Reversible process (thermodynamics)

Last updated November 09, 2022

In thermodynamics, a reversible process is a process, involving a system and its surroundings, whose direction can be reversed by infinitesimal changes in some properties of the surroundings, such as pressure or temperature.^[1]^[2]^[3]

Throughout an entire reversible process, the system is in thermodynamic equilibrium, both physical and chemical, and nearly in pressure and temperature equilibrium with its surroundings. This prevents unbalanced forces and acceleration of moving system boundaries, which in turn avoids friction and other dissipation.

To maintain equilibrium, reversible processes are extremely slow (quasistatic). The process must occur slowly enough that after some small change in a thermodynamic parameter, the physical processes in the system have enough time for the other parameters to self-adjust to match the new, changed parameter value. For example, if a container of water has sat in a room long enough to match the steady temperature of the surrounding air, for a small change in the air temperature to be reversible, the whole system of air, water, and container must wait long enough for the container and air to settle into a new, matching temperature before the next small change can occur.^{[lower-alpha 1]} While processes in isolated systems are never reversible,^[3] cyclical processes can be reversible or irreversible.^[4] Reversible processes are hypothetical or idealized but central to the second law of thermodynamics.^[3] Melting or freezing of ice in water is an example of a realistic process that is nearly reversible.

Additionally, the system must be in (quasistatic) equilibrium with the surroundings at all time, and there must be no dissipative effects, such as friction, for a process to be considered reversible.^[5]

Reversible processes are useful in thermodynamics because they are so idealized that the equations for heat and expansion/compression work are simple.^[6] This enables the analysis of model processes, which usually define the maximum efficiency attainable in corresponding real processes. Other applications exploit that entropy and internal energy are state functions whose change depends only on the initial and final states of the system, not on how the process occurred.^[6] Therefore, the entropy and internal-energy change in a real process can be calculated quite easily by analyzing a reversible process connecting the real initial and final system states. In addition, reversibility defines the thermodynamic condition for chemical equilibrium.

Overview

Thermodynamic processes can be carried out in one of two ways: reversibly or irreversibly. An ideal thermodynamically reversible process is free of dissipative losses and therefore the magnitude of work performed by or on the system would be maximized. The incomplete conversion of heat to work in a cyclic process, however, applies to both reversible and irreversible cycles. The dependence of work on the path of the thermodynamic process is also unrelated to reversibility, since expansion work, which can be visualized on a pressure–volume diagram as the area beneath the equilibrium curve, is different for different reversible expansion processes (e.g. adiabatic, then isothermal; vs. isothermal, then adiabatic) connecting the same initial and final states.

Irreversibility

In an irreversible process, finite changes are made; therefore the system is not at equilibrium throughout the process. In a cyclic process, the difference between the reversible work $(\,W_{\mathsf {rev}}\,)$ and the actual work $(\,W_{\mathsf {act}}\,)$ for a process as shown in the following equation: $\;I=W_{\mathsf {rev}}-W_{\mathsf {act}}~.$

Boundaries and states

Simple^[3] reversible processes change the state of a system in such a way that the net change in the combined entropy of the system and its surroundings is zero. (The entropy of the system alone is conserved only in reversible adiabatic processes.) Nevertheless, the Carnot cycle demonstrates that the state of the surroundings may change in a reversible process as the system returns to its initial state. Reversible processes define the boundaries of how efficient heat engines can be in thermodynamics and engineering: a reversible process is one where the machine has maximum efficiency (see Carnot cycle).

Reversible adiabatic process: The state on the left can be reached from the state on the right as well as vice versa without exchanging heat with the environment. Adiabatic-reversible-state-change.svg — Reversible adiabatic process: The state on the left can be reached from the state on the right as well as vice versa without exchanging heat with the environment.

In some cases, it may be important to distinguish between reversible and quasistatic processes. Reversible processes are always quasistatic, but the converse is not always true.^[2] For example, an infinitesimal compression of a gas in a cylinder where there is friction between the piston and the cylinder is a quasistatic, but not reversible process.^[7] Although the system has been driven from its equilibrium state by only an infinitesimal amount, energy has been irreversibly lost to waste heat, due to friction, and cannot be recovered by simply moving the piston in the opposite direction by the infinitesimally same amount.

