Chemical and engineering thermodynamics sandler pdf download

In writing the first edition of this book I had two objectives that have been retained in the succeeding editions. The other objective was to develop, organize and present material in sufficient detail for students to obtain a good understanding of the basic principles of thermodynamics and a proficiency in applying these principles to the solution of a large variety of energy flow and equilibrium problems.

Since the earlier editions largely met these goals, and since the principles of thermodynamics have not changed over the past decade, this edition is similar in structure to the earlier ones.

During this time, however, important changes in engineering education have taken place. The first is the increasing availability of powerful desktop computers and computational software, along with well-developed and easy-to-use process simulation software.

Another is the increasing application of chemical engineering thermodynamics principles and models to new areas of technology such as polymers, biotechnology, solid-state processing, and the environment. The current edition of this text includes applications that address each of these changes.

The availability of desktop computers and equation-solving software has now made it possible to closely align engineering science, industrial practice, and undergraduate education. In their dormitory rooms or at home, students can now perform sophisticated thermodynamics and phase equilibrium calculations similar to those they will encounter in industry. In this fifth edition, I provide several different methods for making such calculations.

The first is to utilize the set of programs I have developed for making specific types of calculations included in the fourth edition. These programs enable 1 the calculation of thermodynamic properties and vapor-liquid equilibrium of a pure fluid described by a cubic equation of state; 2 the calculation of the thermodynamic properties and phase equilibria for a multicomponent mixture described by a cubic equation of state; and 3 the prediction of activity coefficients in a mixture using the UNIFAC group-contribution activity coefficient model.

These programs are available on the website for this book as both program-code and stand-alone executable modules; they are unchanged from the previous edition of this book. However, I suggest instead the use of the thermodynamics package in Aspen Plus R , which is continually updated and has an easy-to-use interface. Students who develop their own codes for such computer programs can achieve a thorough understanding of the methods required and the computational difficulties involved in solving complex problems without having to become experts in computer programming and numerical analysis.

Students who use my prepared codes will be able to solve interesting problems and concentrate on the subject matter at hand, namely, thermodynamics, without being distracted by computational methods, algorithms, and programming languages. These equation-solving programs are, in my view, valuable educational tools; but there is no material in this textbook that requires their use. Whether to implement them or not is left to the discretion of the instructor.

More recently in engineering practice, these one-off thermodynamics programs written by textbook authors have been replaced by suites of programs, process simulators, that make it possible to quickly model a whole chemical plant using current unit operations and thermodynamics models, as well as to access enormous databanks of pure fluid and mixture thermodynamic data. I recognize, however, that there is no universal agreement on the use of a process simulator in, especially, an undergraduate thermodynamics course.

Indeed, there are those in my own department who argue against it. My argument for using process simulators in undergraduate instructional courses is two-fold.

For example, what happens to the vapor-liquid split and the compositions of each of the co-existing phases in a multi-component Joule-Thomson expansion if the inlet temperature or pressure is changed? Answering such what-if questions allows students to quickly develop an intuitive sense of the way processes behave, an understanding that otherwise might only be attained by repeated, tedious hand calculations. Second, using a process simulator introduces students to a tool they are likely to employ in their professional career.

Moreover, modern process-simulation software is generally bug-free, providing an easy-to-use interface that is the same for all problems. In this argument I have taken the middle road. By means of some of the illustrations and problems provided in this text, students will initially develop an understanding of the basic applications and methods of thermodynamics by doing hand calculations.

Then, once they understand the basic principles and methods, I encourage them to use process simulators rather than my previous programs to explore many additional, and more complicated, applications of thermodynamic principles. Whereas nothing in this new edition requires students or the instructor to use a process simulator, the illustrations do contain examples of the results of using a process simulator.

In addition, many opportunities for using process simulator software are provided in the numerous end-of-chapter problems. Furthermore, by using a process simulator the instructor can easily change the input parameters of a homework problem and obtain the solution, thereby providing unlimited opportunities for creating new problems.

