Editing Closed system

{{Short description|Type of system}}
{{About|the physical sciences concept|the computing concept|Closed source software}}

A '''closed system''' is a natural [[physical system]] that does not allow transfer of [[matter]] in or out of the system, although{{snd}}in the contexts of [[physics]], [[chemistry]], [[engineering]], etc.{{snd}}the transfer of energy (e.g. as work or heat) is allowed.

==Physics==

===In classical mechanics===
In [[Theory of relativity|nonrelativistic]] [[classical mechanics]], a closed system is a [[physical system]] that does not exchange any matter with its surroundings, and is not subject to any net [[force]] whose source is external to the system.<ref>{{cite book|last=Rana|first=N.C.|author2=P.S. Joag|title=Classical Mechanics|date=1991|page=78|publisher=McGraw-Hill Education (India) Pvt Limited |isbn=978-0-07-460315-4}}</ref><ref>{{cite book|last=Landau|first=L.D.|author-link=Lev Landau|author2=E.M. Lifshitz|title=Mechanics|edition=third|date=1976|page=8|publisher=Butterworth-Heinemann |isbn=978-0-7506-2896-9}}</ref> A closed system in classical mechanics would be equivalent to an [[isolated system]] in [[thermodynamics]]. Closed systems are often used to limit the factors that can affect the results of a specific problem or experiment.

===In thermodynamics===
{{main|Thermodynamic system}}
[[File:Diagram Systems.svg|thumb|Properties of isolated, closed, and open systems in exchanging energy and matter]]

In [[thermodynamics]], a closed system can exchange energy (as [[heat]] or [[mechanical work|work]]) but not [[matter]], with its surroundings.
An [[isolated system]] cannot exchange any heat, work, or matter with the surroundings, while an [[Thermodynamic system#Open system|open system]] can exchange energy and matter.<ref>[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London, p. 66.</ref><ref>[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA, pp. 112–113.</ref><ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', (1st edition 1949) 5th edition 1967, North-Holland, Amsterdam, p. 14.</ref><ref>Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London, pp. 6–7.</ref><ref>Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081, p. 3.</ref><ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 5.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ, p. 4.</ref> (This scheme of definition of terms is not uniformly used, though it is convenient for some purposes. In particular, some writers use 'closed system' where 'isolated system' is used here.<ref>[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}, p. 17.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA, p. 43.</ref>)

For a simple system, with only one type of particle (atom or molecule), a closed system amounts to a constant number of particles. However, for systems which are undergoing a [[chemical equilibrium|chemical reaction]], there may be all sorts of molecules being generated and destroyed by the reaction process. In this case, the fact that the system is closed is expressed by stating that the total number of each elemental atom is conserved, no matter what kind of molecule it may be a part of. Mathematically:

:<math>\sum_{j=1}^m a_{ij}N_j=b_i</math>

where <math>N_j</math> is the number of j-type molecules, <math>a_{ij}</math> is the number of atoms of element <math>i</math> in molecule <math>j</math> and <math>b_i</math> is the total number of atoms of element <math>i</math> in the system, which remains constant, since the system is closed. There will be one such equation for each different element in the system.

In thermodynamics, a closed system is important for solving complicated thermodynamic problems. It allows the elimination of some external factors that could alter the results of the experiment or problem thus simplifying it. A closed system can also be used in situations where [[thermodynamic equilibrium]] is required to simplify the situation.

===In quantum physics===
{{further|Quantum field theory}}This equation, called [[Schrödinger equation|Schrödinger's equation]], describes the behavior of an isolated or closed quantum system, that is, by definition, a system which does not interchange information (i.e. energy and/or matter) with another system. So if an isolated system is in some pure state |ψ(t) ∈ H at time t, where H denotes the Hilbert space of the system, the time evolution of this state (between two consecutive measurements).<ref>{{Cite book |last1=Rivas |first1=Ángel |title=Open Quantum Systems |last2=Huelga |first2=Susana F. |author-link2=Susana F. Huelga |date=October 2011 |publisher=Springer-Verlag |isbn=978-3-642-23354-8 |location=Berlin Heidelberg}}</ref>

<math display="block">i\hbar \frac{\partial}{\partial t} \Psi(\mathbf{r}, t) = \hat{H} \Psi(\mathbf{r}, t) </math>

where {{math|''i''}} is the [[imaginary unit]], {{math|''ħ''}} is the [[Planck constant]] divided by {{math|2π}}, the symbol {{math|{{sfrac|∂|∂''t''}}}} indicates a [[partial derivative]] with respect to [[time]] {{math|''t''}}, {{math|Ψ}} (the Greek letter [[Psi (letter)|psi]]) is the [[wave function]] of the quantum system, and {{math|''Ĥ''}} is the [[Hamiltonian (quantum mechanics)|Hamiltonian]] [[Operator (physics)|operator]] (which characterizes the total energy of any given wave function and takes different forms depending on the situation).

==In chemistry==
In chemistry, a closed system is where no reactants or products can escape, only heat can be exchanged freely (e.g. an ice cooler). A closed system can be used when conducting chemical experiments where temperature is not a factor (i.e. reaching [[thermal equilibrium]]).

==In engineering==
In an [[engineering]] context, a closed system is a bound system, i.e. defined, in which every input is known and every resultant is known (or can be known) within a specific time.

==See also==
* [[Glossary of systems theory]]
* [[Dynamical system]]
* [[Isolated system]]
* [[Open system (systems theory)]]
* [[Sense and Respond]]
* [[Thermodynamic system]]

==References==
{{Reflist}}

[[Category:Cybernetics]]
[[Category:Systems theory]]
[[Category:Thermodynamic systems]]