Engineering archaisms

Historically, the term Tesla principle was used to describe (among other things) certain reversible processes invented by Nikola Tesla.^[8] However, this phrase is no longer in conventional use. The principle stated that some systems could be reversed and operated in a complementary manner. It was developed during Tesla's research in alternating currents where the current's magnitude and direction varied cyclically. During a demonstration of the Tesla turbine, the disks revolved and machinery fastened to the shaft was operated by the engine. If the turbine's operation was reversed, the disks acted as a pump.^[9]

Footnotes

↑ The absolute standard for "fast" and "slow" thermodynamic change is the maximum amount of time required for a temperature change (and the consequential changes in pressure, etc.) to travel across each of the parts of the whole system. However, depending on the system or the process considered, thermodynamically "slow" might sometimes seem "fast" in human terms: In the example of the container and room air, if the container is just a porcelain coffee cup, heat can flow fairly quickly between the small object and the larger room. In a different version of the same process where the container is a 40 gallon metal tank of water, one might intuitively expect rematching of temperatures ("equilibration") of the coffee cup to only require a few minutes, which is fast by comparison to the hours one could expect for a 40 gallon tank of water.
Each different physical aspect of a system either increases or reduces the amount of time required for the whole system to re-establish its thermodynamic equilibrium after a small disturbance, and hence changes the time required for a "quasistatic" change. The number of aspects one might consider can become either tedious or overwhelming: The metal skin of the tank will conduct heat more quickly than the porcelain, so that speeds up equilibration, but the much larger mass of water – whose surface is actually smaller in proportion to its volume – will slow down the restoration of equilibrium. If the coffee cup has no lid, then evaporative cooling could speed up its equilibration even more, compared to an almost-sealed tank with only an open, narrow spigot. If the spigot is closed so the tank is sealed, how "springy" its walls are for adapting to consequent pressure change affects the speed of equilibration. Further issues involve whether the room air is stagnant or has forced air circulation (a fan); if the tank nearly fills the room, the smaller amount of heat in the air relative to the heat in the tank may speed up the temperatures settling out; radiative cooling rates depend even on what color the tank is; and so on.
Although standard practice is to ignore as much detail as possible, an ignored process might in fact be the slowest process in the system, and hence set the standard for what "slow" is for a quasistatic change. Physicists and engineers tend to be defensively vague about how long one must wait, and in practice allow ample or excessive time for equilibrium to re-establish.
A experimenter wanting to proceed as quickly as possible can determine the settling time empirically, by placing accurate thermometers throughout the whole system: Equilibration is complete once every one of the thermometers in the system resumes reading the same value as all the others, and the system is then ready for the next small temperature change.

Related Research Articles

In thermodynamics, an adiabatic process is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal process, an adiabatic process transfers energy to the surroundings only as work. As a key concept in thermodynamics, the adiabatic process supports the theory that explains the first law of thermodynamics.

<span class="mw-page-title-main">Carnot heat engine</span> Theoretical engine

A Carnot heat engine is a heat engine that operates on the Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824. The Carnot engine model was graphically expanded by Benoît Paul Émile Clapeyron in 1834 and mathematically explored by Rudolf Clausius in 1857, work that led to the fundamental thermodynamic concept of entropy. The Carnot engine is the most efficient heat engine which is theoretically possible. The efficiency depends only upon the absolute temperatures of the hot and cold heat reservoirs between which it operates.

Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication.

Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology.

The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects, unless energy is supplied to reverse the direction of heat flow. Another definition is: "Not all heat energy can be converted into work in a cyclic process."

The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant amount of matter. The law also defines the internal energy of a system, an extensive property for taking account of the balance of energies in the system.

In thermodynamics, an isentropic process is an idealized thermodynamic process that is both adiabatic and reversible. The work transfers of the system are frictionless, and there is no net transfer of heat or matter. Such an idealized process is useful in engineering as a model of and basis of comparison for real processes. This process is idealized because reversible processes do not occur in reality; thinking of a process as both adiabatic and reversible would show that the initial and final entropies are the same, thus, the reason it is called isentropic. Thermodynamic processes are named based on the effect they would have on the system. Even though in reality it is not necessarily possible to carry out an isentropic process, some may be approximated as such.

In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature T of a system remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and a change in the system occurs slowly enough to allow the system to be continuously adjusted to the temperature of the reservoir through heat exchange. In contrast, an adiabatic process is where a system exchanges no heat with its surroundings (Q = 0).

A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are not thermodynamic systems. A wall of a thermodynamic system may be purely notional, when it is described as being 'permeable' to all matter, all radiation, and all forces. A state of a thermodynamic system can be fully described in several different ways, by several different sets of thermodynamic state variables.

