Closed system

In thermodynamics and physics, a closed system is defined as a physical system that exchanges energy—such as heat or work—with its surroundings but does not allow the transfer of matter across its boundary.^[1] This contrasts with an open system, which permits both energy and matter exchange, and an isolated system, which exchanges neither.^[1] The concept is fundamental to analyzing energy conservation and transformations within bounded quantities of matter, such as a fixed volume of gas in a piston-cylinder assembly.^[2] The first law of thermodynamics, which expresses the conservation of energy, is particularly applied to closed systems through the equation \Delta E = Q - W, where \Delta E represents the change in the system's total energy (including internal, kinetic, and potential components), Q is the heat added to the system, and W is the work done by the system.^[2] For many practical cases, such as stationary processes where kinetic and potential energies remain constant, this simplifies to focus on changes in internal energy, \Delta U = Q - W.^[2] This formulation underscores that energy within a closed system is neither created nor destroyed but can convert between forms, enabling precise predictions of state changes independent of the process path.^[2] Closed systems are ubiquitous in engineering and physical applications, including the combustion chamber of an internal combustion engine, where fuel and oxidizer react without mass loss.^[3] In atmospheric science, air parcels are modeled as closed systems to study thermodynamic processes like adiabatic expansion without moisture exchange.^[4] These models facilitate the design of efficient heat engines, refrigeration cycles, and chemical reactors, where understanding energy balances ensures optimal performance and compliance with physical laws.^[5]

Fundamental Concepts

Basic Definition

A closed system is defined as a physical system that can exchange energy, such as heat or work, with its surroundings but does not allow the transfer of matter across its boundaries.^[6] This concept is fundamental in thermodynamics, where the system's mass remains constant while energy interactions influence its internal state.^[7] Key attributes of a closed system include boundaries that are impermeable to matter but permeable to energy forms like thermal radiation, mechanical work, or pressure-volume changes.^[8] This contrasts with common intuition, where "sealed" or "closed" might suggest no interactions whatsoever; in scientific terms, closure pertains specifically to matter conservation, permitting controlled energy flows. Representative examples illustrate these attributes: a sealed piston-cylinder assembly containing gas, where the piston enables work through volume changes and heat transfer via the cylinder walls, but no gas escapes.^[9] Similarly, a thermos bottle approximates a closed system for short durations, retaining liquid matter while slowly exchanging minimal heat with the environment.^[10] The system boundary is conceptualized as a real or imaginary mathematical surface that delineates the system from its surroundings, facilitating analysis of exchanges without matter crossing. This boundary enables precise modeling of energy transfers in theoretical and practical contexts.

System Classifications

In thermodynamics and physics, systems are classified into three primary categories based on their exchanges with the surroundings: open systems, which can exchange both matter and energy; closed systems, which exchange energy but not matter; and isolated systems, which exchange neither matter nor energy. This typology builds on the concept of a system boundary that delineates interactions with the external environment. Isolated systems represent theoretical idealizations, as achieving complete isolation from all external influences is unattainable in reality; a conceptual example is a perfect vacuum chamber with no thermal, mechanical, or radiative contact with the outside. Closed systems, while also approximations, are more feasible in controlled settings, such as a laboratory beaker sealed with a lid to block matter transfer while permitting heat exchange through the boundary. The classification into open, closed, and isolated systems is a standard convention in modern thermodynamics, evolving from 19th-century foundational work on energy conservation. To illustrate the distinctions, the following table compares the permissible exchanges across system types:

System Type	Matter Exchange	Energy Exchange (e.g., heat or work)
Open	Yes	Yes
Closed	No	Yes
Isolated	No	No

Applications in Physics

In Classical Mechanics

In classical mechanics, a closed system is defined as a collection of particles or bodies where no matter enters or leaves the system, and the net external force acting on it is zero, leading to the application of conservation laws for momentum and angular momentum.^[11]^[12] The conservation of linear momentum is a key principle for such systems, stating that the total linear momentum remains constant over time. This arises from Newton's third law, where internal forces between particles cancel in pairs, producing no net change in the system's momentum. The total linear momentum \vec{P} of the system is given by the vector sum \vec{P} = \sum_i m_i \vec{v_i}, where m_i is the mass of the i-th particle and \vec{v_i} is its velocity, and it equals a constant value: \vec{P} = \constant.^[11]^[13] Similarly, the conservation of angular momentum applies when the net external torque is zero, preserving the total angular momentum \vec{L} = \sum_i \vec{r_i} \times m_i \vec{v_i}, where \vec{r_i} is the position vector relative to a fixed point, such that \vec{L} = \constant.^[14]^[15] A representative example is the collision of two billiard balls on a frictionless table, where the system consists of the balls alone, with interactions governed solely by internal contact forces; the total linear momentum before and after collision remains unchanged, allowing prediction of post-collision velocities.^[16]^[17] Another example is a spacecraft in free space, treating the spacecraft, fuel, and exhaust gases as the closed system; as fuel is ejected, the thrust provides an internal force, conserving the total linear momentum while propelling the spacecraft forward.^[12]^[18] These principles assume non-relativistic speeds, where velocities are much less than the speed of light, and real-world systems approximate closure by neglecting small external influences like air resistance or gravitational gradients.^[11]^[14]

