration of gravity in m s-', potential energy has the units of kg m' s-'. This All else is called the surroundings. When work is done, it is done by the surround­ is the newton-meter or joule, the unit of work, in agreement with Eq. (1.6). ings on the system, or vice versa, and energy is transferred from the surroundings 16 INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS INTRODUCTION 17 to the system, or the reverse. It is only during this transfer that the form of energy However, Exz and EI\ are zero. Therefore known as work exists. In contrast, kinetic and potential energy reside with the E ) = E = 2,450,000 J system. Their values, however, are measured with reference to the surroundings, K pl i.e., kinetic energy depends on velocity with respect to the surroundings, and Since E K, = !m"~, potential energy depends on elevation with respect to a datum level. Changes in , 2EK, (2)(2,450,000) kinetic and potential energy do not depend on these reference conditions, pro­ "3 = m 2,500 vided they are fixed. whence Example 1.5 An elevator with a mass of 2,500 kg rests at a level of 10m above the "3 = 44.27 m S-I base of an elevator shaft. It is raised to 100m above the base of the shaft, where the p (e) f1E •Ptl". + f1EK.,,!ev.u.r = 0 cable holding it breaks. The elevator falls freely to the base of the shaft and strikes a strong spring. The spring is designed to bring the elevator to rest and, by means of Since the initial potential energy of the spring and the final kinetic energy of the a catch arrangement, to hold the elevator at the position of maximum spring com­ elevator are zero, the final potential energy of the spring must equal the kinetic energy pression. Assuming the entire process to be frictionless, and taking 9 = 9.8 m S-2, of the elevator just before it strikes the spring. Thus the final potential energy of the calculate: spring is 2,450,000 J. (a) The potential energy of the elevator in its initial position relative to the base (f) If the elevator and the spring together are taken as the system, the initial of the shaft. energy of the system is the potential energy of the elevator, or 245,000 J. The total (b) The work done in raising the elevator. energy of the system can change only if work is transferred between it and the (c) The potential energy of the elevator in its highest position relative to the surroundings. As the elevator is raised, work is done on the system by the surroundings base of the shaft. in Ule, amount of 2,205,000 J. Thus the energy of the system when the elevator reaches (d) The velocity and kinetic energy of the elevator just before it strikes the spring. its maximum height is 245,000 + 2,205,000 = 2,450,000 1. Subsequent changes occur (e) The potential energy of the compressed spring. entirely within the system, with no work transfer between the system and surroundings. (f) The energy of the system consisting of the elevator and spring (I) at the Hence the total energy of the system remains constant at 2,450,000 J. It merely changes start of the process, (2) when the elevator reaches its maximum height, (3) just before from potential energy of position (elevation) of the elevator to kinetic energy of the the elevator strikes the spring, and (4) after the elevator has come to rest. elevator to potential energy of configuration of the spring. This example serves to illustrate the application of the law of conservation of SOLUTION Let SUbscript I designate the initial conditions; subscript 2, conditions mechanical energy. However, the entire process is assumed to occur without friction; when the elevator is at its highest position; and SUbscript 3, conditions just before the results obtained are exact only for such an idealized process. the elevator strikes the spring. (a) By Eq. (1.7), During the period of development of the law of conservation of mechanical energy, heat was not generally recognized as a form of energy, but was considered Ep , = mz,g = (2,500)(10)(9.8) = 245,000 1 an indestructible fluid called caloric. This concept was so firmly entrenched that no connection was made between heat resulting from friction and the established (b) W = J" Fdl = J" mgdl = mg(z, - z,) z, z) forms of energy, and the law of conservation of energy was limited in application whence to frictionless mechanical processes. Such a limitation is no longer appropriate; the concept that heat like work is energy in transit gained acceptance during the W = (2,500)(9.8)(100 - 10) = 2,205,000 1 years following 1850, largely on account of the classic experiments of J. P. Joule