In thermodynamics, a quasi-static process, is a thermodynamic process that happens slowly enough for the system to remain in internal physical thermodynamic equilibrium. An example of this is quasi-static expansion of a mixture of hydrogen and oxygen gas, where the volume of the system changes so slowly that the pressure remains uniform throughout the system at each instant of time during the process. Such an idealized process is a succession of physical equilibrium states, characterized by infinite slowness.

In science, a process that is not reversible is called irreversible. This concept arises frequently in thermodynamics. All complex natural processes are irreversible, although a phase transition at the coexistence temperature is well approximated as reversible.

<span class="mw-page-title-main">Joule expansion</span>

The Joule expansion is an irreversible process in thermodynamics in which a volume of gas is kept in one side of a thermally isolated container, with the other side of the container being evacuated. The partition between the two parts of the container is then opened, and the gas fills the whole container.

Classical thermodynamics considers three main kinds of thermodynamic process: (1) changes in a system, (2) cycles in a system, and (3) flow processes.

A thermodynamic cycle consists of a linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. In the process of passing through a cycle, the working fluid (system) may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a heat engine. Conversely, the cycle may be reversed and use work to move heat from a cold source and transfer it to a warm sink thereby acting as a heat pump. If at every point in the cycle the system is in thermodynamic equilibrium, the cycle is reversible. Whether carried out reversible or irreversibly, the net entropy change of the system is zero, as entropy is a state function.

In thermodynamics, work is one of the principal processes by which a thermodynamic system can interact with its surroundings and exchange energy. An exchange of energy is facilitated by a mechanism through which the system can spontaneously exert macroscopic forces on its surroundings, or vice versa. In the surroundings, this mechanical work can lift a weight, for example.

The Clausius theorem (1855), also known as the Clausius inequality, states that for a thermodynamic system exchanging heat with external thermal reservoirs and undergoing a thermodynamic cycle,

In classical thermodynamics, entropy is a property of a thermodynamic system that expresses the direction or outcome of spontaneous changes in the system. The term was introduced by Rudolf Clausius in the mid-nineteenth century from the Greek word τρoπή (transformation) to explain the relationship of the internal energy that is available or unavailable for transformations in form of heat and work. Entropy predicts that certain processes are irreversible or impossible, despite not violating the conservation of energy. The definition of entropy is central to the establishment of the second law of thermodynamics, which states that the entropy of isolated systems cannot decrease with time, as they always tend to arrive at a state of thermodynamic equilibrium, where the entropy is highest. Entropy is therefore also considered to be a measure of disorder in the system.

A Carnot cycle is an ideal thermodynamic cycle proposed by French physicist Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. By Carnot's theorem, it provides an upper limit on the efficiency of any classical thermodynamic engine during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference through the application of work to the system.

In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not contain heat. Nevertheless, the term is also often used to refer to the thermal energy contained in a system as a component of its internal energy and that is reflected in the temperature of the system. For both uses of the term, heat is a form of energy.

Adiabatic accessibility denotes a certain relation between two equilibrium states of a thermodynamic system. The concept was coined by Constantin Carathéodory in 1909 and taken up 90 years later by Elliott Lieb and J. Yngvason in their axiomatic approach to the foundations of thermodynamics. It was also used by R. Giles in his 1964 monograph.

References

↑ McGovern, Judith (17 March 2020). "Reversible processes". PHYS20352 Thermal and Statistical Physics. University of Manchester. Retrieved 2 November 2020. This is the hallmark of a reversible process: An infinitesimal change in the external conditions reverses the direction of the change.
1 2 Sears, F.W. & Salinger, G.L. (1986). Thermodynamics, Kinetic Theory, and Statistical Thermodynamics (3rd ed.). Addison-Wesley.
1 2 3 4 DeVoe, H. (2020). "Spontaneous reversible and irreversible processes". Thermodynamics and Chemistry. chem.libretexts.org. Bookshelves.
↑ Zumdahl, Steven S. (2005). "§ 10.2 The isothermal expansion and compression of an ideal gas". Chemical Principles (5th ed.). Houghton Mifflin.
↑ Çengel, Yunus; Boles, Michael (1 January 2006). Thermodynamics, An Engineering Approach (PDF) (5th ed.). Boston, Massachusetts: Tata McGraw-Hill. p. 299. ISBN 978-0070606593 . Retrieved 8 November 2022.
1 2 Atkins, P.; Jones, L.; Laverman, L. (2016). Chemical Principles (7th ed.). Freeman. ISBN 978-1-4641-8395-9.
↑ Giancoli, D.C. (2000). Physics for Scientists and Engineers (with Modern Physics) (3rd ed.). Prentice-Hall.
↑ "[no title cited]". Electrical Experimenter (low-res. text photo). January 1919. p. 615 – via teslasociety.com.
↑ "Tesla's new monarch of machines". The New York Herald Tribune . Tesla Engine Builders Association. 15 Oct 1911. Archived from the original on September 28, 2011.

