Technology & Engineering
Thermodynamic Relations
Thermodynamic relations are mathematical relationships that describe the interdependence of thermodynamic properties such as temperature, pressure, and volume. These relations are derived from the laws of thermodynamics and are used to analyze and predict the behavior of thermodynamic systems. They are fundamental in the study and application of thermodynamics, providing a framework for understanding and manipulating energy and heat transfer processes.
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6 Key excerpts on "Thermodynamic Relations"
- Willem Norde(Author)
- 2011(Publication Date)
- CRC Press(Publisher)
19 3 Some Thermodynamic Principles and Relations, with Special Attention to Interfaces THE THERMODYNAMIC ROUTE World of the mind: Problem Solution Real world: Problem Solution Mathematics Introduction of abstract notions Model assumptions ? in terms of abstract notions in terms of abstract notions with respect to relations between physical quantities in terms of measurable, observable quantities Thermodynamics.deals.with.the.exchange.and.transformation.of.energy.and. matter.between.a.system.and.its.surroundings . .It.is.based.on.two.universal.prin-ciples.and.may.therefore.be.applied.to.any.process.occurring.in.nature,.in.engi-neering,.or.wherever . .Thus,.thermodynamics.is.a.powerful.intellectual.method. to.help.us.understand.the.world.around.us . .The.problem.to.solve.is.taken.from. the.“real.world,.physical.world”.into.the.“world.of.the.mind”.by.introducing. abstract. concepts. like. energy,. entropy,. chemical. potential,. etc . . Then,. in. the. abstract.world.of.our.minds,.we.use.mathematics.to.work.on.the.problem . .The. solution.will.consequently.present.itself.in.terms.of.these.abstract.notions . .By. way. of. example,. the. thermodynamic. answer. to. the. question. as. to. the. equi-librium.distribution.of.a.compound.partitioning.between.two.phases.is.equal. values.for.the.chemical.potential.of.that.component.in.the.two.phases . .Now,. to.bring.back.the.thermodynamic.solution.into.the.real.world.we.have.to.call. upon.model-assumptions,.such.as,.for.instance,.ideal.behavior.of.a.solution.or. a.gas . .Thus,.by.taking.a.thermodynamic.detour,.a.large.collection.of.relations. between.(experimentally).observable.variables.may.be.derived . 20 Colloids and Interfaces in Life Sciences and Bionanotechnology In.the.following.chapters.thermodynamics.is.frequently.applied.to.derive.relations. between.macroscopic.parameters . .In.writing.this.book,.it.is.assumed.that.the.reader. is.familiar.with.the.basics.of.thermodynamics.of.reversible.processes .
- Allan D. Kraus, James R. Welty, Abdul Aziz(Authors)
- 2011(Publication Date)
- CRC Press(Publisher)
2 Thermodynamics: Preliminary Concepts and Definitions Chapter Objectives • To briefly introduce the subject of thermodynamics. • To provide precise definitions of some of the working terms used in a study of thermodynamics. • To consider the dimensions and units that pertain to thermodynamics. • To examine density and its related properties. • To define pressure and consider how it is measured. • To define temperature and to present the zeroth law of thermodynamics. • To outline a problem-solving methodology. 2.1 The Study of Thermodynamics When most people think about thermodynamics, they think about the transfer of energy and the utilization of such energy transfer for the useful production of work. This often leads many engineering students in fields such as computer science and electrical or civil engineering to wonder why this particular subject is relevant to them. In reality, thermody-namics deals with much more than the study of heat or energy transfer and the development of work. Indeed, it deals with virtually all aspects of our lives, from the combustion pro-cesses that run our automobiles and produce our electric power in power plants to the refrigeration cycles that cool our beer, from the cryogenic pumping of liquids and gases in space to the distillation processes used to produce the gasoline that runs our automobiles. Thermodynamics is important to electrical engineers so that they can better understand that the limiting factor in the microminiaturization of electronic components is the rejec-tion of heat. It is important to civil engineers because a knowledge of thermal expansion and thermal stresses is requisite to the design of structures and to the computer scien-tists who need to thoroughly understand the systems that they are trying to model and develop.
eBook - PDFPhysical Principles of Food Preservation
Revised and Expanded
- Marcus Karel, Daryl Lund(Authors)
- 2003(Publication Date)
- CRC Press(Publisher)
1 Thermodynamics I. INTRODUCTION The development of chemical engineering occurred in part because the fundamental laws of cause and effect associated with chemical transformations and phenomena were expressed quantitatively and codified. For food engineering, significant progress occurred in engineering design of food processes when these same fundamental principles were applied to complex mixtures of chemicals and biochemicals calledfood. Unfortunately, with food the mixtures are very complex and the chemical and thermodynamic parameters are not easily estimated from first principles or easily determined experimentally. Although this situation has led to empiricism, nonetheless, knowledge of physical-chemical principles is essential to enhance our understanding of unit operations and behavior of foods. II. THERMODYNAMIC FUNDAMENTALS Food engineering requires an appreCIatIOn for the fundamental laws of thermodynamics even though some principles apply in only highly select conditions. Here we will briefly introduce the laws of thermodynamics recognizing that the reader may wish to refer to more extensive treatments elsewhere [e.g., Chang (1977), Tinoco et al. (2002), Baianu (1992)]. 1 2 Chapter 1 A. Definition of Systems When an operation is described, frequently it is helpful to envision a physical boundary around the operation. The elements contained within the boundary is called a system. If no mass or energy crosses the boundary of the system, the system is said to be isolated; if mass and energy crosses the boundary, the system is open; and if no mass crosses the boundary, the systems is said to be closed. A system with no heat flow across the boundary is adiabatic, whereas one with no work transfer is anergic. If the pressure does not change, the system is isopiestic or isobaric and if the temperature of the system does not change, the system is isothermal.