I have chosen ASPEN because it appears to be the process simulator most widely used in industry and at colleges and universities, in the United States at least. Clearly, any other process simulation software could be employed, but in these cases users will need to develop their own input files. Since I am introducing ASPEN in this fifth edition, I have not updated the thermodynamics programs included in previous editions of this textbook, and they remain available on the website.

Still, I encourage the use of Aspen or other process-simulation software rather than these more primitive programs.

We refer to pressures on such a scale as gauge pressures, and will designate such a pressure as, for example, 30 psig.

Note that gauge pressures may be negative in partially or completely evacuated systems , zero, or positive, and errors in pressure measurement result from changes in atmospheric pressure from the gauge calibration conditions e.

We define the total pressure P to be equal to the sum of the gauge pressure P, and the ambient atmospheric pressure Pam. By accounting for the atmospheric pressure in this way we have, in fact, developed an absolute pressure scale; that is, a pressure scale whose zero is the lowest pressure attainable the pressure in a completely evacuated region of space.

One advantage of such a scale is its simplicity; the pressure is always a positive quantity and measurements do not have to be corrected for either fluctuations in atmospheric pressure or its change with height above sea level.

We will frequently be concerned with interrelations between the temperature, pressure, and specific volume of fluids. Pressure, temperature, and equilibrium 9 Table 1. Conse- quently, unless otherwise indicated, the term pressure in this book will refer to absolute pressure. The notation psia or merely psi will be used to denote pounds force per square inch absolute pressure.

Although pressure arises quite naturally from mechanics, the concept of temperature is more abstract. To the nonscientist temperature is a measure of hotness or coldness, and as such is not carefully defined, but rather is a quantity related to such things as physical comfort, cooking conditions, or the level of mercury or colored alcohol in a thermometer. To the scientist temperature is a precisely defined quantity, deeply rooted in the concept of equilibrium, and related to the energy content of a substance.

The origin of the formal definition of temperature is in the concept of thermal equilibrium. Consider a thermodynamic system composed of two subsystems that are in thermal contact, but do not interchange mass for example, the two subsystems may be two solids in contact, or liquids or gases separated by a thin, impenetrable barrier or membrane and are isolated from their surroundings. In accord with this observation, temperature is defined to be that system property which, if it has the same value for any two systems, indicates that these systems are in thermal equilibrium if they are in contact, or would be in thermal equilibrium if they were placed in thermal contact.

Although this definition provides the link between temperature and thermal equilibrium, it does not suggest a scale for temperature. If temperature is used only as an indicator of thermal equilibrium, any quantification or scale of temperature is satisfactory provided that it is generally understood and reproducible, though the accepted convention is that increasing hotness of a substance should correspond to increasing values of temperature.

An impor- tant consideration in developing a thermodynamic scale of temperature is that it, like all other aspects of thermodynamics, should be quite general and not depend on the properties of any one fluid such as the specific volume of liquid mercury. Some experimental evidence indicates that it should be possible to formulate a completely universal temperature scale.

The first indication came from the study of gases at densities so-low that intermolecular interactions are unimportant such gases are called ideal gases , where it was found that the product of the absolute pressure P and the molar volume V of any low-density gas away from its condensation line see Chapter 5 increases with increasing hotness.

To complete this low-density gas temperature scale it still remains to specify the constant R, or equivalently the size of a unit of temperature. This can be done in two equivalent ways. The first is to specify the value of T fora given value of PV and thus determine the constant R; the second is to choose two reproducible points on a hotness scale, and to arbitrarily decide how many units of T correspond to the difference in the product of PV at these two fixed points.

What is done, then, is to allow a low-density gas to achieve thermal equilibrium with water at its ice point and measure the product PV, and then repeat the process at the boiling temperature. One then decides how many units of temperature correspond to this measured difference in the product PY; the choice of units or degrees leads to the Kelvin temperature scale, while the use of degrees leads to the Rankine scale.