(e) Ep, = mz,g = (2,500)(100)(9.8) = 2,450,0001 (1818-1889), a brewer of Manchester, England. These experiments are considered in detail in Chap. 2, but first we examine some of the characteristics of heat. Note that W = Ep2 - Epl • (d) From the principle of conservation of mechanical energy, one may write that the sum of the kinetic- and potential-energy changes during the process from 1.9 HEAT ... conditions 2 to 3 is zero; that is, We know from experience that a hot object brought in contact with a cold object becomes cooler, whereas the cold object becomes warmer. A reasonable view is or that something is transferred from the hot object to the cold one, and we call that something heat Q. Two theories of heat developed by the Greek philosophers 18 INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS INTRODUCTION 19 have been in contention until modern tillies. The one most generally accepted as being stored within a body. Like work, it exists only as energy in transit from until the middle of the nineteenth century was that heat is a weightless and one body to another, or between a system and its surroundings. When energy in indestructible substance called caloric. The other represented heat as connected the form of heat is added to a body, it is stored not as heat but as kinetic and in some way with motion, either of the ultimate particles of a body or of some potential energy of the atoms and molecules making up the body. Not surprisingly, medium permeating all matter. This latter view was held by Francis Bacon, the energy theory of heat did not prevail until the atomic theory of matter was Newton, Robert Boyle, and others during the seventeenth century. Without the well established. concept of energy this view could not be exploited, and by the middle of the In spite of the transient nature of heat, it is often thought of in terms of its eighteenth century the caloric theory of heat gained ascendancy. However, a few effects on the body from which or to which it is transferred. As a matter of fact men of science did retain the other view, notably Benjamin Thompsont (1753- until about 1930 definitions of the quantitative units of heat were based on th~ 1814) and Sir Humphrey Davy (1778-1829). Both submitted experimental temperature changes of a unit mass of water. Thus the calorie was long defined evidence contrary to the caloric theory of heat, but their work went unheeded. as that quantity of heat which must be transferred to one gram of water to raise Moreover, the steam engine, a working example of the conversion of heat into its temperature one degree Celsius. Likewise, the British thermal unit, or (Btu), work, had been perfected by James Watt (1736-1819) and was in common use was defined as that quantity of heat which must be transferred to one pound at the time. mass of water to raise its temperature one degree Fahrenheit. Although these One notable advance in the theory of heat was made by Joseph Black definitions provide a "feel" for the size of heat units, they depend on the accuracy (1728-1799), a Scottish chemist and a collaborator of James Watt. Prior to Black's of experiments made with water and are thus subject to change with each time no distinction was made between heat and temperature, just as no distinction incre~singly accurate measurement. The calorie and (Btu) are now recognized was made between force and work. Temperature was regarded as the measure as umts of energy, and are defined in relation to the joule, the only SI unit of of the quantity of heat or caloric in a body, and a thermometer reading was energy. It is defined as 1 N m, and is therefore equal to the mechanical work referred to as a "number of degrees of heat." In fact, the word temperature still done when a force of one newton acts through a distance of one meter. All other had its archaic meaning of mixture or blend. Thus a given temperature indicated energy u~its ar~ defined as multiples of the joule. The foot-pound jorce, for a given mixture or blend of caloric with matter. Black correctly recognized example, IS eqUivalent to 1.3558179J, and the calorie to 4.184OJ. The SI unit of temperature as a property which must be carefully distinguished from quantity power is the watt, symbol W, defined as an energy rate of one joule per second. of heat. In addition, he showed experimentally that different substances of the Appendix A gives an extensive table of conversion factors for energy as well same mass vary in their capacity to absorb heat when they are warmed through as for other units. . the same temperature range. Moreover, he was the discoverer of latent heat. In spite of the difficulty of explaining these phenomena by the caloric theory, Black supported this theory throughout his life. Here the matter rested until near the PROBLEMS middle of the nineteenth century. Among the early champions of the energy concept of heat were Mohr, Mayer, 1.1 Using data given in Table 1.3, confirm one of the results given in the last three columns of Table 1.4. and Helmholtz in Germany; Colding, a Dane; and especially James P. Joule in England. Joule presented the experimental evidence which conclusively demon­ 1.2 Pr~ssures up to 3.000 bar are measured with a dead-weight gauge. The piston diameter is 0.35 cm. What IS the approximate mass in kg of the weights required? strated the energy theory, and thus made possible the generalization of the law 1.3 ,:essures up to 3.000(atm) are measured With a'dead-weight gauge. The piston diameter is of conservation of energy to include heat. The concept of heat as a form of energy 0.14(m). What is the approximate mass in (Ibm) of the