In Thermodynamics

In thermodynamics, a closed system is defined as one that permits no transfer of matter across its boundary but allows the exchange of energy through heat and work.^[6] The internal energy U of such a system serves as a state function, meaning its value depends solely on the system's current thermodynamic state, independent of the path taken to reach that state.^[19] The first law of thermodynamics for closed systems embodies the conservation of energy, stating that the change in internal energy equals the heat added to the system minus the work done by the system:

\Delta U = Q - W

where Q represents heat transfer into the system and W denotes work output from the system.^[19] This equation highlights how energy transformations occur without mass flow, such as during compression or expansion in a fixed volume. The second law introduces directionality to these processes, asserting that the entropy S of a closed system either increases for irreversible processes or remains constant for reversible ones, reflecting the tendency toward greater disorder.^[20] Various thermodynamic processes can be analyzed within closed systems, including isobaric processes at constant pressure, isothermal processes maintaining constant temperature, and adiabatic processes with no heat exchange. For instance, the behavior of an ideal gas confined in a piston-cylinder assembly exemplifies these: in an isobaric expansion, the gas absorbs heat while performing boundary work; an isothermal process involves heat input to offset work output, keeping temperature steady; and an adiabatic compression raises internal energy solely through work input.^[21] Practical examples illustrate these principles. In a steam engine, the cylinder functions as a closed system during the power stroke, where high-pressure steam expands, transferring heat and performing work on the piston without mass exchange across the boundary.^[22] Similarly, a bomb calorimeter approximates a closed system for combustion experiments, containing reactants in a sealed vessel where the released heat alters the temperature of surrounding water, enabling precise measurement of internal energy changes without matter transfer.^[23] For constant-pressure processes in closed systems, enthalpy H, defined as

H = U + PV

provides a convenient measure, as the change in enthalpy \Delta H equals the heat transferred Q_p under these conditions, simplifying energy balance calculations.^[24] This property is particularly valuable in analyzing expansions or reactions where pressure remains fixed, linking internal energy directly to observable heat flows.^[25]

In Quantum Physics

In quantum physics, a closed system refers to a quantum system that evolves solely under its internal Hamiltonian, without any interaction with external degrees of freedom, thereby preventing the leakage of matter, energy, or information.^[26] This isolation ensures that the system's dynamics remain self-contained, allowing for purely internal processes without external influences./06:_Time_Evolution_in_Quantum_Mechanics/6.01:_Time-dependent_Schrodinger_equation) The time evolution of such a system is governed by the time-dependent Schrödinger equation:

i \hbar \frac{\partial}{\partial t} |\psi(t)\rangle = H |\psi(t)\rangle

where |\psi(t)\rangle is the state vector, H is the time-independent Hamiltonian operator, \hbar is the reduced Planck's constant, and the solution yields a unitary operator U(t) = e^{-iHt/\hbar} that propagates the initial state |\psi(0)\rangle to |\psi(t)\rangle = U(t) |\psi(0)\rangle./06:_Time_Evolution_in_Quantum_Mechanics/6.01:_Time-dependent_Schrodinger_equation) Unitarity guarantees the preservation of the norm of the wave function, ensuring that total probabilities sum to unity and information within the system remains conserved.^[26] In an ideal closed quantum system, coherent superpositions of states are preserved throughout the evolution, as the unitary dynamics maintain quantum interference effects without dissipation.^[27] However, real systems are rarely perfectly isolated; any unintended coupling to the environment leads to decoherence, where entanglement with external modes causes the loss of observable coherence and the apparent collapse of superpositions into classical mixtures.^[28] This distinction underscores the fragility of quantum coherence, which is central to phenomena like interference but rapidly degrades in open systems.^[27] Representative examples of closed quantum systems include an isolated atom in a high-vacuum environment, where its discrete energy levels and electronic transitions evolve unitarily without broadening due to external perturbations.^[29] Another is a single qubit in quantum computing during gate operations prior to measurement, which remains in a coherent superposition until deliberate coupling to a measurement apparatus or environment induces decoherence.^[30] In contrast to classical closed systems, which follow deterministic trajectories, quantum closed systems can develop internal entanglement among subsystems, enabling non-local correlations, while the overall isolation avoids wave function collapse from external observations.