With either of these choices, the constant R can be evaluated for a given low-density gas. The important fact for the formulation of a universal temperature scale is that the constant R, and hence the temperature scales, determined in this way are the same for all low-density gases! Values of the gas constant R are given in Table 1. More common than the Rankine and Kelvin temperature scales, particularly for nonscientific uses of temperature, are the closely related Fahrenheit and Celsius scales.

Consequently, if the data for a thermodynamic calculation are not given in terms of absolute temperature, it will generally be necessary to convert these data to absolute temperatures using Eqs. The ideal gas thermometer is not convenient to use, however, both because of its mechanical construction see Fig. Therefore, common thermometers make use of thermometric properties of other materials; for example, the single-valued relation between temperature and the specific volume of liquid mercury Problem 1.

There are two steps in the construction of thermometers based on these other thermometric properties. First, fabrication of the device, such as sealing liquid mercury in an otherwise evacuated tube, and then the calibration of the thermometric indicator with a known temperature scale.

For each measurement the mercury reser- voir is raised or lowered until the mercury columnat the lefttouches an index mark. The pressure of the gas in the bulb is then equal to the atmospheric pressure plus the pressure due to the height of the mercury column. Energy transfer by any mechanism that involves mechanical motion of or across the system boundaries is called work.

Finally, it is possible to increase the energy of a system by supplying it with electrical energy in the form of an electrical current driven by a potential difference. This electrical energy can be converted into mechanical energy if the system contains an electric motor, it can increase the temperature of the system if it is dissipated through a resistor resistive heating , or it can be used to cause an electrochemical change in the system for example, recharging a Jead storage battery.

Throughout this book we consider the flow of electrical energy to be a form of work. The reason for this choice will become clear shortly. The amount of mechanical work is, from mechanics, equal to the product of the force exerted times the distance moved in the direction of the applied force.

Similarly, the electrical work is equal to the product of the current flow through the system, the potential difference across the system, and the time interval over which the current flow takes place. Therefore, the total amount of work supplied to a system is frequently easy to calculate. An important experimental observation, initially made by James Prescott Joule between the years and , is that a specified amount of energy can always be used in such a way as to produce the same temperature rise in a given mass of water, regardless of the precise mechanism or device used to supply the energy, and regardless of whether this energy is in the form of mechanical work, electrical work.

Suppose a sample of water at temperature T, is placed in a well-insulated container for example, a Dewar flask and, by the series of experiments in Table 1. Based on the experiments of Joule and others, we would expect to find that this energy determined by correcting the measurements of column 4 for the temperature rise of the container and the effects of column 5 to be precisely the same in all cases.

By comparing the first two experiments with the third and fourth, we conclude that there is an equivalence between mechanical energy or work and heat, in that precisely the same amount of energy was required to produce a given temperature rise, independent of whether this energy was delivered as heat or work. Furthermore, since both mechanical and electrical energy sources have been used see column 3 , there is similar equivalence between mechanical and electrical energy, and hence among all three energy forms.

Returning to the experiments of Table 1. The answer, of course, is that at the end of the experiment the temperature, and hence the molecular energy, of the water has increased. Consequently, the energy added to the water is now present as increased internal energy. It is possible to extract this increased internal energy by processes that return the water to its original temperature.

One could, for example, use the warm water to heat a metal bar. The important experimental observation here is that if you measured the temperature rise in the metal, which occurred in returning the water to its initial state, and compared it with the electrical or mechanical energy required to cause the same temperature rise in the metal, you would find that all the energy added to the water in raising its temperature could be recovered as heat by returning the water to its initial state, Thus, total energy has been conserved in the process.

The observation that energy has been conserved in this experiment is only one example of a quite general energy conservation principle which is based on a much wider range of experiments. The more general principle is that in any change of state, the total energy, which is the sum of the internal, kinetic, and potential energy of the system, heat, and electrical and mechanical work, is conserved. A more succinct statement is that energy is neither created nor destroyed, but may change in form.

