Dissipation

Last updated

In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy (internal, bulk flow kinetic, or system potential) transforms from an initial form to a final form, where the capacity of the final form to do thermodynamic work is less than that of the initial form. For example, heat transfer is dissipative because it is a transfer of internal energy from a hotter body to a colder one. Following the second law of thermodynamics, the entropy varies with temperature (reduces the capacity of the combination of the two bodies to do work), but never decreases in an isolated system.

Contents

These processes produce entropy at a certain rate. The entropy production rate times ambient temperature gives the dissipated power. Important examples of irreversible processes are: heat flow through a thermal resistance, fluid flow through a flow resistance, diffusion (mixing), chemical reactions, and electric current flow through an electrical resistance (Joule heating).

Definition

Thermodynamic dissipative processes are essentially irreversible. They produce entropy at a finite rate. In a process in which the temperature is locally continuously defined, the local density of rate of entropy production times local temperature gives the local density of dissipated power.[ definition needed ]

A particular occurrence of a dissipative process cannot be described by a single individual Hamiltonian formalism. A dissipative process requires a collection of admissible individual Hamiltonian descriptions, exactly which one describes the actual particular occurrence of the process of interest being unknown. This includes friction, and all similar forces that result in decoherency of energythat is, conversion of coherent or directed energy flow into an indirected or more isotropic distribution of energy.

Energy

"The conversion of mechanical energy into heat is called energy dissipation." – François Roddier [1] The term is also applied to the loss of energy due to generation of unwanted heat in electric and electronic circuits.

Computational physics

In computational physics, numerical dissipation (also known as "numerical diffusion") refers to certain side-effects that may occur as a result of a numerical solution to a differential equation. When the pure advection equation, which is free of dissipation, is solved by a numerical approximation method, the energy of the initial wave may be reduced in a way analogous to a diffusional process. Such a method is said to contain 'dissipation'. In some cases, "artificial dissipation" is intentionally added to improve the numerical stability characteristics of the solution. [2]

Mathematics

A formal, mathematical definition of dissipation, as commonly used in the mathematical study of measure-preserving dynamical systems, is given in the article wandering set .

Examples

In hydraulic engineering

Dissipation is the process of converting mechanical energy of downward-flowing water into thermal and acoustical energy. Various devices are designed in stream beds to reduce the kinetic energy of flowing waters to reduce their erosive potential on banks and river bottoms. Very often, these devices look like small waterfalls or cascades, where water flows vertically or over riprap to lose some of its kinetic energy.

Irreversible processes

Important examples of irreversible processes are:

  1. Heat flow through a thermal resistance
  2. Fluid flow through a flow resistance
  3. Diffusion (mixing)
  4. Chemical reactions [3] [4]
  5. Electrical current flow through an electrical resistance (Joule heating).

Waves or oscillations

Waves or oscillations, lose energy over time, typically from friction or turbulence. In many cases, the "lost" energy raises the temperature of the system. For example, a wave that loses amplitude is said to dissipate. The precise nature of the effects depends on the nature of the wave: an atmospheric wave, for instance, may dissipate close to the surface due to friction with the land mass, and at higher levels due to radiative cooling.

History

The concept of dissipation was introduced in the field of thermodynamics by William Thomson (Lord Kelvin) in 1852. [5] Lord Kelvin deduced that a subset of the above-mentioned irreversible dissipative processes will occur unless a process is governed by a "perfect thermodynamic engine". The processes that Lord Kelvin identified were friction, diffusion, conduction of heat and the absorption of light.

See also

Related Research Articles

Energy Physical property enabling work, heat, and light

In physics, energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule, defined as "the energy transferred to an object by the work of moving it a distance of one metre against a force of one newton".

Entropy Property of a thermodynamic system

Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication.

In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles.

Timeline of thermodynamics

A timeline of events in the history of thermodynamics.

Second law of thermodynamics Law of physics

The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves "downhill", that is, from hotter objects to colder objects, unless energy is supplied to reverse the direction of heat flow. Another definition is: "Not all heat energy can be converted into work in a cyclic process."

First law of thermodynamics Law of thermodynamics distinguishing heat, work, and matter transfers

The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes, distinguishing three kinds of transfer of energy, as heat, as thermodynamic work, and as energy associated with matter transfer, and relating them to a function of a body's state, called internal energy.

Heat transfer Transport of thermal energy in physical systems

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.

Heat death of the universe Possible fate of the universe

The heat death of the universe is a hypothesis on the ultimate fate of the universe, which suggests the universe will evolve to a state of no thermodynamic free energy and will, therefore, be unable to sustain processes that increase entropy. Heat death does not imply any particular absolute temperature; it only requires that temperature differences or other processes may no longer be exploited to perform work. In the language of physics, this is when the universe reaches thermodynamic equilibrium.

Reversible process (thermodynamics) Thermodynamic process whose direction can be reversed to return the system to its original state

In thermodynamics, a reversible process is a process, involving a system and its surroundings, whose direction can be reversed by infinitesimal changes in some properties of the surroundings, such as pressure or temperature.

