Closed system

Closed systems are often used to limit the factors that can affect the results of a specific problem or experiment.

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.

[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.

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.

It allows the elimination of some external factors that could alter the results of the experiment or problem thus simplifying it.

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).

where i is the imaginary unit, ħ is the Planck constant divided by 2π, the symbol ⁠∂/∂t⁠ indicates a partial derivative with respect to time t, Ψ (the Greek letter psi) is the wave function of the quantum system, and Ĥ is the Hamiltonian operator (which characterizes the total energy of any given wave function and takes different forms depending on the situation).

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).