Although heat and mechanical and electrical work are equivalent in that a given energy input, in any form, can be made to produce the same internal energy increase in —system, there is equally important difference among the various energy forms. To see this suppose that the internal energy of some system perhaps the water sample in the experiments just considered has been increased by increasing its temperature from T, to a higher temperature 72, and we now wish to recover the added energy by returning the system to its initial state at temperature T;.

It is clear that we can recover the added energy completely as a heat flow merely by putting the system in contact with another system at a lower temperature. There is, however, no process or device by which it is possible to convert all the added internal energy of the system to mechanical energy, even though the increased internal energy may have resulted from adding only mechanical energy to the system.

At most, only a portion of the increased internal energy can be recovered as mechanical energy, the remainder appearing as heat. This situation is not specific to the experi- ments discussed here; it occurs in all similar efforts to convert both heat and internal energy to work or mechanical energy.

This distinction is based on the general experimental observation that while, in principle, any form of mechani- cal energy can be completely converted to other forms of mechanical energy or thermal energy, only a fraction of thermal energy can be converted into mechanical energy.

In Chapter 3 we consider what this fraction is and what it depends on. The units of mechanical work arise quite naturally from its definition as the product of a force and a distance. The unit of electrical work is the volt-ampere-second or, equivalently, the watt-second. Heat, however, not having a mechanical definition, has traditionally been defined experimentally. These experimental definitions of heat units have proved unsatisfactory because the amount of heat in both the calorie and the BTU has been subject to continua] change as caloric measurement techniques improved.

Consequently, there are several different definitions of the unit calorie which differ by less than one part in a thousand. Current practice is to recognize the energy equivalence of heat and work, and to use a common energy unit for both. Thus, 1 BTU is defined to be equal to In this system seven basic units length, mass, time, electric current, temperature, amount of substance, and luminous intensity are identified and their values assigned.

All other scientific units such as those for energy, power, electrical potential difference, and resistance are derived from the basic units. Since SI units are not yet in common use we have made no attempt to use them, other than occasionally, in this text. For reference, Table 1. This international conference was one of a series which are convened periodically to obtain international agreement on questions of metrology.

Table 1. Derived units without assigned names Area square meter m Volume cubic meter mn Density kilogram per kgm? BTU Pressure: newton m? The questions we are asking then, is what sort of properties, and how many properties, must correspond if all the properties of both systems are to be identical? The fact that we are interested only in stable equilibrium states is sufficient to decide the type of properties needed to specify the equilibrium state.

First, since gradients in velocity, pressure, and temperature cannot be present in the equilibrium state, they do not enter into its characterization.

Next, since, as we saw in Sec. The remaining question, that of how many equilibrium properties are necessary to specify the equilibrium state of the system, can only be answered by experiment. The important experimental observation here is that an equilibrium state of a single-phase, one-component system in the absence of external electric and magnetic fields is completely specified if its mass and two other thermodynamic properties are given.

Thus, to go back to our example, if the second oxygen sample also weighs one pound, and if it were made to have the same temperature and pressure as the first sample, it would also be found to have the same volume, refractive index, etc. If, however, only the temperature of the second one-pound sample was set equal to that of the first sample, neither its pressure, nor any other physical property, would necessarily be the same as those of the first sample.

Consequently, the values of the density, refractive index, and more generally, all thermodynamic properties of an equilibrium single-component, single-phase fluid are completely fixed once the mass of the system and the values of at least two other system parameters are given. The specification of an equilibrium system can be made slightly simpler by recognizing that the variables used in thermodynamic descriptions are of two quite different types. To see this, consider a gas of mass M, which has a temperature T, pressure P, and is confined to a glass bulb of volume V.

Suppose that an identical glass bulb is also filled with mass M of the same gas, and heated to the same temperature T, Based on the discussion above, the pressure in the second glass bulb is also P. If these two bulbs are now connected to form a new system, the temperature and pressure of this composite system are unchanged from those of the separated systems, although the volume and mass of this new system are clearly twice that of the original single glass bulb.

