Synergistically, these two tacks are intended to impart a deep understanding of ther- modynamics.1 In demonstrating a deep understanding, you will need to do more than regurgitate isolated facts and fi nd the right equation to “plug and chug.” Instead, you will need to search for connections and patterns in the material, understand the physical meaning of the equations you use, and creatively apply the fundamental principles that have been covered to entirely new problems. In fact, it is through this depth of learn- ing that you will be able to transfer the synthesized information you are learning in the classroom and usefully and creatively apply it to new problems in the fi eld or in the lab as a professional chemical engineer.
► 1.2 PRELIMINARY CONCEPTS—THE LANGUAGE OF THERMO
In engineering and science, we try to be precise with the language that we use. This exactness allows us to translate the concepts we develop into quantitative, mathematical form.2 We are then able to use the rules of mathematics to further develop relationships and solve problems. This section introduces some fundamental concepts and defi nitions that we will use as a foundation for constructing the laws of thermodynamics and quan- tifying them with mathematics.
In thermodynamics, the universe represents all measured space. It is not very conveni- ent, however, to consider the entire universe every time we need to do a calculation.
Therefore, we break down the universe into the region in which we are interested, the system, and the rest of the universe, the surroundings. The system is usually chosen so that it contains the substance of interest, but not the physical apparatus itself. It may be of fi xed volume, or its volume may change with time. Similarly, it may be of fi xed compo- sition, or the composition may change due to mass fl ow or chemical reaction. The system is separated from the surroundings by its boundary. The boundary may be real and physical, or it may be an imaginary construct. There are times when a judicious choice of the system and its boundary saves a great deal of computational effort.
In an open system both mass and energy can fl ow across the boundary. In a closed system no mass fl ows across the boundary. We call the system isolated if neither mass nor energy crosses its boundaries. You will fi nd that some refer to an open system as a control volume and its boundary as a control surface.
For example, say we wish to study the piston–cylinder assembly in Figure 1.1.
The usual choice of system, surroundings, and boundary are labeled. The boundary is depicted by the dashed line just inside the walls of the cylinder and below the piston.
The system contains the gas within the piston–cylinder assembly but not the physical housing. The surroundings are on the other side of the boundary and comprise the rest of the universe. Likewise the system, surroundings, and boundary of an open system are labeled in Figure 1.2. In this case, the inlet and outlet fl ow streams, labeled “in”
and “out,” respectively, allow mass to fl ow into and out of the system, across the system boundary.
Thermodynamic Systems
1 For more discussion on deep learning vs. shallow learning in engineering education, see Philip C. Wancat,
“Engineering Education: Not Enough Education and Not Enough Engineering,” 2nd International Conference on Teaching Science for Technology at the Tertiary Level, Stockholm, Sweden, June 14, 1997.
2 It can be argued that the ultimate language of science and engineering is mathematics.
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4 ► Chapter 1. Measured Thermodynamic Properties and Other Basic Concepts
The substance contained within a system can be characterized by its properties. These include measured properties of volume, pressure, and temperature. The properties of the gas in Figure 1.1 are labeled as T1, the temperature at which it exists; P1, its pressure;
and v1, its molar volume. The properties of the open system depicted in Figure 1.2 are also labeled, Tsys and Psys. In this case, we can characterize the properties of the fl uid in the inlet and outlet streams as well, as shown in the fi gure. Here n˙ represents the molar fl ow rate into and out of the system. As we develop and apply the laws of thermodynam- ics, we will learn about other properties; for example, internal energy, enthalpy, entropy, and Gibbs energy are all useful thermodynamic properties.
Thermodynamic properties can be either extensive or intensive. Extensive proper- ties depend on the size of the system while intensive properties do not. In other words, extensive properties are additive; intensive properties are not additive. An easy way to test whether a property is intensive or extensive is to ask yourself, “Would the value for this property change if I divided the system in half?” If the answer is “no,” the property is inten- sive. If the answer is “yes,” the property is extensive. For example, if we divide the system depicted in Figure 1.1 in half, the temperature on either side remains the same. Thus, the value of temperature does not change, and we conclude that temperature is intensive.
Many properties can be expressed in both extensive and intensive forms. We must be careful with our nomenclature to distinguish between the different forms of these properties. We will use a capital letter for the extensive form of such a thermodynamic property. For example, extensive volume would be V of 3m34. The intensive form will be lowercase. We denote molar volume with a lowercase v 3m3/mol4 and specifi c volume by v^ 3m3/kg4. On the other hand, pressure and temperature are always intensive and are written P and T, by convention.
Properties
Figure 1.1 Schematic of a piston–cylinder assembly.
The system, surroundings, and boundary are delineated.
