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<title>Thermodynamic process</title>

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</style><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><th class="sidebar-title" style="padding-bottom:0.3em;border-bottom:1px solid #aaa;"><a href="Thermodynamics" title="Thermodynamics">Thermodynamics</a></th></tr><tr><td class="sidebar-image" style="display:block;margin:0.3em 0 0.4em;"><div class="sidebar-caption">The classical <a href="Carnot_heat_engine" title="Carnot heat engine">Carnot heat engine</a></div></td></tr><tr><td class="sidebar-content">

<ul><li><a href="Thermodynamics" title="Thermodynamics">Classical</a></li>

<li><a href="Statistical_mechanics" title="Statistical mechanics">Statistical</a></li>

<li><a href="Chemical_thermodynamics" title="Chemical thermodynamics">Chemical</a></li>

<li><a href="Quantum_thermodynamics" title="Quantum thermodynamics">Quantum thermodynamics</a></li></ul>

</div>

<ul><li><a href="Equilibrium_thermodynamics" title="Equilibrium thermodynamics">Equilibrium</a> / <a href="Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-content">

<ul><li><a href="Zeroth_law_of_thermodynamics" title="Zeroth law of thermodynamics">Zeroth</a></li>

<li><a href="First_law_of_thermodynamics" title="First law of thermodynamics">First</a></li>

<li><a href="Second_law_of_thermodynamics" title="Second law of thermodynamics">Second</a></li>

<li><a href="Third_law_of_thermodynamics" title="Third law of thermodynamics">Third</a></li></ul>

</div></div></div></td>

</tr><tr><td class="sidebar-content">

<ul><li><a href="Closed_system" title="Closed system">Closed system</a></li>

<li><a href="Thermodynamic_system#Open_system" title="Thermodynamic system">Open system</a></li>

<li><a href="Isolated_system" title="Isolated system">Isolated system</a></li></ul>

<a href="Thermodynamic_state" title="Thermodynamic state">State</a></th></tr><tr><td class="sidebar-content hlist">

<ul><li><a href="Equation_of_state" title="Equation of state">Equation of state</a></li>

<li><a href="Ideal_gas" title="Ideal gas">Ideal gas</a></li>

<li><a href="State_of_matter" title="State of matter">State of matter</a></li>

<li><a href="Phase_(matter)" title="Phase (matter)">Phase (matter)</a></li>

<li><a href="Thermodynamic_equilibrium" title="Thermodynamic equilibrium">Equilibrium</a></li>

<li><a href="Control_volume" title="Control volume">Control volume</a></li>

<li><a href="Thermodynamic_instruments" title="Thermodynamic instruments">Instruments</a></li></ul></td>

</tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;">

</th></tr><tr><td class="sidebar-content hlist">

<ul><li><a href="Isobaric_process" title="Isobaric process">Isobaric</a></li>

<li><a href="Isochoric_process" title="Isochoric process">Isochoric</a></li>

<li><a href="Isothermal_process" title="Isothermal process">Isothermal</a></li>

<li><a href="Adiabatic_process" title="Adiabatic process">Adiabatic</a></li>

<li><a href="Isentropic_process" title="Isentropic process">Isentropic</a></li>

<li><a href="Isenthalpic_process" title="Isenthalpic process">Isenthalpic</a></li>

<li><a href="Quasistatic_process" title="Quasistatic process">Quasistatic</a></li>

<li><a href="Polytropic_process" title="Polytropic process">Polytropic</a></li>

<li><a href="Free_expansion" class="mw-redirect" title="Free expansion">Free expansion</a></li>

<li><a href="Reversible_process_(thermodynamics)" title="Reversible process (thermodynamics)">Reversibility</a></li>

<li><a href="Irreversible_process" title="Irreversible process">Irreversibility</a></li>

<li><a href="Endoreversible_thermodynamics" title="Endoreversible thermodynamics">Endoreversibility</a></li></ul></td>

</tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;">

<a href="Thermodynamic_cycle" title="Thermodynamic cycle">Cycles</a></th></tr><tr><td class="sidebar-content hlist">

<ul><li><a href="Heat_engine" title="Heat engine">Heat engines</a></li>

<li><a href="Heat_pump_and_refrigeration_cycle" title="Heat pump and refrigeration cycle">Heat pumps</a></li>

<li><a href="Thermal_efficiency" title="Thermal efficiency">Thermal efficiency</a></li></ul></td>