What is this value of the pressure P? To know this we either have to have done the experiment sometime in the past, or know the exact functional relationship between T, V, and P for the fluid being considered. What is frequently done for fluids of scientific or engineering interest is to make a large number of measurements of P, V, and T, and then try to infer the volumetric equation of state for the fluid, that is, the mathematical relationship between the variables P, V, and T.

Similarly, measurements of U, V, and T are made to infer a thermal equation of state for the fluid. Alternatively, the data that have been obtained may be presented directly in graphical or tabular form. There are some complications in the description of thermodynamic states of systems. For certain idealized fluids, such as the ideal gas and the incompressible liquid both discussed in Sec. To be specific, the internal energy of the ideal gas is a function only of its temperature, and not its pressure or density.

Thus, the specification of the energy and temperature of an ideal gas contains no more information than specifying only its temperature, and is insufficient to determine its pressure. Similarly, if a liquid is incompressible, its molar volume will depend on temperature but not on the pressure exerted on it.

Consequently, specifying the temperature and the specific volume of an incompressible liquid contains no more information than specifying only its temperature. The ideal gas and the incompressible liquid are limiting cases of the behavior of real fluids, so that while the internal energy of a real gas depends on density and temperature, the density dependence may be quite weak, and the densities of most liquids are only weakly dependent on their pressure.

Therefore, while in principle any two state variables may be used to describe the thermodynamic state of a system, it is best to avoid the combinations of U and T in gases, and V and T in liquids and solids.

As was pointed out in the previous paragraphs, two state variables are needed to fix the thermodynamic state of an equilibrium system. The obvious next question is how does one specify the thermodynamic state of a nonequilib- rium system? This is clearly a much more complicated question to answer, and the detailed answer would involve a discussion of the relative time scales for changes imposed upon the system, and the changes that occur within the system as a result of chemical reaction, internal energy flows and fluid motion.

Such a discussion is beyond the scope of this book. The important observation is that if we do not consider very fast system changes as occur within a shock wave , nor systems that relax at a very slow, but perceptible rate for example, molten polymers , the equilibrium relationships between the fluid properties, such as the volumetric and thermal equations of state, are also satisfied in nonequilibrium flows on a point-by-point basis.

This is an important result, since it allows us to consider not only equilibrium phenomena in thermo- dynamics, but also energy flow problems involving distinctly nonequilibrium processes. We will try to do this by demonstrating how the complete structure of thermodynamics can be built from a number of important experimental observations, some of which have been introduced in this chapter, some of which are familiar from mechanics, and others which will be introduced in the following chapters.

For convenience, the most important of these observations are listed below. From classical mechanics and chemistry we have the following observa- tions: Experimental Observation 1. In any change of state except those involving nuclear reaction, which will not be considered in this book total mass is conserved. Experimental Observation 2. In any change of state total momentum is a conserved quantity.

In this chapter the following experimental facts have been mentioned: Experimental Observation 3 Section 1. In any change of state the total energy, which includes internal, potential, and kinetic energy, heat and work, is a conserved quantity.

Experimental Observation 4 Section 1. A flow of heat and a work flow are equivalent in that supplying a given amount of energy to a system in either of these forms can be. Heat and work, or more generally, thermal and mechanical energy, are not equivalent in the sense that mechanical energy can be completely converted into thermal energy, but thermal energy can be only partially converted into mechanical energy. Experimental Observation 5 Section 1.

A system that is not subject to forced flows of. This is the equilibrium state. Experimental Observation 6 Section 1. A system in equilibrium with its surroundings will never spontaneously revert to a nonequilibrium state. In fact, it is, by far, the most frequent case in engineering. It is the only case that will be considered in this book. Equilibrium states that arise naturally are stable to small disturbances.

