Isolated system
An isolated system is a thermodynamic system in which neither matter nor energy can be exchanged with its surroundings, making it completely self-contained and independent of external influences.[1] This concept is fundamental in physics and chemistry, where it represents an idealized boundary condition for analyzing processes without interference.[2] Thermodynamic systems are broadly classified into three types based on their interactions with the environment: open systems, which exchange both matter and energy; closed systems, which exchange energy but not matter; and isolated systems, which exchange neither.[3] In an isolated system, properties such as internal energy remain constant because no heat, work, or mass transfer occurs across the boundary, aligning directly with the first law of thermodynamics, which states that energy is conserved.[4] The universe itself is often regarded as the quintessential isolated system, as it encompasses all matter and energy without any external surroundings.[1] Isolated systems play a pivotal role in the second law of thermodynamics, which asserts that in such systems, entropy—a measure of disorder—spontaneously increases or remains constant, but never decreases, driving natural processes toward equilibrium.[5] This principle explains irreversible phenomena like heat flow from hot to cold objects without external input. Practical approximations of isolated systems include a sealed, rigid, and perfectly insulated container, such as the interior of a high-quality thermos, though true isolation is theoretically unattainable in reality due to unavoidable interactions at the quantum or cosmic scales.[6] The study of isolated systems underpins advancements in fields like statistical mechanics, where entropy is quantified as the logarithm of the system's accessible microstates.[7]Definition and Fundamentals
Core Definition
In thermodynamic analysis, the universe is partitioned into a system, defined as the specific portion of matter or region of space selected for study, and the surroundings, which include everything external to the system. This division establishes a conceptual boundary that governs potential interactions, such as transfers of matter or energy, allowing for controlled examination of physical processes.[2] An isolated system is a thermodynamic system that exchanges neither matter nor energy—including forms such as heat, work, or electromagnetic radiation—with its surroundings, ensuring complete independence from external influences. This strict separation implies that any changes within the system arise solely from internal dynamics, without input or output across the boundary. In practice, perfectly isolated systems are idealized, as real-world approximations always involve minimal interactions, but the concept serves as a foundational idealization in thermodynamic theory.[8] The concept of an isolated system originated in classical thermodynamics, developed by Rudolf Clausius in the 1850s amid his foundational work on the laws of thermodynamics, particularly through analyses of heat engines and energy transformations that presupposed systems impervious to external exchanges. Clausius' contributions, building on earlier ideas from Sadi Carnot, emphasized such systems to explore principles like the equivalence of heat and work without external interference. Within an isolated system, the total energy remains constant, aligning with the broader principle of energy conservation.[9][10]Fundamental Properties
An isolated system exhibits invariance in its total energy, meaning the internal energy remains constant over time because there are no exchanges of energy or matter with the surroundings.[11] This conservation arises from the first law of thermodynamics applied to systems without heat transfer, work, or mass flow, ensuring that any internal transformations do not alter the overall energy content.[12] Isolated systems also demonstrate a natural tendency to evolve toward thermodynamic equilibrium, where they reach a state of maximum entropy without external influences.[13] This progression reflects the second law of thermodynamics, which dictates that entropy in an isolated system increases monotonically until equilibrium is achieved, marking the point of highest disorder or uniformity.[12] In ideal theoretical scenarios, processes within a perfectly isolated system can be reversible, maintaining constant entropy throughout.[13] However, real-world approximations of isolation inevitably introduce irreversibility due to unavoidable dissipative effects, leading to entropy production and a one-way evolution toward equilibrium.[12] Mathematically, the isolation condition is represented by the absence of changes in total energy and mass, expressed as: dE = 0 for no net energy transfer, and dm = 0 for no mass transfer across the system boundary.[12] These relations encapsulate the defining constraints that preserve the system's intrinsic quantities.[11]System Classifications
Closed Systems