</tr></tbody></table></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="List_of_thermodynamic_properties" title="List of thermodynamic properties">System properties</a></div></div><div class="sidebar-list-content mw-collapsible-content"><div style="font-size:90%;padding-bottom:0.2em;border-bottom:1px solid #aaa;">Note: <a href="Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">Conjugate variables</a> in <i>italics</i></div>

<ul><li><a href="Thermodynamic_diagrams" title="Thermodynamic diagrams">Property diagrams</a></li>

<li><a href="Intensive_and_extensive_properties" title="Intensive and extensive properties">Intensive and extensive properties</a></li></ul></td>

</tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;">

<a href="Process_function" title="Process function">Process functions</a></th></tr><tr><td class="sidebar-content" style="padding-bottom:0.7em;;padding-bottom:0.4em;">

</div></td>

</tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;">

<a href="State_function" title="State function">Functions of state</a></th></tr><tr><td class="sidebar-content" style="padding-bottom:0.7em;">

<ul><li><a href="Thermodynamic_temperature" title="Thermodynamic temperature">Temperature</a> / <i><a href="Entropy" title="Entropy">Entropy</a></i> (<a href="Introduction_to_entropy" title="Introduction to entropy">introduction</a>)</li>

<li><a href="Pressure" title="Pressure">Pressure</a> / <i><a href="Volume_(thermodynamics)" title="Volume (thermodynamics)">Volume</a></i></li>

<li><a href="Chemical_potential" title="Chemical potential">Chemical potential</a> / <i><a href="Particle_number" title="Particle number">Particle number</a></i></li>

<li><a href="Vapor_quality" title="Vapor quality">Vapor quality</a></li>

<li><a href="Reduced_properties" title="Reduced properties">Reduced properties</a></li></ul></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="Material_properties_(thermodynamics)" title="Material properties (thermodynamics)">Material properties</a></div></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Thermodynamic_databases_for_pure_substances" title="Thermodynamic databases for pure substances">Property databases</a></li></ul>

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<tbody><tr><td style="vertical-align:middle; text-align:right"><a href="Heat_capacity" title="Heat capacity">Specific heat capacity</a> </td>

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<annotation encoding="application/x-tex">{\displaystyle N}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle \partial T}</annotation>

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<tr><td style="vertical-align:middle; text-align:right"><a href="Compressibility" title="Compressibility">Compressibility</a> </td>

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<annotation encoding="application/x-tex">{\displaystyle 1}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle \partial V}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle V}</annotation>

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<tr><td style="vertical-align:middle; text-align:right"><a href="Thermal_expansion" title="Thermal expansion">Thermal expansion</a> </td>

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<annotation encoding="application/x-tex">{\displaystyle \alpha =}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle \partial V}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle V}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle \partial T}</annotation>

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</tbody></table></div></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="Thermodynamic_equations" title="Thermodynamic equations">Equations</a></div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist">

<ul><li><a href="Carnot's_theorem_(thermodynamics)" title="Carnot's theorem (thermodynamics)">Carnot's theorem</a></li>

<li><a href="Clausius_theorem" title="Clausius theorem">Clausius theorem</a></li>

<li><a href="Fundamental_thermodynamic_relation" title="Fundamental thermodynamic relation">Fundamental relation</a></li>

<li><a href="Ideal_gas_law" title="Ideal gas law">Ideal gas law</a></li></ul>

</div>

<ul><li><a href="Maxwell_relations" title="Maxwell relations">Maxwell relations</a></li>

<li><a href="Onsager_reciprocal_relations" title="Onsager reciprocal relations">Onsager reciprocal relations</a></li>

<li><a href="Bridgman's_thermodynamic_equations" title="Bridgman's thermodynamic equations">Bridgman's equations</a></li>

<li><i><a href="Table_of_thermodynamic_equations" title="Table of thermodynamic equations">Table of thermodynamic equations</a></i></li></ul></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="Thermodynamic_potential" title="Thermodynamic potential">Potentials</a></div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist">

<ul><li><a href="Thermodynamic_free_energy" title="Thermodynamic free energy">Free energy</a></li>

<li><a href="Free_entropy" title="Free entropy">Free entropy</a></li></ul>

</div>

<div class="plainlist"><ul><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="Internal_energy" title="Internal energy">Internal energy</a><br><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U(S,V)}">

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<annotation encoding="application/x-tex">{\displaystyle U(S,V)}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle H(S,p)=U+pV}</annotation>