Applications in Chemistry

Closed Reaction Systems

In chemical kinetics, a closed reaction system is defined as one containing a fixed amount of reactants and products, with no influx or outflow of chemical species, thereby enabling precise mass balance calculations based on conservation principles.^[31] This setup is characteristic of batch reactors, where the total mass remains constant over time since no material crosses the system boundary.^[32] Key concepts in closed reaction systems include stoichiometric constraints, which dictate the proportional relationships among species based on the reaction's balanced equation, and reaction rates that depend solely on the concentrations of species within the system.^[33] These constraints ensure that changes in one species' concentration are linked to others via the stoichiometry, facilitating the tracking of composition evolution without external inputs. Reaction rates are governed by intrinsic kinetic laws, unaffected by continuous feeding or removal, allowing isolation of mechanistic effects.^[34] A fundamental equation for mass balance in such systems is the conservation of total mass, expressed as \frac{dM}{dt} = 0, where M is the total mass, confirming its constancy.^[32] For species kinetics, rate laws describe the dynamics, such as \frac{d[C]}{dt} = k [A]^m [B]^n in a closed batch reactor, where k is the rate constant, and m and n are reaction orders determined experimentally.^[33] Representative examples include a sealed flask conducting the gas-phase reaction \mathrm{H_2 + I_2 \rightleftharpoons 2HI}, where initial reactants evolve to equilibrium without species exchange, enabling study of second-order kinetics.^[35] Another is a constant-volume combustion chamber, used to model fuel oxidation in a closed environment, such as methane-air mixtures, to analyze heat release and species depletion.^[36] Limitations of closed reaction systems arise from potential pressure or volume changes during reactions involving gases, which can shift chemical equilibria despite fixed mass, complicating interpretations of kinetic data.^[31] Nonetheless, they are ideal for investigating reaction orders and mechanisms in isolation from external perturbations. While matter is conserved internally, energy exchanges with surroundings may occur, influencing temperature-dependent rates.^[34]

Phase and Equilibrium Considerations

In chemical thermodynamics, a closed system achieves equilibrium when its fixed composition allows multiple phases to coexist without any exchange of matter with the surroundings, ensuring that the chemical potentials of each component are equal across all phases. This state is characterized by the minimization of the Gibbs free energy at constant temperature and pressure, leading to stable phase distributions that persist unless externally perturbed. The Gibbs phase rule governs the degrees of freedom in such systems, stated as F = C - P + 2, where F represents the number of intensive variables (like temperature, pressure, or composition) that can be independently varied without altering the number of phases, C is the number of independent components, and P is the number of phases in equilibrium. This rule, derived from the conditions for thermodynamic equilibrium in heterogeneous systems, applies directly to closed systems by accounting for constraints on temperature and pressure as two of the variables. For instance, in a single-component closed system (C = 1) with three phases (P = 3), F = 0, rendering the system invariant at specific conditions like the triple point.^[37] At equilibrium, the chemical equilibrium constant K is expressed in terms of activities a_i, where K = \prod a_i^{\nu_i} for the reaction \sum \nu_i A_i = 0, with \nu_i as stoichiometric coefficients (positive for products, negative for reactants); activities account for non-ideal behavior through a_i = \gamma_i x_i in solutions or fugacity-based forms in gases. Perturbations to this equilibrium in closed systems follow Le Chatelier's principle, which predicts that the system shifts to counteract the disturbance, such as increasing pressure favoring the phase with lower volume or temperature changes altering endothermic/exothermic reaction extents.^[38]/Equilibria/Le_Chateliers_Principle/Le_Chatelier%27s_Principle_Fundamentals) A representative example is a closed vessel containing pure water in equilibrium among solid (ice), liquid, and vapor phases, approximating the triple point at 0.01°C and 611 Pa, where the system is invariant (F = 0) and all phases coexist stably without matter exchange. In multi-component scenarios, such as the solidification of a binary alloy like lead-tin in a sealed crucible, liquid and solid phases coexist along the eutectic line (F = 1 at constant pressure), with fixed composition dictating the phase boundaries during cooling.^[39]^[40] For non-ideal closed systems, deviations from ideality are quantified using fugacity f_i = \phi_i P y_i for gaseous components (where \phi_i is the fugacity coefficient, P is pressure, and y_i is mole fraction) and activity coefficients \gamma_i for liquid phases, enabling accurate equilibrium calculations via modified chemical potentials \mu_i = \mu_i^\circ + RT \ln a_i. These corrections, essential for real mixtures, ensure the phase rule holds while incorporating intermolecular interactions that affect phase stability.^[41]

