# Closed system

A closed system is a physical system which does not allow certain types of transfers (such as transfer of mass) in or out of the system. The specification of what types of transfers are excluded varies in the closed systems of physics, chemistry or engineering.

## In physics

### In classical mechanics

In nonrelativistic classical mechanics, a closed system is a physical system which doesn't exchange any matter with its surroundings, and isn't subject to any force whose source is external to the system.[1][2] A closed system in classical mechanics would be considered an isolated system in thermodynamics.

### In thermodynamics

Main article: Thermodynamic system

In thermodynamics, a closed system can exchange energy (as heat or work) but not matter, with its surroundings. An isolated system cannot exchange any heat, work, or matter with the surroundings, while an open system can exchange energy and matter.[3][4][5][6][7][8][9] (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 here used.[10][11]) 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 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:

$\sum_{j=1}^m a_{ij}N_j=b_i$

where $N_j$ is the number of j-type molecules, $a_{ij}$ is the number of atoms of element i in molecule j and bi is the total number of atoms of element i 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 quantum physics

Further information: Quantum field theory

## In chemistry

In chemistry, a closed system is where no reactants or products can escape.

## 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.

## References

1. ^ Rana, N.C.; P.S. Joag (1991). Classical Mechanics. p. 78. ISBN 978-0-07-460315-4.
2. ^ Landau, L.D.; E.M. Lifshitz (1976). Mechanics (third ed.). p. 8. ISBN 978-0-7506-2896-9.
3. ^ Prigogine, I., Defay, R. (1950/1954). Chemical Thermodynamics, Longmans, Green & Co, London, p. 66.
4. ^ Tisza, L. (1966). Generalized Thermodynamics, M.I.T Press, Cambridge MA, pp. 112–113.
5. ^ Guggenheim, E.A. (1949/1967). Thermodynamics. An Advanced Treatment for Chemists and Physicists, (1st edition 1949) 5th edition 1967, North-Holland, Amsterdam, p. 14.
6. ^ Münster, A. (1970). Classical Thermodynamics, translated by E.S. Halberstadt, Wiley–Interscience, London, pp. 6–7.
7. ^ 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.
8. ^ Tschoegl, N.W. (2000). Fundamentals of Equilibrium and Steady-State Thermodynamics, Elsevier, Amsterdam, ISBN 0-444-50426-5, p. 5.
9. ^ Silbey, R.J., Alberty, R.A., Bawendi, M.G. (1955/2005). Physical Chemistry, fourth edition, Wiley, Hoboken NJ, p. 4.
10. ^ 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.
11. ^ ter Haar, D., Wergeland, H. (1966). Elements of Thermodynamics, Addison-Wesley Publishing, Reading MA, p. 43.