Physics
Thermodynamic Diagram
A thermodynamic diagram is a graphical representation of the relationships between different thermodynamic properties, such as pressure, volume, and temperature, for a given substance. These diagrams are used to analyze and visualize the behavior of substances undergoing thermodynamic processes, making it easier to understand and interpret complex thermodynamic concepts and principles.
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10 Key excerpts on "Thermodynamic Diagram"
- Lucien Borel, Daniel Favrat(Authors)
- 2010(Publication Date)
- PPUR(Publisher)
Convention The following convention is used to systematize all Thermodynamic Diagrams. When we, in a process represented in a diagram, wish to indicate an entity that is measured along one of the coordinate axis, we do not draw a measurement data, but rather a vector parallel to this axis, as shown in Figure 8.22. Generally speaking, the direction of the vector indicates the direction of the process, i.e., that its origin corresponds to the initial state and its extremity to the final state of the process. The algebraic value of the projection of the vector is positive or negative, depending on ln ln ln P P P P 1 0 1 0 − = Fig. 8.22 Convention of use of a Thermodynamic Diagram. Δ Δ 374 Thermodynamics and Energy Systems Analysis: from Energy to Exergy whether or not its direction is identical or opposite to the direction of the coordinate axis. For instance, considering the process 1-2 represented in the h-s diagram of Figure 8.22, we have (8.56) This convention is very convenient, since it allows, like the one linked to the symbol Δ, to utilize the resources of calculus. Other Thermodynamic Diagrams Acknowledging the multiplicity of the state functions, it is obvious that the number of combinations of independent state functions considered two by two is very large. Consequently, the number of conceivable diagrams is also significant. The choice of one or the other of these diagrams depends essentially on its use, i.e., on the prob- lem that needs to be solved. The other diagrams, often encountered in technical papers and representing the thermodynamic behavior of a simple system, are the following: • P-V (or Watt) diagram; • vP-P (or Amagat) diagram; • P-T diagram (cf. Figures 5.20 and 5.21); • v-h diagram; • ln v-h diagram; • P-h diagram; • T-h diagram; • u-s diagram; • and T- (or pinch) diagram. 8.4 PARAISOTHERMAL PROCESS 8.4.1 Introduction As demonstrated in Chapter 13, dealing with thermodynamic cycles, it is often desirable to use isothermal processes.
- John Reisel(Author)
- 2021(Publication Date)
- Cengage Learning EMEA(Publisher)
All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 71 3.2 Phase Diagrams volume or specific internal energy is. Those quantities depend on the relative amount of the water that is in liquid and in vapor form. Although P-v-T diagrams are useful in helping understand phases of a substance, they are often more cumbersome than nec- essary for illustrating a process that the sub- stance is undergoing. As such, we usually will rely on two-dimensional projections of this surface to illustrate thermodynamic processes. A P-T projection of water (such that the volume is into the page) is shown in Figure 3.3, and a P-T projection that is indicative of the behavior of most other sub- stances is shown in Figure 3.4. As can be seen in Figures 3.3 and 3.4, the diagrams are similar, with the exception being the slope of the line dividing the solid and liquid phases: this is a consequence of the feature of water expanding upon freezing, whereas most substances contract upon freezing. The lines between two phases represent states where both states exist. At the intersection of all three phases, there is a pressure and temperature where all three phases coexist. On a P-T diagram, this is called the triple point; however, it should be noted that this state exists at a range of specific volumes and FIGURE 3.2 A P-v-T surface for substances that contract upon freezing (most substances).