State 1
=
System
Boundary Psurr
P1 T1
V1
v1 n
Surroundings m
m
Figure 1.2 Schematic of an open system into and out of which mass flows. The system, surroundings, and boundary are delineated.
in out
System
Surroundings
Boundary
Tout Tsys
Psys
Pout
vout
Tin nin
Pin
vin
nout
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1.2 Preliminary Concepts—The Language of Thermo ◄ 5
The thermodynamic state of a system is the condition in which we fi nd the system at any given time. The state fi xes the values of a substance’s intensive properties. Thus, two systems comprised of the same substance whose intensive properties have iden- tical values are in the same state. The system in Figure 1.1 is in state 1. Hence, we label the properties with a subscript “1.” A system is said to undergo a process when it goes from one thermodynamic state to another. Figure 1.3 illustrates a process instigated by removing a block of mass m from the piston of Figure 1.1. The result- ing force imbalance will cause the gas to expand and the piston to rise. As the gas expands, its pressure will drop. The expansion process will continue until the forces once again balance. Once the piston comes to rest, the system is in a new state, state 2. State 2 is defi ned by the properties T2, P2 and v2. The expansion process takes the system from state 1 to state 2. As the dashed line in Figure 1.3 illustrates, we have chosen our system boundary so that it expands with the piston during the process.
Thus, no mass fl ows across the boundary and we have a closed system. Alternatively, we could have chosen a boundary that makes the volume of the system constant. In that case, mass would fl ow across the system boundary as the piston expands, mak- ing it an open system. In general, the former choice is more convenient for solving problems.
Similarly, a process is depicted for the open system in Figure 1.2. However, we view this process slightly differently. In this case, the fl uid enters the system in the inlet stream at a given state “in,” with properties Tin, Pin, and vin. It undergoes the process in the system and changes state. Thus, it exits in a different state, with properties Tout, Pout, and vout.
During a process, at least some of the properties of the substances contained in the system change. In an adiabatic process, no heat transfer occurs across the system boundary. In an isothermal process, the temperature of the system remains constant.
Similarly, isobaric and isochoric processes occur at constant pressure and volume, respectively.
Processes
Figure 1.3 Schematic of a piston–cylinder assembly undergoing an expansion process from state 1 to state 2. This process is initiated by removal of a block of mass m.
State 1 State 2
Process
P2
T2
=V2
v2 n P1
T1
=V1
v1 n
m m
m
Psurr
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6 ► Chapter 1. Measured Thermodynamic Properties and Other Basic Concepts
A given phase of matter is characterized by both uniform physical structure and uniform chemical composition. It can be solid, liquid, or gas. The bonds between the atoms in a solid hold them in a specifi c position relative to other atoms in the solid. However, they are free to vibrate about this fi xed position. A solid is called crystalline if it has a long- range, periodic order. The spatial arrangement in which the atoms are bonded is termed the lattice structure. A given substance can exist in several different crystalline lattice structures. Each different crystal structure represents a different phase, since the physi- cal structure is different. For example, solid carbon can exist in the diamond phase or the graphite phase. A solid with no long-range order is called amorphous. Like a solid, mol- ecules within the liquid phase are in close proximity to one another due to intermolecular attractive forces. However, the molecules in a liquid are not fi xed in place by directional bonds; rather, they are in motion, free to move relative to one another. Multicomponent liquid mixtures can form different phases if the composition of the species differs in dif- ferent regions. For example, while oil and water can coexist as liquids, they are consid- ered separate liquid phases, since their compositions differ. Similarly, solids of different composition can coexist in different phases. Gas molecules show relatively weak intermo- lecular interactions. They move about to fi ll the entire volume of the container in which they are housed. This movement occurs in a random manner as the molecules continually change direction as they collide with one another and bounce off the container surfaces.
More than one phase can coexist within the system at equilibrium. When this phe- nomenon occurs, a phase boundary separates the phases from each other. One of the major topics in chemical thermodynamics, phase equilibrium, is used to determine the chemical compositions of the different phases that coexist in a given mixture at a speci- fi ed temperature and pressure.
Phases of Matter
Length Scales
In this text, we will refer to three length scales: the macroscopic, microscopic, and molecu- lar. The macroscopic scale is the largest; it represents the bulk systems we observe in everyday life. We will often consider the entire macroscopic system to be in a uniform thermodynamic state. In this case, its properties (e.g., T, P, v) are uniform throughout the Hypothetical Paths
The values of thermodynamic properties do not depend on the process (i.e., path) through which the system arrived at its state; they depend only on the state itself. Thus, the change in a given property between states 1 and 2 will be the same for any process that starts at state 1 and ends at state 2. This aspect of thermodynamic properties is very useful in solving problems; we will exploit it often. We will devise hypothetical paths between thermodynamic states so that we can use data that are readily available to more easily perform computation. Thus, we may choose the following hypothetical path to calculate the change in any property for the process illustrated in Figure 1.3: We fi rst consider an isothermal expansion from P1, T1 to P2, T1. We then execute an isobaric cooling from P2, T1 to P2, T2. The hypothetical path takes us to the same state as the real process—so all the properties must be identical. Since properties depend only on the state itself, they are often termed state functions. On the other hand, there are quanti- ties that we will be interested in, such as heat and work, that depend on path. These are referred to as path functions. When calculating values for these quantities, we must use the real path the system takes during the process.
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