eBook - ePubFluid and Thermal Dynamics Answer Bank for Engineers
The Concise Guide with Formulas and Principles for Students and Professionals
- Ethirajan Rathakrishnan(Author)
- 2023(Publication Date)
- BrownWalker Press(Publisher)
Chapter 8
Thermodynamics
8.1Basic Concepts and Definitions
Thermodynamics may be defined as the study of energy, its forms and transformations, and the interaction of energy with matter. Thermodynamics deals with the conservation of energy from one form to another.The first law of thermodynamics is an expression of the energy conservation principle. The second law of thermodynamics asserts that spontaneous processes occur only in a particular direction and never in a direction opposite to that. Further, it ascertains that energy has quality as well as quantity .A macroscopic approach to the study of thermodynamics which does not require a knowledge of the behaviour of the individual particles of the substance is called classical thermodynamics . An elaborate approach, based on the behaviour of individual particles is called statistical thermodynamics .A closed system or control mass is a fixed amount of mass, and no mass can cross its boundaries but energy can cross its boundaries. An open system or control volume is a properly chosen region in space. Both mass and energy can cross the boundary of a control volume but the shape of the control volume will remain unchanged.The sum of all forms of energy of a system is called its total energy E . The total energy of a system is made up of microscopic energy group and macroscopic energy group . The internal energy is the sum of all the microscopic forms of energy.The portion of the internal energy of a system, associated with the kinetic energy of the molecules is called the sensible energy . The internal energy associated with the phase of a system is called the latent energy . The internal energy associated with the bonds in a molecule is called the chemical or bond energy
- Lucien Borel, Daniel Favrat(Authors)
- 2010(Publication Date)
- PPUR(Publisher)
Closed systems and general Thermodynamic Relations 81 In addition, let us note that • two other relations analogous to Relation (2.7) can be developed by permu- ting X, Y , Z; • Relation 2.10 can be established from Relations (2.9) and (2.7) by writing which, for Z = Cst, reduces to: • and Relation (2.11) refers to an additional state function N. 2.3 THERMODYNAMIC PROCESSES AND DIAGRAMS 2.3.1 Thermodynamic processes Fixing any one of the thermodynamic variables implies removing a degree of free- dom from the system, i.e., reducing the bivariant system to a monovariant one. We employ the designation typical thermodynamic process for all thermodynamic states that are possible provided that one of the thermodynamic variables is fixed, i.e., if the system is monovariant. To each thermodynamic variable thus corresponds a series of processes of a given type. It should be noted that the fact of arbitrarily imposing a certain relation between given thermodynamic variables also results in removing a degree of free- dom from the system, i.e., in rendering it monovalent. Consequently, such a relation also corresponds to a typical process. We will indeed see, in Subsection 2.4.2, that it is often useful to introduce Relation (2.21): (2.12) in which a series of discrete values may be given to so that it may be considered as a parameter. The factor is called the polytropic factor . We distinguish the following typical thermodynamic processes: • Isochoric process v = Cst • Isobaric process P = Cst • Isothermal process T = Cst • Isoenergy process u = Cst (2.13) • Isenthalpic process h = Cst • Isentropic process s = Cst • Polytropic process = Cst d d d d Z X Z X Z Y Y X Y X = ∂ ∂ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + ∂ ∂ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 0 = ∂ ∂ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + ∂ ∂ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⋅ ∂ ∂ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Z X Z Y Y X Y X Z T s P d d − = σ v 0 σ σ σ 82 Thermodynamics and Energy Systems Analysis: from Energy to Exergy An in-depth analysis of the above-mentioned typical thermodynamic processes is described in Chapter 8.
eBook - PDF- Marc J. Assael, William A. Wakeham, Anthony R. H. Goodwin, Stefan Will, Michael Stamatoudis(Authors)
- 2011(Publication Date)
- CRC Press(Publisher)
These formulations include con-tributions from pressure, volume, chemical potential, and electrical work, but there can also be significant energy contributions arising from electromagnetic sources, gravitation, and relativity. The contributions that are important change with the discipline in which the problem arises. For example, for the majority of chemists the inclusion of gravitational and relativistic contributions is unimport-ant because of their dominant requirement to understand chemical reactions and equilibrium, whereas for physicists the same contributions may be dominant and chemical and mechanical engineers may need to include electromagnetic forces but will also need to account for phenomena associated with nonequilibrium states such as the processes that describe the movement of energy, momentum, and matter. The fact that thermodynamics relates measurable physical quantities implies that measurements of those properties must be carried out for use-ful work to be done in the field. Generally speaking, the properties of inter-est are called thermophysical properties , a subset that pertains to equilibrium states being referred to as thermodynamic properties and a further subset that refers to dynamic processes in nonequilibrium states being called transport properties . Thermodynamics is an exacting experimental science because it has turned out to be quite diffi cult and time consuming to make very accu-rate measurements of properties over a range of conditions (temperature, pressure, and composition) for the wide range of materials of interest in the modern world. Given the exact relationship between properties that follows from thermodynamics the lack of accuracy has proved problematic. Thus, very considerable efforts have been made over many decades to refi ne experimen-tal measurements, using methods for which complete working equations are
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