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[relative_speed_note-4] The absolute standard for "fast" and "slow" thermodynamic change is the maximum amount of time required for a temperature change (and the consequential changes in pressure, etc.) to travel across each of the parts of the whole system. However, depending on the system or the process considered, thermodynamically "slow" might sometimes seem "fast" in human terms: In the example of the container and room air, if the container is just a porcelain coffee cup, heat can flow fairly quickly between the small object and the larger room. In a different version of the same process where the container is a 40 gallon metal tank of water, one might intuitively expect rematching of temperatures ("equilibration") of the coffee cup to only require a few minutes, which is fast by comparison to the hours one could expect for a 40 gallon tank of water.
Each different physical aspect of a system either increases or reduces the amount of time required for the whole system to re-establish its thermodynamic equilibrium after a small disturbance, and hence changes the time required for a "quasistatic" change. The number of aspects one might consider can become either tedious or overwhelming: The metal skin of the tank will conduct heat more quickly than the porcelain, so that speeds up equilibration, but the much larger mass of water – whose surface is actually smaller in proportion to its volume – will slow down the restoration of equilibrium. If the coffee cup has no lid, then evaporative cooling could speed up its equilibration even more, compared to an almost-sealed tank with only an open, narrow spigot. If the spigot is closed so the tank is sealed, how "springy" its walls are for adapting to consequent pressure change affects the speed of equilibration. Further issues involve whether the room air is stagnant or has forced air circulation (a fan); if the tank nearly fills the room, the smaller amount of heat in the air relative to the heat in the tank may speed up the temperatures settling out; radiative cooling rates depend even on what color the tank is; and so on.
Although standard practice is to ignore as much detail as possible, an ignored process might in fact be the slowest process in the system, and hence set the standard for what "slow" is for a quasistatic change. Physicists and engineers tend to be defensively vague about how long one must wait, and in practice allow ample or excessive time for equilibrium to re-establish.
A experimenter wanting to proceed as quickly as possible can determine the settling time empirically, by placing accurate thermometers throughout the whole system: Equilibration is complete once every one of the thermometers in the system resumes reading the same value as all the others, and the system is then ready for the next small temperature change.

[McGovern-2020-03-17-1] McGovern, Judith (17 March 2020). "Reversible processes". PHYS20352 Thermal and Statistical Physics. University of Manchester. Retrieved 2 November 2020. This is the hallmark of a reversible process: An infinitesimal change in the external conditions reverses the direction of the change.

[Sears-Salinger-1986-2] 1 2 Sears, F.W. & Salinger, G.L. (1986). Thermodynamics, Kinetic Theory, and Statistical Thermodynamics (3rd ed.). Addison-Wesley.

[deVoe-2020-3] 1 2 3 4 DeVoe, H. (2020). "Spontaneous reversible and irreversible processes". Thermodynamics and Chemistry. chem.libretexts.org. Bookshelves.

[Zumdahl-2005-5] Zumdahl, Steven S. (2005). "§ 10.2 The isothermal expansion and compression of an ideal gas". Chemical Principles (5th ed.). Houghton Mifflin.

[6] Çengel, Yunus; Boles, Michael (1 January 2006). Thermodynamics, An Engineering Approach (PDF) (5th ed.). Boston, Massachusetts: Tata McGraw-Hill. p. 299. ISBN 978-0070606593 . Retrieved 8 November 2022.

[Atkins-Jones-Laverman-2016-7] 1 2 Atkins, P.; Jones, L.; Laverman, L. (2016). Chemical Principles (7th ed.). Freeman. ISBN 978-1-4641-8395-9.

[Giancoli-2000-8] Giancoli, D.C. (2000). Physics for Scientists and Engineers (with Modern Physics) (3rd ed.). Prentice-Hall.

[ElectrExpm-1919-01-9] "[no title cited]". Electrical Experimenter (low-res. text photo). January 1919. p. 615 – via teslasociety.com.

[NYTribune-1911-10-15-10] "Tesla's new monarch of machines". The New York Herald Tribune . Tesla Engine Builders Association. 15 Oct 1911. Archived from the original on September 28, 2011.

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