Applications in Engineering

Thermodynamic Cycles

In engineering thermodynamics, a thermodynamic cycle in a closed system refers to a sequence of processes through which the working fluid undergoes changes in state and returns to its initial conditions, enabling the net conversion of heat absorbed from a high-temperature source into work output, with the remainder rejected to a low-temperature sink.^[42] This cyclic operation adheres to the first law of thermodynamics for closed systems, where the net work equals the difference between heat input and heat rejection over the cycle. The system boundary is defined to include only the working fluid, such as gas or vapor, while excluding interactions with external surroundings beyond heat and work transfers.^[43] Prominent examples of such cycles include the Carnot cycle, an idealized reversible process comprising two isothermal heat transfers and two adiabatic expansions and compressions, achieving maximum theoretical efficiency given by \eta = 1 - \frac{T_c}{T_h}, where T_h and T_c are the absolute temperatures of the hot and cold reservoirs, respectively.^[44] The Rankine cycle, fundamental to steam power generation, involves heating liquid water to produce high-pressure steam in a boiler, expanding the steam through a turbine to generate work, condensing the exhaust steam to liquid in a condenser, and pumping it back to the boiler, all within a closed loop of the working fluid.^[43] These cycles are graphically depicted on pressure-volume (PV) diagrams as closed loops, where the area enclosed by the path quantifies the net work performed by the system.^[45] In practical closed systems, real-world irreversibilities—such as fluid friction, pressure drops, and non-equilibrium heat transfers—degrade performance, resulting in efficiencies lower than the reversible ideals like the Carnot limit.^[46] For instance, in an internal combustion engine, the cylinder contents form a closed system during the compression and expansion phases when intake and exhaust valves are shut, allowing the air-fuel mixture to undergo a cycle that converts chemical energy into mechanical work via pressure-volume changes.^[47] Similarly, the vapor-compression refrigeration cycle operates as a closed system where a refrigerant fluid cycles through compression to high-pressure vapor, condensation to release heat, expansion to low-pressure liquid, and evaporation to absorb heat from the cooled space, thereby achieving refrigeration effect.^[48]

Mechanical and Fluid Systems

In mechanical and fluid engineering, a closed system is defined as an enclosed mechanical assembly or fluid volume where the mass content remains constant, with no transfer across boundaries, while allowing energy exchange through work, pressure, or motion. Such systems are fundamental in applications requiring precise control of internal dynamics without environmental interaction. For instance, closed hydraulic circuits operate by recirculating fluid directly from actuators back to the pump inlet, ensuring efficient power transmission in a sealed loop.^[49] A core principle governing fluid behavior in these systems is Bernoulli's equation for incompressible flows in closed loops, which expresses energy conservation along a streamline as P + \frac{1}{2} \rho v^2 + \rho g h = \constant, where P denotes static pressure, \rho is fluid density, v is velocity, g is gravitational acceleration, and h is elevation. This equation applies to steady, inviscid flows in enclosed conduits, such as pipes or channels, highlighting how pressure, kinetic, and potential energies balance without mass ingress or egress. In closed mechanical systems, vibration isolation principles are equally vital, employing passive or active mechanisms to decouple internal components from external disturbances while preserving system enclosure.^[50]^[51] Key concepts include damping and resonance management, where energy dissipation prevents amplification of oscillations in isolated structures. Tuned mass dampers, for example, consist of an auxiliary mass-spring system attached to the primary structure, tuned to the natural frequency to absorb vibrational energy and reduce resonance effects in enclosed mechanical setups. In hydraulic closed circuits, these principles extend to fluid containment, where viscous damping in seals and lines controls flow-induced vibrations, maintaining system stability without external mass addition.^[49] Practical examples illustrate these dynamics. A sealed hydraulic jack operates as a closed fluid system, where incompressible oil confined in a chamber transmits force via Pascal's principle: applied pressure on a small piston generates equal pressure throughout the enclosure, elevating a larger load piston without fluid loss. Similarly, a torsion pendulum exemplifies a closed rotational mechanical system, with a suspended mass oscillating about a torsion wire axis, conserving angular momentum internally as external influences like air resistance are minimized through enclosure.^[52]^[53] Engineering considerations for closed systems prioritize leak-proof designs, using high-integrity seals and gaskets to prevent unintended mass transfer that could compromise closure and efficiency. In finite-time operations, such as rapid cyclic motions, ideal closed system models are approximated to account for transient effects, ensuring stability through control strategies that achieve convergence in bounded durations without violating mass conservation.^[54]^[55]