Experimental Observation 8 Sections 1. The stable equilibrium state of a system is completely characterized by values of only equilibrium properties and not properties that describe the approach to equilibrium. For a single-component, single- phase system the values of only two state variables are needed to completely fix the thermodynamic state of the equilibrium system; the further specification of an extensive variable of the system fixes its size.

Experimental Observation 9 Section 1. The interrelationships that exist between the thermodynamic state variables for a fluid in equilibrium also prevail locally that is, at each point for a fluid not in equilibrium, provided the internal relaxation processes are rapid with respect to the rate at which changes are imposed on the system.

For fluids of interest in this book, this condition is satisfied. While we will not, in general, be interested in the detailed description of nonequilibrium systems, it is useful to note that the rates at which natural relaxation processes i. Experimental Observation If, however, were taken to be the mass of benzene in the system, the internal generation term for benzene would be positive, since benzene is produced by the chemical reaction.

Conversely, if were taken to be the mass of cyclohexane in the system, the internal generation term would be negative. In either case the magnitude of the internal generation term would depend on the rate of reaction. The balance equation Eq. We can also obtain an equation for computing the instantaneous rate of change of by letting the time interval At go to zero. This is done as follows.

There is, however, the important advantage of not having to formulate an expression for the internal generation term when using this equation for conserved quantities.

For example, to use the total mass balance to compute the rate of change of mass in the system, we need know only the mass flows into and out of the system.

On the other hand, to compute the rate of change of the mass of cyclohexane undergoing a dehydrogenation reaction in a chemical reactor, we would need data on the rate of reaction in the system, which may be a function of concentration, temperature, catalyst activity and structure, and other internal characteristics of the system.

Thus, a wealth of information may be needed to use the balance equation for the mass of cyclohexane, and, more generally, for any nonconserved quantity. Unfortunately, the study of thermodynamics sometimes requires the use of balance equations for nonconserved quantities. Conservation of mass 3 designated by the symbol M, we have, from Eq. Using M, to represent the mass flow rate into the system at the kth entry point, we have, from Eq.

Since we are interested only in pure fluids, we can divide Eqs. In Sec. Here we will demonstrate precisely how this integration is accom- plished. Integrating Eg. Equation 2. At steady flows 2. If the system consists of several distinct parts, for example, a gas and a liquid, or a gas and the piston and cylinder containing it, the total energy, which isan extensive property, is the sum of the energies of the constituent parts.

These are listed below: a Energy flow accompanying mass flow. As a fluid element enters or leaves the system, it carries with it internal, potential, and kinetic energy. We will use Q to denote the total rate of flow of heat into the system, so that Q is positive if energy in the form of heat flows into the system, and negative if heat flows from the system to its surroundings.

The total energy flow into the system due to work will be divided into several parts. The first part, called shaft work and denoted by the symbol W,, is the mechanical energy flow that occurs without a deformation of the system boundaries. For example, if the system under consideration were a steam turbine or an internal combustion engine, the rate of shaft work W, would be equal to the rate at which energy was transferred across the stationary system boundaries by the drive shaft or push rod.

Following the convention that energy flow into the system is positive, W, is positive if the surroundings do work on the system, and negative if the system does work on its surroundings. For convenience, the flow of electrical energy into or out of the system will be included in the shaft work term. The positive sign applies if electrical energy is being supplied to the system and the negative sign applies if the system is the source of electrical energy.

Work also results from the movement of the system boundaries. The pressure at the boundaries of a nonstationary system will be opposed by a the pressure of the environment surrounding the system, b inertial forces if the expansion or compression of the system results in an acceleration or deceleration of the surroundings, and c other external forces such as gravity.

As we shall see in Illustration 2. One additional flow of energy for systems open to the flow of mass must be included in the energy balance equation; it is more subtle than the energy flows considered above.

This is the energy flow that arises from the fact that as an element of fluid moves it does work on the fluid ahead of it, and the fluid behind it does work on it. Clearly each of these work terms are of the PAV type. To evaluate this energy flow term, which occurs only in systems open to the flow of mass, we will compute the net work done as one fluid element of mass AM, enters a system, such as the valve in Fig. The pressure of the fluid at the inlet side of the valve is P, and the fluid pressure at the outlet side is P2, so that we have: 2.