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</math></span><img src="./6407d78e5f39d07f70e2414a92e08e2e068519f3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.254ex; height:2.843ex;" alt="{\displaystyle H(S,p)=U+pV}" loading="lazy"></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="Helmholtz_free_energy" title="Helmholtz free energy">Helmholtz free energy</a><br><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A(T,V)=U-TS}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A(T,V)=U-TS}</annotation>

</semantics>

</math></span><img src="./5e93692f031ba6484d82731c54db83a69daed3f0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.867ex; height:2.843ex;" alt="{\displaystyle A(T,V)=U-TS}" loading="lazy"></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a><br><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G(T,p)=H-TS}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle G(T,p)=H-TS}</annotation>

</semantics>

</math></span><img src="./8dd7a8f0b8ae04963da133e3b202432e1b6caed4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.614ex; height:2.843ex;" alt="{\displaystyle G(T,p)=H-TS}" loading="lazy"></span></li></ul></div></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><div class="hlist"><ul><li>History</li><li>Culture</li></ul></div></div></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;">

History</th></tr><tr><td class="sidebar-content">

<ul><li><a href="History_of_thermodynamics" title="History of thermodynamics">General</a></li>

<li><a href="History_of_entropy" title="History of entropy">Entropy</a></li>

</div>

<ul><li><a href="History_of_perpetual_motion_machines" title="History of perpetual motion machines">"Perpetual motion" machines</a></li></ul></td>

</tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;">

<a href="Philosophy_of_thermal_and_statistical_physics" class="mw-redirect" title="Philosophy of thermal and statistical physics">Philosophy</a></th></tr><tr><td class="sidebar-content">

<ul><li><a href="Entropy_(arrow_of_time)" class="mw-redirect" title="Entropy (arrow of time)">Entropy and time</a></li>

<li><a href="Entropy_and_life" title="Entropy and life">Entropy and life</a></li>

<li><a href="Brownian_ratchet" title="Brownian ratchet">Brownian ratchet</a></li>

<li><a href="Maxwell's_demon" title="Maxwell's demon">Maxwell's demon</a></li>

<li><a href="Heat_death_paradox" title="Heat death paradox">Heat death paradox</a></li>

<li><a href="Loschmidt's_paradox" title="Loschmidt's paradox">Loschmidt's paradox</a></li>

<li><a href="Synergetics_(Haken)" title="Synergetics (Haken)">Synergetics</a></li></ul>

</div></td>

</tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;">

Theories</th></tr><tr><td class="sidebar-content">

<ul><li><a href="Caloric_theory" title="Caloric theory">Caloric theory</a></li></ul>

</div>

<ul><li><a href="Vis_viva" title="Vis viva"><i>Vis viva</i> <span style="font-size: 85%;">("living force")</span></a></li>

<li><a href="Mechanical_equivalent_of_heat" title="Mechanical equivalent of heat">Mechanical equivalent of heat</a></li>

<li><a href="Power_(physics)" title="Power (physics)">Motive power</a></li></ul></td>

</tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;">

<a href="List_of_important_publications_in_physics" class="mw-redirect" title="List of important publications in physics">Key publications</a></th></tr><tr><td class="sidebar-content">

<ul><li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="An_Inquiry_Concerning_the_Source_of_the_Heat_Which_Is_Excited_by_Friction" title="An Inquiry Concerning the Source of the Heat Which Is Excited by Friction">An Inquiry Concerning the<br>Source ... Friction</a></i></div></li>

<li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="On_the_Equilibrium_of_Heterogeneous_Substances" title="On the Equilibrium of Heterogeneous Substances">On the Equilibrium of<br>Heterogeneous Substances</a></i></div></li>

<li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="Reflections_on_the_Motive_Power_of_Fire" title="Reflections on the Motive Power of Fire">Reflections on the<br>Motive Power of Fire</a></i></div></li></ul></td>

</tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;">

Timelines</th></tr><tr><td class="sidebar-content">

<ul><li><a href="Timeline_of_thermodynamics" title="Timeline of thermodynamics">Thermodynamics</a></li>

<li><a href="Timeline_of_heat_engine_technology" title="Timeline of heat engine technology">Heat engines</a></li></ul>

</div></td>

</tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;">

<div class="hlist"><ul><li>Art</li><li>Education</li></ul></div></th></tr><tr><td class="sidebar-content">

<ul><li><a href="Maxwell's_thermodynamic_surface" title="Maxwell's thermodynamic surface">Maxwell's thermodynamic surface</a></li>

<li><a href="Entropy_(energy_dispersal)" title="Entropy (energy dispersal)">Entropy as energy dispersal</a></li></ul></td>