Non-equilibrium thermodynamics Branch of thermodynamics

Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions.

Quasistatic process Thermodynamic process in which equilibrium is maintained throughout the processs duration

In thermodynamics, a quasi-static process, is a thermodynamic process that happens slowly enough for the system to remain in internal physical thermodynamic equilibrium. An example of this is quasi-static expansion of a mixture of hydrogen and oxygen gas, where the volume of the system changes so slowly that the pressure remains uniform throughout the system at each instant of time during the process. Such an idealized process is a succession of physical equilibrium states, characterized by infinite slowness.

Irreversible process Process that cannot be undone

In science, a process that is not reversible is called irreversible. This concept arises frequently in thermodynamics. All complex natural processes are irreversible, although a phase transition at the coexistence temperature is well approximated as reversible.

In thermodynamics, the exergy of a system is the maximum useful work possible during a process that brings the system into equilibrium with a heat reservoir, reaching maximum entropy. When the surroundings are the reservoir, exergy is the potential of a system to cause a change as it achieves equilibrium with its environment. Exergy is the energy that is available to be used. After the system and surroundings reach equilibrium, the exergy is zero. Determining exergy was also the first goal of thermodynamics. The term "exergy" was coined in 1956 by Zoran Rant (1904–1972) by using the Greek ex and ergon meaning "from work", but the concept had been earlier developed by J Willard Gibbs in 1873.

Joule expansion

The Joule expansion is an irreversible process in thermodynamics in which a volume of gas is kept in one side of a thermally isolated container, with the other side of the container being evacuated. The partition between the two parts of the container is then opened, and the gas fills the whole container.

Thermodynamic process Passage of a system from an initial to a final state of thermodynamic equilibrium

Classical thermodynamics considers three main kinds of thermodynamic process: (1) changes in a system, (2) cycles in a system, and (3) flow processes.

Work (thermodynamics) Form of energy defined in the first law of thermodynamics

In thermodynamics, work performed by a system is energy transferred by the system to its surroundings, by a mechanism through which the system can spontaneously exert macroscopic forces on its surroundings. In the surroundings, through suitable passive linkages, the work can lift a weight, for example. Energy can also transfer from the surroundings to the system; in a sign convention used in physics, such work has a negative magnitude.

Heat Thermodynamic energy transfer, other than by thermodynamic work or by transfer of matter

In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter.

Temperature Physical quantity that expresses hot and cold

Temperature is a physical quantity that expresses how hot matter is, or as a measure of the average translational kinetic energy per atom or molecule in the system. It is the detectable portion of the molar thermal energy of matter; a temperature difference allows heat transfer to occur, as energy flows from a hotter body to a colder body.

Energy dissipation and entropy production extremal principles are ideas developed within non-equilibrium thermodynamics that attempt to predict the likely steady states and dynamical structures that a physical system might show. The search for extremum principles for non-equilibrium thermodynamics follows their successful use in other branches of physics. According to Kondepudi (2008), and to Grandy (2008), there is no general rule that provides an extremum principle that governs the evolution of a far-from-equilibrium system to a steady state. According to Glansdorff and Prigogine, irreversible processes usually are not governed by global extremal principles because description of their evolution requires differential equations which are not self-adjoint, but local extremal principles can be used for local solutions. Lebon Jou and Casas-Vásquez (2008) state that "In non-equilibrium ... it is generally not possible to construct thermodynamic potentials depending on the whole set of variables". Šilhavý (1997) offers the opinion that "... the extremum principles of thermodynamics ... do not have any counterpart for [non-equilibrium] steady states ." It follows that any general extremal principle for a non-equilibrium problem will need to refer in some detail to the constraints that are specific for the structure of the system considered in the problem.

Entropy production Development of entropy in a thermodynamic system

Entropy production is the amount of entropy which is produced in any irreversible processes such as heat and mass transfer processes including motion of bodies, heat exchange, fluid flow, substances expanding or mixing, anelastic deformation of solids, and any irreversible thermodynamic cycle, including thermal machines such as power plants, heat engines, refrigerators, heat pumps, and air conditioners.

References

  1. Roddier F., Thermodynamique de l'évolution (The Thermodynamics of Evolution), parole éditions, 2012
  2. Thomas, J.W. Numerical Partial Differential Equation: Finite Difference Methods. Springer-Verlag. New York. (1995)
  3. Glansdorff, P., Prigogine, I. (1971). Thermodynamic Theory of Structure, Stability, and Fluctuations, Wiley-Interscience, London, 1971, ISBN   0-471-30280-5, p. 61.
  4. Eu, B.C. (1998). Nonequilibrium Thermodynamics: Ensemble Method, Kluwer Academic Publications, Dordrecht, ISBN   0-7923-4980-6, p. 49,
  5. W. Thomson On the universal tendency in nature to the dissipation of mechanical energy Philosophical Magazine, Ser. 4, p. 304 (1852).