weights required? is now universally accepted and is implicit in the modern science of thermody­ 0 1.4 A mercury manometer at 20 e and open at one end to the atmosphere reads 38.72 cm. The local namics. ~cceleration of gravity is 9.790 m s-z. Atmospheric pressure is 99.24 kPa. What is the absolute pressure One of the most important observations about heat is that it always flows 10 kPa being measured '! from a higher temperature to a lower one. This leads to the concept of temperature 1.5 A mercury manometer at 75(OF) and open at one end to the atmosphere reads 16.810n). The as the driving force for the transfer of energy as heat. More precisely, the rate local acceleration of gravity is 32.143(ft)(s)-z. Atmospheric pressure is 29.480n Hg). What is the of heat transfer from one body to another is proportional to the temperature absolute pressure in (psi~ being measured? difference between the two bodies; when there is no temperature difference, there ~~. An. instrument to measure the acceleration of gravity on Mars is constructed of a spring from Ich IS suspended a mass of 0.24 kg. At a place on earth where the local acceleration of gravity is is no net transfer of heat. In the thermodynamic sense, heat is never !egarded 9.80ms-2 th . t d 061 Wh h· . . . ,e spnng ex en s . em. en t e mstrument package IS landed on Mars. It radios the tnformation that the spring is extended 0.20 em. What is the Martian acceleration of gravity? t Better known as Count Rumford. Born in Woburn. Mass .• unsympathetic to the American cause 1.7 A group of engineers has landed on the moon, and would like to detennine the mass of several during the Revolution. he spent most of his extraordinary Jife in Europe. unusual rocks. They have a spring scale calibrated to read pounds mass at a location where the ". INTRODUCTION TO CHEMICAL ENGINEERING THERMODYNAMICS apceleration of gravity is 32.20(ft)(S)-2. One of the moon rocks gives a reading of 25 on the scale. What is its mass? What is its weight on the moon? Take 9 = 5.47(ft)(s)-2. moon CHAPTER .,8 Agas is confined by a piston. 5(in) in diameter, on which rests a weight. The mass of the piston ¥d weight together is 6O(Ib ). The local acceleration of gravity is 32.13(ft)(s)-2, and atmospheric m TWO f)ressure is 30.16(in Hg). (a) What is the force in (Ibr) exerted on the gas by the atmosphere, the piston. and the weight, THE FIRST LAW AND ~suming no friction between the piston and cylinder? (b) What is the pressure of the gas in (psia)? OTHER BASIC CONCEPTS (c) If the gas in the cylinder is heated. it expands. pushing the piston and weight upward. If tfle piston and weight are raised 15(in). what is the work done by the gas in (ft lbr)? What is the cbange in potential energy of the piston and weight? 1.9 A gas is confined by a pi~ton, 10 em in diameter, on which rests a weight. The mass of the piston and weight together is 30 kg. The local acceleration of gravity is 9.805 m S-2, and atmospheric pressure is 101.22 kPa. (a) What is the force in newtons exerted on the gas by the atmosphere, the piston, and the weight, assuming no friction between the piston and cylinder? (b) What is the pressure of the gas in kPa? (c) If the gas in the cylinder is heated, it expands, pushing the piston and weight upward. If the piston and weight are raised 40 cm, what is the work done by the gas in kJ? What is the change in potential energy of the piston and weight? 1.10 Verify that the SI unit of kinetic and potential energy is the joule. 1.11 An automobile having a mass of 1,500 kg is traveling at 25 m S-I. What is its kinetic energy in kJ? How much work must be done to bring it to a stop? 3 1.12 Liquid water at O°C and atmospheric pressure has a density of 1.000 g em- . At the same 3 conditions, ice has a density of 0.917 g em- • How much work is done at these conditions by 1 kg of ice as it melts to liquid water?

2.1 JOULE'S EXPERIMENTS

During the years 1840-1878, J. P. Joulet carried out careful experiments on the nature of heat and work. These experiments are fundamental to an under­ standing of the first law of thermodynamics and of the underlying concept of energy. In their essential elements Joule's experiments were simple enough, but he took elaborate precautions to ensure accuracy. In his most famous series of experiments, he placed measured amounts of water in an insulated container and agitated the water with a rotating stirrer. The amounts of work done on the water by the stirrer were accurately measured, and the temperature changes of the water were carefully noted. He found that a fixed amount of work was required per unit mass of water for every degree of temperature rise caused by the stirring. The original temperature of the water could then be restored by the transfer of heat through siIRJlle contact with a cooler object. Thus Joule was able to show conclusively that a quantitative relationship exists between work and heat and, therefore, that heat is a form of energy.

t For a fascinating account of Joule's celebrated experiments, see T. W. Chalmers, Historic Researches, chap. II, Scribner. New York, 1952.