</tr></tbody></table></div></div></td>

</tr><tr><td class="sidebar-content">

<ul><li><a href="Daniel_Bernoulli" title="Daniel Bernoulli">Bernoulli</a></li>

<li><a href="Ludwig_Boltzmann" title="Ludwig Boltzmann">Boltzmann</a></li>

<li><a href="Percy_Williams_Bridgman" title="Percy Williams Bridgman">Bridgman</a></li>

<li><a href="Constantin_Carath%C3%A9odory" title="Constantin Carathéodory">Carathéodory</a></li>

<li><a href="Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Carnot</a></li>

<li><a href="Beno%C3%AEt_Paul_%C3%89mile_Clapeyron" class="mw-redirect" title="Benoît Paul Émile Clapeyron">Clapeyron</a></li>

<li><a href="Rudolf_Clausius" title="Rudolf Clausius">Clausius</a></li>

<li><a href="Th%C3%A9ophile_de_Donder" class="mw-redirect" title="Théophile de Donder">de Donder</a></li>

<li><a href="Pierre_Duhem" title="Pierre Duhem">Duhem</a></li>

<li><a href="Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Gibbs</a></li>

<li><a href="Hermann_von_Helmholtz" title="Hermann von Helmholtz">von Helmholtz</a></li>

<li><a href="James_Prescott_Joule" title="James Prescott Joule">Joule</a></li>

<li><a href="Lord_Kelvin" title="Lord Kelvin">Kelvin</a></li>

<li><a href="Gilbert_N._Lewis" title="Gilbert N. Lewis">Lewis</a></li>

<li><a href="Fran%C3%A7ois_Massieu" title="François Massieu">Massieu</a></li>

<li><a href="James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li>

<li><a href="Julius_von_Mayer" title="Julius von Mayer">von Mayer</a></li>

<li><a href="Walther_Nernst" title="Walther Nernst">Nernst</a></li>

<li><a href="Lars_Onsager" title="Lars Onsager">Onsager</a></li>

<li><a href="Max_Planck" title="Max Planck">Planck</a></li>

<li><a href="William_John_Macquorn_Rankine" class="mw-redirect" title="William John Macquorn Rankine">Rankine</a></li>

<li><a href="John_Smeaton" title="John Smeaton">Smeaton</a></li>

<li><a href="Georg_Ernst_Stahl" title="Georg Ernst Stahl">Stahl</a></li>

<li><a href="Benjamin_Thompson" title="Benjamin Thompson">Thompson</a></li>

<li><a href="Johannes_Diderik_van_der_Waals" title="Johannes Diderik van der Waals">van der Waals</a></li>

<li><a href="John_James_Waterston" title="John James Waterston">Waterston</a></li></ul>

</div></div></div></td>

</tr><tr><td class="sidebar-content">

<ul><li><a href="Nucleation" title="Nucleation">Nucleation</a></li>

<li><a href="Self-assembly" title="Self-assembly">Self-assembly</a></li>

<li><a href="Self-organization" title="Self-organization">Self-organization</a></li></ul></div></div></td>

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<p><a href="Classical_thermodynamics" class="mw-redirect" title="Classical thermodynamics">Classical thermodynamics</a> considers three main kinds of <b>thermodynamic processes</b>: (1) changes in a system, (2) cycles in a system, and (3) flow processes.

</p><p>(1) A Thermodynamic process is a process in which the <a href="Thermodynamic_state" title="Thermodynamic state">thermodynamic state</a> of a system is changed. A change in a system is defined by a passage from an initial to a final state of <a href="Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a>. In classical thermodynamics, the actual course of the process is not the primary concern, and often is ignored. A state of thermodynamic equilibrium endures unchangingly unless it is interrupted by a thermodynamic operation that initiates a thermodynamic process. The equilibrium states are each respectively fully specified by a suitable set of thermodynamic state variables, that depend only on the current state of the system, not on the path taken by the processes that produce the state. In general, during the actual course of a thermodynamic process, the system may pass through physical states which are not describable as thermodynamic states, because they are far from internal thermodynamic equilibrium. <a href="Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium thermodynamics</a>, however, considers processes in which the states of the system are close to thermodynamic equilibrium, and aims to describe the continuous passage along the path, at definite rates of progress.

</p><p>As a useful theoretical but not actually physically realizable limiting case, a process may be imagined to take place practically infinitely slowly or smoothly enough to allow it to be described by a continuous path of equilibrium thermodynamic states, when it is called a "<a href="Quasistatic_process" title="Quasistatic process">quasi-static</a>" process. This is a theoretical exercise in differential geometry, as opposed to a description of an actually possible physical process; in this idealized case, the calculation may be exact.