eBook - PDF- Robert DeHoff(Author)
- 2006(Publication Date)
- CRC Press(Publisher)
3. A universal absolute temperature scale exists and has a minimum value, defined to be absolute zero, and the entropy of all substances is the same at that temperature. More precise, mathematically formulated statements of the laws are developed in Chapter 3. In practice, the focus of thermodynamics is on a subset of the universe, called a system, (Figure 2.1). In order to apply thermodynamics, the first step is to identify the subset of the universe that encompasses the problem at hand. It is necessary to be explicit about the nature of the contents of the system, and the specific location and character of its boundary. 17 The condition of the system at the time of observation is described in terms of its properties, quantities that report aspects of the state of the system such as its temperature, T , its pressure, P , its volume, V , its chemical composition, and so on. As the system is caused to pass through a process its properties experience changes (Figure 2.1). A very common application of thermodynamics is a calculation of the changes that occur in the properties of some specified system as it is taken through some specified process. Thus, an important aspect of the development of thermodynamics is the deduction of relationships between the properties of a system, so that changes in some properties of interest, e.g., the entropy of the system, may be computed from information given or determined about changes in other properties of the system, e.g., temperature and pressure. An understanding of the structure of thermodynamics is aided greatly by deliberately organizing the presentation on the basis of a series of classifications, which compartmentalize these characteristics of the field, and thus permit a focus upon the subset of the thermodynamic apparatus that is appropriate to a specific problem. Accordingly, presented in this chapter are classifications of: 1. Thermodynamic systems. 2. Thermodynamic properties. 3.
eBook - PDF- Pierluigi Zotto, Sergio Lo Russo, Paolo Sartori(Authors)
- 2022(Publication Date)
- Società Editrice Esculapio(Publisher)
General Concepts of Thermodynamics 14.1 Introduction The statistical description of the behaviour of gases expressed by the kinetic theory of gases or by more advanced models of statistical mechanics is not the only possible ap- proach. It is in fact possible to abstract from a microscopic description by identifying some macroscopic variables which can anyway provide full information about the state of a solid, liquid or gaseous substance. This way to represent the behaviour of matter is the basis of Thermodynamics. Definitions and general concepts of thermodynamics are introduced into this chapter, focussing in particular on heat, and the discipline, called calorimetry, which studies it. 14.2 Thermodynamic System Thermodynamics studies the description of the evolution of a thermodynamic system, defined as a body or a group of bodies whose chemical composition is well defined. Everything which does not belong to a thermodynamic system is its thermodynamic environment. Every chemical species which belongs to a thermodynamic system is a constituent of the system. A thermodynamic system is called a homogeneous system if its chemical composition and its physical properties are the same everywhere in it: in such a case a thermodynamic system has got only one phase, which can be solid, liquid or gaseous. The macroscopic quantities which completely specify its state, called thermodynamic state, are variables called thermodynamic coordinates or variables of state. These quantities must be measurable physical quantities, such as, for instance, pressure, volume, tempera- ture, chemical concentrations, electric or magnetic states of matter. The state of a system is known only once all its thermodynamics coordinates are exactly defined, meaning that no thermodynamic coordinate can have a different value in different parts of the thermodynamic system.
- Neil Birks, Gerald H. Meier, Frederick S. Pettit(Authors)
- 2006(Publication Date)
- Cambridge University Press(Publisher)
(2) Standard free energy of formation versus temperature diagrams which allow the ther-modynamic data for a given class of compounds, oxides, sulphides, carbides, etc., to be presented in a compact form. (3) Vapour-species diagrams which allow the vapour pressures of compounds to be presented as a function of convenient variables such as partial pressure of a gaseous component. 16 Basic thermodynamics 17 (4) Two-dimensional, isothermal stability diagrams, which map the stable phases in systems involving one metallic and two reactive, non-metallic components. (5) Two-dimensional, isothermal stability diagrams which map the stable phases in systems involving two metallic components and one reactive, non-metallic component. (6) Three-dimensional, isothermal stability diagrams which map the stable phases in sys-tems involving two metallic and two reactive, non-metallic components. Basic thermodynamics The question of whether or not a reaction can occur is answered by the second law of thermodynamics. Since the conditions most often encountered in high-temperature reactions are constant temperature and pressure, the second law is most conveniently written in terms of the Gibbs free energy ( G ) of a system, Equation ( 2.1 ), G = H − T S , (2.1) where H is the enthalpy and S the entropy of the system. Under these conditions the second law states that the free-energy change of a process will have the follow-ing significance: G < 0, spontaneous reaction expected; G = 0, equilibrium; G > 0, thermodynamically impossible process. For a chemical reaction, e.g. Equation ( 2.2 ), a A + b B = c C + d D , (2.2) G is expressed as in Equation ( 2.3 ), G = G ◦ + RT ln a c C a d D a a A a b B , (2.3) where G ◦ is the free-energy change when all species are present in their standard states; a is the thermodynamic activity, which describes the deviation from the standard state for a given species and may be expressed for a given species i as in Equation ( 2.4 ), a i = p i p ◦ i .