Figure 2. If this is not the case, Eq. This change is easily accomplished by recognizing that M. The changes in energy associated with either the kinetic energy or potential energy terms, especially for gases, are usually very small compared to the thermal internal energy terms, unless the fluid velocity is near the velocity of sound, the change in height is very large, or the system temperature is nearly constant.

This point will become evident in some of the examples and problems see particularly Illustration 2. Therefore, it is frequently possible to approximate Eqs. Table 2. This is easily obtained by integrating Eq.

If the thermodynamic properties of the fluid entering the system are independent of time even though the mass flow rate may depend on time , we have s. The usual procedure, then, is to try to choose a new system or subsystem for the description of the process in which these time-dependent flows do not occur or are more easily handled see Illustration 2.

For the study of thermodynamics it will be useful to have equations that relate the differential change in certain thermodynamic variables of the system to differential changes in other system properties.

Such equations can be obtained from the differential form of the mass and energy balances. It is part of the traditional notation of thermodynamics to use d to indicate a differential change in the property.

The mass and energy balance equations developed so far in this chapter can be used for the description of any process. As the first step in using these equations, it is necessary to choose a black-box system. The important fact for the student of thermodynamics to recognize is that processes occurring in nature are in no way influenced by our mathematical description of them.

Therefore, if our descriptions are correct, they must lead to the same final result for the system and its surroundings regardless of which system choice is made. This is demonstrated in the example below, where the same result is obtained by choosing for the system first a given mass of material and then a specified region in space. Establish this result by first writing the balance equations for a closed system consisting of some convenient element of mass, and then by writing the balance equations for the compressor and its contents, which is an open system.

This system is enclosed by the dotted lines in the figure below. Conservation of energy 45 Since the compressor is in steady-state operation, the amount of gas contained within it, and the properties of this gas, are constant. Thus, M. PVM; — P:V. Mz Now using Eq. Each of these terms is calculable as a f PdV type work term.

For the open system this work term has been included in the energy balance as a PVAM term so that it is the enthalpy, rather than the internal energy, of the flow streams that appear in the equation. The explicit [ PdV term that does appear in the open system energy balance represents only the work done as the system boundaries deform; this term is zero here unless the compressor the boundary of our system explodes.

Conservation of energy 41 choose to compute this sum from the closed system analysis on a mass of gas or from an open system analysis on a given volume in space. In the illustration below we consider another problem, the compression of a gas by two different processes, the first being a closed system piston and cylinder process and the second being a flow compressor process.

The origin of the difference in the flow and nonflow energy changes accompanying a change of state is easily identified by considering two different ways of compressing a mass M of gas in a piston and cylinder from T1, P, to T:, P. Here, however, it results from an energy requirement of M 4:— Hi in the flow compressor and the two pumping terms.

Find an expression relating the downstream gas temperature T; to P,, P,and T;. Since the gas flows through the valve rapidly, one can assume that there is no heat transfer to the gas. Also, the potential and kinetic energy terms can be neglected. We will consider the region of space that includes the flow obstruction indicated by the dashed line to be the system, though, as in Illustration 2.

It is not completely obvious that these two pressures should be the same. However, in the laboratory we find that the velocity of the flowing fluid will always adjust in such a way that the fluid exit and surroundings pressures are equal. Consequently, if we knew how the enthalpy of the gas depended on its temperature and pressure, we could use the known values of T;, Pi, and P2 to determine the unknown downstream temperature T:.

To proceed further we need constitutive information that is, an equation of state or experimental data interrelating H, T, and P.

Equations of state are discussed in the following section and much of Chapter 4. Joule to study departures from ideal gas behavior. The Joule-Thomson expansion, as it is called, is still used in the liquifaction of gases and in refrigeration processes. See Problems 3.