</p><p>A really possible or actual thermodynamic process, considered closely, involves <a href="Friction" title="Friction">friction</a>. This contrasts with theoretically idealized, imagined, or limiting, but not actually possible, quasi-static processes which may occur with a theoretical slowness that avoids friction. It also contrasts with idealized frictionless processes in the surroundings, which may be thought of as including 'purely mechanical systems'; this difference comes close to defining a thermodynamic process.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>(2) A <a href="Thermodynamic_cycle" title="Thermodynamic cycle">cyclic process</a> carries the system through a cycle of stages, starting and being completed in some particular state. The descriptions of the staged states of the system are not the primary concern. The primary concern is the sums of matter and energy inputs and outputs to the cycle. Cyclic processes were important conceptual devices in the early days of thermodynamical investigation, while the concept of the thermodynamic state variable was being developed.

</p><p>(3) Defined by flows through a system, a <i>flow process</i> is a steady state of flows into and out of a vessel with definite wall properties. The internal state of the vessel contents is not the primary concern. The quantities of primary concern describe the states of the inflow and the outflow materials, and, on the side, the transfers of heat, work, and <a href="Kinetic_energy" title="Kinetic energy">kinetic</a> and <a href="Potential_energy" title="Potential energy">potential energies</a> for the vessel. Flow processes are of interest in engineering.

</p>

<div class="mw-heading mw-heading2"><h2 id="Kinds_of_process">Kinds of process</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Cyclic_process">Cyclic process</h3></div>

<p>Defined by a cycle of transfers into and out of a system, a cyclic process is described by the quantities transferred in the several stages of the cycle. The descriptions of the staged states of the system may be of little or even no interest. A cycle is a sequence of a small number of thermodynamic processes that indefinitely often, repeatedly returns the system to its original state. For this, the staged states themselves are not necessarily described, because it is the transfers that are of interest. It is reasoned that if the cycle can be repeated indefinitely often, then it can be assumed that the states are recurrently unchanged. The condition of the system during the several staged processes may be of even less interest than is the precise nature of the recurrent states. If, however, the several staged processes are idealized and quasi-static, then the cycle is described by a path through a continuous progression of equilibrium states.

</p>

<div class="mw-heading mw-heading3"><h3 id="Flow_process">Flow process</h3></div>

<p>Defined by flows through a system, a flow process is a steady state of flow into and out of a vessel with definite wall properties. The internal state of the vessel contents is not the primary concern. The quantities of primary concern describe the states of the inflow and the outflow materials, and, on the side, the transfers of heat, work, and kinetic and potential energies for the vessel. The states of the inflow and outflow materials consist of their internal states, and of their kinetic and potential energies as whole bodies. Very often, the quantities that describe the internal states of the input and output materials are estimated on the assumption that they are bodies in their own states of internal thermodynamic equilibrium. Because rapid reactions are permitted, the thermodynamic treatment may be approximate, not exact.

</p>

<div class="mw-heading mw-heading2"><h2 id="A_cycle_of_quasi-static_processes">A cycle of quasi-static processes</h2></div>

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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Stirling_cycle" title="Stirling cycle">Stirling cycle</a></div>

<p>A quasi-static thermodynamic process can be visualized by <a href="Thermodynamic_diagram" class="mw-redirect" title="Thermodynamic diagram">graphically plotting</a> the path of idealized changes to the system's <a href="State_variable" title="State variable">state variables</a>. In the example, a cycle consisting of four quasi-static processes is shown. Each process has a well-defined start and end point in the pressure-volume <a href="State_space" class="mw-redirect" title="State space">state space</a>. In this particular example, processes 1 and 3 are <a href="Isothermal" class="mw-redirect" title="Isothermal">isothermal</a>, whereas processes 2 and 4 are <a href="Isochoric_process" title="Isochoric process">isochoric</a>. The <a href="PV_diagram" class="mw-redirect" title="PV diagram">PV diagram</a> is a particularly useful visualization of a quasi-static process, because the area under the curve of a process is the amount of <a href="Work_(thermodynamics)" title="Work (thermodynamics)">work</a> done by the system during that process. Thus work is considered to be a <a href="Process_variable" title="Process variable">process variable</a>, as its exact value depends on the particular path taken between the start and end points of the process. Similarly, <a href="Heat" title="Heat">heat</a> may be transferred during a process, and it too is a process variable.