A closed system in thermodynamics is a physical system that exchanges energy with its surroundings in the form of heat or work, but does not permit the transfer of matter across its boundaries.[14] This definition ensures that the mass within the system remains constant, while allowing interactions that can alter its energetic state.[15] The primary distinction from an isolated system lies in this permitted energy exchange: in a closed system, heat transfer (Q ≠ 0) or work (W ≠ 0) can occur, potentially leading to changes in the system's internal energy. For instance, unlike the stricter isolation where no such exchanges happen, a closed system might undergo heating or mechanical compression without mass loss. Boundaries of closed systems are typically impermeable to matter, such as rigid, diathermic walls that conduct heat while preventing particle passage, or movable pistons in a sealed cylinder that enable work via expansion or contraction.[16] These configurations are common in laboratory devices like sealed calorimeters with conductive walls. The concept of closed systems emerged in the 19th-century development of thermodynamics, distinguished alongside isolated systems in the foundational work on entropy by Rudolf Clausius, who analyzed heat transformations in systems allowing energy interactions to formulate principles of irreversibility.[9] Clausius's 1850 and 1865 contributions emphasized such systems in deriving the second law, where entropy changes arise from heat flows across boundaries without matter exchange.[17] This framework provided a basis for understanding processes like heat engines, where closed-system behavior underpins efficiency limits.Open Systems
An open system in thermodynamics is defined as a region of space or a physical entity that can exchange both matter and energy with its surroundings, allowing for the inflow and outflow of mass as well as heat and work transfers.[18] This permeability distinguishes open systems from more restricted classifications, enabling dynamic interactions that drive processes far from equilibrium.[2] Analyzing open systems necessitates incorporating mass flow rates—such as the rate at which substances enter or exit the system—alongside energy fluxes like heat addition or mechanical work, which complicates thermodynamic balances compared to systems without mass exchange. These considerations are essential for applying conservation laws, where the first law must account for the enthalpy carried by flowing matter, ensuring accurate predictions of system behavior under continuous operation.[19] Common examples of open systems include biological organisms, which continuously intake nutrients and oxygen while expelling waste and carbon dioxide to maintain metabolic functions, and chemical reactors, where reactants are introduced, undergo transformations, and products are removed in a steady stream.[20] In these realizations, the ongoing exchange sustains non-equilibrium states that support complex, self-organizing processes.[21] The conceptual evolution of open systems extended significantly in the 20th century through the framework of non-equilibrium thermodynamics, pioneered by Ilya Prigogine, who demonstrated how such systems can exhibit dissipative structures and order emerging from irreversible processes.[22] Prigogine's work, recognized with the 1977 Nobel Prize in Chemistry, shifted focus from classical equilibrium assumptions to the dynamics of open systems driven by external fluxes, influencing fields from chemistry to biology.[23]Thermodynamic Principles
First Law Application
The first law of thermodynamics, which expresses the conservation of energy, states that the change in the internal energy of a system, \Delta U, equals the heat added to the system, Q, minus the work done by the system, W: \Delta U = Q - W [24]For an isolated system, by definition, there is no exchange of heat or matter with the surroundings, so Q = 0, and no work can be performed across the impermeable boundary, so W = 0.[25] [26] This leads to the direct consequence that \Delta U = 0, meaning the internal energy of an isolated system remains constant throughout any process occurring within it.[26] [27] The isolation enforces energy conservation by preventing any net inflow or outflow, ensuring that all transformations—such as conversions between kinetic, potential, and thermal forms—occur without altering the total energy content.[27] The implications of this constancy are profound for analyzing system behavior: the total energy, encompassing kinetic, potential, and thermal components, stays fixed, allowing predictions of equilibrium states or dynamic evolutions solely from internal rearrangements without reliance on external energy inputs.[28] This fixed energy budget underpins the ability to model processes like free expansion or internal collisions in isolation, where state changes are determined entirely by initial conditions.[24] In the framework of special relativity, the concept extends to the conservation of four-momentum for isolated systems, where the total four-momentum remains invariant in the absence of external interactions, unifying energy and momentum conservation across inertial frames.[29]