eBook - PDFPhase Equilibria, Phase Diagrams and Phase Transformations
Their Thermodynamic Basis
- Mats Hillert(Author)
- 2007(Publication Date)
- Cambridge University Press(Publisher)
All the states to be considered will thus be situated along a single axis, which may now be regarded as the state diagram. We may then plot a dependent variable by introducing a second axis. That property is thus represented by a line. We may call such a diagram a property diagram . An example is shown in Fig. 1.1 . Of course, we may arbitrarily choose to consider any one of the two axes as the independent variable. The shape of the line is independent of that choice and it is thus the line itself that represents the property of the system. In many cases the content of matter in a system is kept constant and the wall is only open for exchange of mechanical work and heat. Such a system is often called a closed system and we shall start by discussing the properties of such a system. In other cases the content of matter may change and, in particular, the composition of the system by which we mean the relative amounts of the various components independent of the size of the system. In materials science such an open system is called an ‘alloy system’ and its behaviour as a function of composition is often shown in so-called phase diagrams , 1.2 Internal state variables 3 which are state diagrams with some additional information on what phases are present in various regions. We shall later discuss the properties of phase diagrams in considerable detail. The state variables are of two kinds, which we shall call intensive and extensive . Temperature T and pressure P are intensive variables because they can be defined at each point of the system. As we shall see later, T must have the same value at all points in a system at equilibrium. An intensive variable with this property will be called potential . We shall later meet intensive variables, which may have different values at different parts of the system. They will not be regarded as potentials. Volume V is an extensive variable because its value for a system is equal to the sum of its values of all parts of the system.
eBook - PDFThermo and Fluid Dynamics
Recent Advances
- Dritan Hoxha(Author)
- 2019(Publication Date)
- Arcler Press(Publisher)
A GENERAL VIEW ON THERMODYNAMICS CHAPTER 1 CONTENTS 1.1. What Is Thermodynamics? ....................................................................................... 2 1.2. Etymology of Thermodynamics ................................................................................ 3 1.3. Why is Thermodynamics Important? ........................................................................ 8 1.4. A Short View of The Quantities Involved in Thermodynamics ................................. 10 1.5. A Short View of the Theories and Laws Contained in Thermodynamics .................. 12 References .................................................................................................................... 17 Thermo and Fluid Dynamics: Recent Advances 2 1.1. WHAT IS THERMODYNAMICS? All of us would have heard at least once the words “thermo” or “thermodynamics” but only a few people know what do they really stand for. From the Greek language, “thermo” means heat and “dynamics” means something in motion. Thus, by definition, “ Thermodynamics is the branch of Physics that deals with the relationships and interaction between heat and other forms of energy. In particular, it describes how thermal energy turns into other forms of energy and vice-versa and how it affects the behavior of matter” [1]. The type of energy involved in Thermodynamics is known as “thermal energy.” It is the kind of energy that a certain substance or system owns due to its temperature [1]. As you may know, temperature is a physical quantity related to the particles’ motion, thus thermal energy represents the energy of molecules motion or vibration. Here I will make a parenthesis. People often confuse heat and thermal energy or worse, they consider them as the same thing. Heat and thermal energy, earlier, used to be considered as synonyms. But they differ as follows: Heat is the thermal energy transferred across a boundary of one region of matter to another.