</p>

<div class="mw-heading mw-heading2"><h2 id="Conjugate_variable_processes">Conjugate variable processes</h2></div>

<p>It is often useful to group processes into pairs, in which each variable held constant is one member of a <a href="Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">conjugate</a> pair.

</p>

<div class="mw-heading mw-heading3"><h3 id="Pressure_–_volume">Pressure – volume</h3></div>

<p>The pressure–volume conjugate pair is concerned with the transfer of mechanical energy as the result of work.

</p>

<ul><li>An <b><a href="Isobaric_process" title="Isobaric process">isobaric process</a></b> occurs at constant pressure. An example would be to have a movable piston in a cylinder, so that the pressure inside the cylinder is always at atmospheric pressure, although it is separated from the atmosphere. In other words, the system is <b>dynamically connected</b>, by a movable boundary, to a constant-pressure reservoir.</li>

<li>An <b><a href="Isochoric_process" title="Isochoric process">isochoric process</a></b> is one in which the volume is held constant, with the result that the mechanical PV work done by the system will be zero. On the other hand, work can be done isochorically on the system, for example by a shaft that drives a rotary paddle located inside the system. It follows that, for the simple system of one deformation variable, any heat energy transferred to the system externally will be absorbed as internal energy. An isochoric process is also known as an <b>isometric</b> process or an <b>isovolumetric</b> process. An example would be to place a closed tin can of material into a fire. To a first approximation, the can will not expand, and the only change will be that the contents gain internal energy, evidenced by increase in temperature and pressure. Mathematically, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q=dU}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \delta Q=dU}</annotation>

</semantics>

</math></span><img src="./3922ea81b45ba8fa68d1e69e735c172199621c58.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.984ex; height:2.676ex;" alt="{\displaystyle \delta Q=dU}" loading="lazy"></span>. The system is <b>dynamically insulated</b>, by a rigid boundary, from the environment.</li></ul>

<div class="mw-heading mw-heading3"><h3 id="Temperature_–_entropy">Temperature – entropy</h3></div>

<p>The temperature-entropy conjugate pair is concerned with the transfer of energy, especially for a closed system.

</p>

<ul><li>An <b><a href="Isothermal_process" title="Isothermal process">isothermal process</a></b> occurs at a constant temperature. An example would be a closed system immersed in and <b>thermally connected</b> with a large constant-temperature bath. Energy gained by the system, through work done on it, is lost to the bath, so that its temperature remains constant.</li>

<li>An <b><a href="Adiabatic_process" title="Adiabatic process">adiabatic process</a></b> is a process in which there is no matter or heat transfer, because a <b>thermally insulating wall</b> separates the system from its surroundings. For the process to be natural, either (a) work must be done on the system at a finite rate, so that the internal energy of the system increases; the entropy of the system increases even though it is thermally insulated; or (b) the system must do work on the surroundings, which then suffer increase of entropy, as well as gaining energy from the system.</li>

<li>An <b><a href="Isentropic_process" title="Isentropic process">isentropic process</a></b> is customarily defined as an idealized quasi-static reversible adiabatic process, of transfer of energy as work. Otherwise, for a constant-entropy process, if work is done irreversibly, heat transfer is necessary, so that the process is not adiabatic, and an accurate artificial control mechanism is necessary; such is therefore not an ordinary natural thermodynamic process.</li></ul>

<div class="mw-heading mw-heading3"><h3 id="Chemical_potential_-_particle_number">Chemical potential - particle number</h3></div>

<p>The processes just above have assumed that the boundaries are also impermeable to particles. Otherwise, we may assume boundaries that are rigid, but are permeable to one or more types of particle. Similar considerations then hold for the <a href="Chemical_potential" title="Chemical potential">chemical potential</a>–<a href="Particle_number" title="Particle number">particle number</a> conjugate pair, which is concerned with the transfer of energy via this transfer of particles.

