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A closed system is a physical system that 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 nonrelativistic classical mechanics, a closed system is a physical system that 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, 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 b_{i} 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 chemistry, a closed system is where no reactants or products can escape.
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.
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