In thermodynamics, dissipation is the result of an irreversible process that affects a thermodynamic system. In a dissipative process, energy (Internal energy, bulk flow Kinetic energy, or system Potential energy) 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 energy other than by thermodynamic work or by transfer of matter, and spreads previously concentrated energy. Following the second law of thermodynamics, in conduction and radiation from one body to another, 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.
In mechanical engineering, dissipation is the irreversible conversion of mechanical energy into thermal energy with an associated increase in entropy.
Processes with defined local temperature produce entropy at a certain rate. The entropy production rate times local 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
Dissipative thermodynamic processes are essentially irreversible because they produce entropy.
Max Planck regarded friction as the prime example of an irreversible thermodynamic process.
[Max Planck (1926). "Über die Begründung des zweiten Hauptsatzes der Thermodynamik", Sitzungsber. Preuss. Akad. Wiss., Phys. Math. Kl., 453—463.] 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.
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 hammering, and all similar forces that result in decoherence of energy—that 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[ Roddier F., Thermodynamique de l'évolution (The Thermodynamics of Evolution), parole éditions, 2012] 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.
[Thomas, J.W. Numerical Partial Differential Equation: Finite Difference Methods. Springer-Verlag. New York. (1995)]
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
erosion on banks and
stream bed. Very often, these devices look like small
or cascades, where water flows vertically or over
riprap to lose some of its
kinetic energy.
Irreversible processes
Important examples of irreversible processes are:
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Heat flow through a thermal resistance
-
Fluid flow through a flow resistance
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Diffusion (mixing)
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Chemical reactions
[Glansdorff, P., Ilya Prigogine (1971). Thermodynamic Theory of Structure, Stability, and Fluctuations, Wiley-Interscience, London, 1971, , p. 61.][Eu, B.C. (1998). Nonequilibrium Thermodynamics: Ensemble Method, Kluwer Academic Publications, Dordrecht, , p. 49,]
-
Electrical current flow through an electrical resistance (Joule heating).
Waves or oscillations
or
, 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.
[W. Thomson On the universal tendency in nature to the dissipation of mechanical energy Philosophical Magazine, Ser. 4, p. 304 (1852).] 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
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Entropy production
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General equation of heat transfer
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Flood control
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Principle of maximum entropy
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Two-dimensional gas
General References
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"Dissipative system, a system that loses energy in the course of its time evolution."