</p>

<ul><li>In a <i>constant chemical potential process</i> the system is <i>particle-transfer connected</i>, by a particle-permeable boundary, to a constant-μ reservoir.</li>

<li>The conjugate here is a constant particle number process. These are the processes outlined just above. There is no energy added or subtracted from the system by particle transfer. The system is <i>particle-transfer-insulated</i> from its environment by a boundary that is impermeable to particles, but permissive of transfers of energy as work or heat. These processes are the ones by which thermodynamic work and heat are defined, and for them, the system is said to be <a href="Thermodynamics#System_models" title="Thermodynamics">closed</a>.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Thermodynamic_potentials">Thermodynamic potentials</h2></div>

<p>Any of the <a href="Thermodynamic_potential" title="Thermodynamic potential">thermodynamic potentials</a> may be held constant during a process. For example:

</p>

<ul><li>An <b><a href="Isenthalpic_process" title="Isenthalpic process">isenthalpic process</a></b> introduces no change in <a href="Enthalpy" title="Enthalpy">enthalpy</a> in the system.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Polytropic_processes">Polytropic processes</h2></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Polytropic_process" title="Polytropic process">Polytropic process</a></div>

<p>A <b>polytropic process</b> is a thermodynamic process that obeys the relation:

</p>

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle PV^{\,n}=C,}</annotation>

</semantics>

</math></span><img src="./7c0d60b4ac61d7b5d73d1ef747063b4408388ce3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.78ex; height:2.676ex;" alt="{\displaystyle PV^{\,n}=C,}" loading="lazy"></span></dd></dl>

<p>where <i>P</i> is the pressure, <i>V</i> is volume, <i>n</i> is any <a href="Real_number" title="Real number">real number</a> (the "polytropic index"), and <i>C</i> is a constant. This equation can be used to accurately characterize processes of certain <a href="Thermodynamic_system" title="Thermodynamic system">systems</a>, notably the <a href="Compression_(physical)" class="mw-redirect" title="Compression (physical)">compression</a> or <a href="Thermal_expansion" title="Thermal expansion">expansion</a> of a <a href="Gas" title="Gas">gas</a>, but in some cases, <a href="Liquid" title="Liquid">liquids</a> and <a href="Solid" title="Solid">solids</a>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Processes_classified_by_the_second_law_of_thermodynamics">Processes classified by the second law of thermodynamics</h2></div>

<p>According to Planck, one may think of three main classes of thermodynamic process: natural, fictively reversible, and impossible or unnatural.<sup id="cite_ref-Guggenheim_2-0" class="reference"><a href="#cite_note-Guggenheim-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Natural_process">Natural process</h3></div>

<p>Only natural processes occur in nature. For thermodynamics, a <i>natural process</i> is a transfer between systems that increases the sum of their entropies, and is irreversible.<sup id="cite_ref-Guggenheim_2-1" class="reference"><a href="#cite_note-Guggenheim-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Natural processes may occur spontaneously upon the removal of a constraint, or upon some other <a href="Thermodynamic_operation" title="Thermodynamic operation">thermodynamic operation</a>, or may be triggered in a <a href="Metastability" title="Metastability">metastable</a> or unstable system, as for example in the condensation of a supersaturated vapour.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Planck emphasised the occurrence of friction as an important characteristic of natural thermodynamic processes that involve transfer of matter or energy between system and surroundings.

</p>

<div class="mw-heading mw-heading3"><h3 id="Effectively_reversible_process">Effectively reversible process</h3></div>

<p>To describe the geometry of graphical surfaces that illustrate equilibrium relations between thermodynamic functions of state, no one can fictively think of so-called "reversible processes". They are convenient theoretical objects that trace paths across graphical surfaces. They are called "processes" but do not describe naturally occurring processes, which are always irreversible. Because the points on the paths are points of thermodynamic equilibrium, it is customary to think of the "processes" described by the paths as fictively "reversible".<sup id="cite_ref-Guggenheim_2-2" class="reference"><a href="#cite_note-Guggenheim-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <a href="Reversible_process_(thermodynamics)" title="Reversible process (thermodynamics)">Reversible processes</a> are always quasistatic processes, but the converse is not always true.

</p>

<div class="mw-heading mw-heading3"><h3 id="Unnatural_process">Unnatural process</h3></div>

<p>Unnatural processes are logically conceivable but do not occur in nature. They would decrease the sum of the entropies if they occurred.<sup id="cite_ref-Guggenheim_2-3" class="reference"><a href="#cite_note-Guggenheim-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Quasistatic_process">Quasistatic process</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Quasistatic_process" title="Quasistatic process">Quasistatic process</a></div>

<p>A <b>quasistatic process</b> is an idealized or fictive model of a thermodynamic "process" considered in theoretical studies. It does not occur in physical reality. It may be imagined as happening infinitely slowly so that the system passes through a continuum of states that are infinitesimally close to <a href="Thermodynamic_equilibrium" title="Thermodynamic equilibrium">equilibrium</a>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Artificial_intelligence_for_thermodynamics_process">Artificial intelligence for thermodynamics process</h2></div>