eBook - PDF- S. C. McBirnie(Author)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
Lines of constant super-heat for various other superheats could be drawn by the same methods. We could also plot lines of constant specific volume, but for the present, these we will not consider so as to avoid too much complication. A complete temperature-entropy diagram, as illustrated in Figure 8.5, having lines of constant pressure, dryness, super-heat and specific volume could be drawn. Since however, the use to which we propose to put the temperature-entropy diagram in the next chapter is to illustrate the thermodynam-ical steam cycles, it is necessary only to sketch a skeleton temperature-entropy diagram on which appear only the lines and state points applying to the particular cycle being studied at any one time. Relation between temperature, reception of heat and change of entropy We have seen that on a temperature-entropy (Ts) diagram, areas represent heat quantities (enthalpies). Hence in Figure 8.6, the shaded area h 2 ~ h 1 - T(s 2 — ^i ) from which h 2 — / i i s 2 -S l = —ψ— E N T R O P Y A N D I T S U S E S 3 3 7 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 ENTROPY, s k j / k g Κ Figure 8.5 A complete temperature entropy diagram 3 3 8 E N T R O P Y A N D I T S U S E S Figure 8.6 Heat quantities on Ts diagram Thus, if a substance receives heat, The change of entropy heat received average temperature of heat reception and the unit of entropy is therefore kj/kg K. (In practice, it has become conventional to omit the units, i.e. when writing down an entropy, it is written only as a number). The above is also valid for rejection of heat. Entropy has been variously defined, e.g. entropy is that characteristic, or state, or function of a substance which in-creases or diminishes accordingly as the substance receives or rejects heat; or again, entropy is a measure of the unavaila-bility of a system's thermal energy for conversion into mechanical work.
eBook - PDF- Donald Olander(Author)
- 2007(Publication Date)
- CRC Press(Publisher)
Such representations are called phase diagrams . They show the regions of existence of various phases on a plot with temperature as the ordinate and composition as the abscissa. A simple phase diagram of the binary A–B FIGURE 1.19 Pressure-temperature diagram for a pure substance. 40 General Thermodynamics system is shown in Figure 1.20. The ends of the lens-shaped portion of the diagram intersect at the melting points of pure A, T MA , on the left, and the corresponding temperature T MB for component B on the right. Below the lower curve, the system is a single-phase solid solution, in which A and B are homogeneously mixed in a specific crystal lattice structure called α . Above the upper curve, the system is a single liquid without, of course, a regular structure. In between these two curves is the two-phase region designated α + L, where the solid and the liquid coexist. Two-component systems (or phase diagrams) are usually termed binary systems (or phase diagrams). 1.12.3 C OUNTING C OMPONENTS Specification of the number of components in a system is less clear-cut than fixing the number of phases present. Each chemical species of fixed molecular makeup that can be mixed in arbitrary amounts in the system is considered to be a compo-nent. Composition is dictated by various measures of concentration. The most common is the mole fraction , or occasionally the mass fraction. If the system contains C components, only C – 1 mole fractions need be specified in order to fix unambiguously the composition. For example, a mixture of O 2 and N 2 is a two component system, but the mole fraction of only one component is needed to specify the system’s composition. In addition, if the composition of the mixture does not change during the process under consideration, the binary system can be treated as a pseudo single-component system.
eBook - PDFStatistical and Thermal Physics
With Computer Applications, Second Edition
- Harvey Gould, Jan Tobochnik(Authors)
- 2021(Publication Date)
- Princeton University Press(Publisher)
2 The nature of thermodynamics is summarized in the song “First and Second Law” by Michael Flanders and Donald Swann. 2.3 THERMODYNAMIC EQUILIBRIUM • 31 Surroundings Boundary System Figure 2.1. Schematic of a thermodynamic system. Thermodynamics describes the properties of macroscopic systems without appeal to the nature of their microscopic constituents. So why bother introducing thermo-dynamics as a subject in its own right, when we could more easily introduce energy and entropy from microscopic considerations? Besides the intellectual challenge, an important reason is that the way of thinking required by thermodynamics can be applied in other contexts where the microscopic properties of the system are poorly understood or very complex. However, there is no need to forget what we learned in Chapter 1. You are also encouraged to jump ahead, especially to Chapter 4, where the nature of entropy is introduced from first principles. 2.2 The System The first step in applying thermodynamics is to select the part of the universe of interest. This part of the universe is called the system . The system is anything that we wish to consider and is defined by a closed surface called the boundary (see Figure 2.1). The boundary may be real or imaginary and may or may not be fixed in shape or size. The system might be as obvious as a block of steel, water in a container, or the gas in a balloon. Or the system might be defined by an imaginary fixed boundary within a flowing liquid. The surroundings are the rest of the universe that can in any significant way affect or be affected by the system. If an ice cube is placed in a glass of water, we might take the ice to be the system and the water to be the surroundings. In this example we usually ignore the interaction of the ice cube with the air in the room and the interaction of the glass with the table on which the glass is set.
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