<p>Artificial intelligence (AI) has significantly transformed the field of thermodynamics by enhancing predictive modeling, simulation, and process optimization. Through the integration of machine learning algorithms and statistical techniques, AI enables the development of highly accurate models that can forecast system behavior based on historical data, which is particularly valuable when traditional experimentation is costly or impractical. AI-driven approaches, such as surrogate modeling, facilitate rapid evaluations of complex thermodynamic processes, allowing engineers to perform extensive “what-if” analyses and optimize system designs efficiently. Additionally, AI enhances operational safety and efficiency, especially in high-stakes environments like nuclear power plants and chemical processing facilities, by providing deeper insights into system performance and potential failure modes<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>. These advancements promote proactive maintenance, reduce operational costs, and support the development of innovative solutions aimed at sustainability and energy efficiency<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>.

</p><p>Moreover, AI techniques such as genetic algorithms and reinforcement learning are pivotal in optimizing thermodynamic processes and control systems across various industries. These methods enable dynamic adjustments in real time, improving energy utilization, system reliability, and resilience. For instance, AI-driven control strategies allow for adaptive management of engines, HVAC systems, and power generation units, responding effectively to fluctuating demands and operating conditions. The combination of predictive modeling, simulation, and intelligent control not only accelerates technological innovation but also contributes to a more sustainable energy landscape by facilitating the integration of renewable sources, optimizing energy storage, and advancing materials discovery. As ongoing research continues to address challenges related to data quality, system complexity, and interpretability, the fusion of AI and thermodynamics is poised to play a critical role in shaping a more efficient and environmentally responsible future.

</p>

<ul><li><a href="Flow_process" title="Flow process">Flow process</a></li>

<li><a href="Phase_transition" title="Phase transition">Phase transition</a></li>

<li><a href="Work_(thermodynamics)" title="Work (thermodynamics)">Work (thermodynamics)</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Reiss, H. (1965). <i>Methods of Thermodynamics</i>, Blaisdell, New York, page 52: "The frictionless systems may be referred to as purely mechanical systems whereas those with friction are thermodynamic systems."</span>

</li>

<li id="cite_note-Guggenheim-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Guggenheim_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Guggenheim_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Guggenheim_2-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Guggenheim_2-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><a href="Edward_A._Guggenheim" title="Edward A. Guggenheim">Guggenheim, E.A.</a> (1949/1967). <i>Thermodynamics. An Advanced Treatment for Chemists and Physicists</i>, fifth revised edition, North-Holland, Amsterdam, p. 12.</span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><a href="L%C3%A1szl%C3%B3_Tisza" title="László Tisza">Tisza, L.</a> (1966). <i>Generalized Thermodynamics</i>, M.I.T. Press, Cambridge MA, p. 32.</span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a href="Max_Planck" title="Max Planck">Planck, M.</a>(1897/1903). <a rel="nofollow" class="external text" href="https://archive.org/details/treatiseonthermo00planrich"><i>Treatise on Thermodynamics</i>, translated by A. Ogg, Longmans, Green & Co., London</a>, p. 82.</span>

</li>

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</style><cite id="CITEREFHuangGongXiaoGao2025" class="citation journal cs1">Huang, Zhen; Gong, Jiawei; Xiao, Xuechun; Gao, Yuan; Xia, Yonghong; Wheeler, Pat; Ji, Bing (2025). <a rel="nofollow" class="external text" href="https://onlinelibrary.wiley.com/doi/abs/10.1049/pel2.70013">"Artificial Intelligence and Digital Twin Technologies for Power Converter Control in Transportation Applications: A Review"</a>. <i>IET Power Electronics</i>. <b>18</b> (1): e70013. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1049%2Fpel2.70013">10.1049/pel2.70013</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1755-4543">1755-4543</a>.</cite></span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFKeramati_Feyz_AbadiLiuZhangHu2025" class="citation journal cs1">Keramati Feyz Abadi, Mohammad Mehdi; Liu, Chao; Zhang, Ming; Hu, Youxi; Xu, Yuchun (2025-02-01). <a rel="nofollow" class="external text" href="https://www.sciencedirect.com/science/article/pii/S0278612524002711">"Leveraging AI for energy-efficient manufacturing systems: Review and future prospectives"</a>. <i>Journal of Manufacturing Systems</i>. <b>78</b>: <span class="nowrap">153–</span>177. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.jmsy.2024.11.017">10.1016/j.jmsy.2024.11.017</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0278-6125">0278-6125</a>.</cite></span>

</li>

<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite id="CITEREFAl-Raeei2025" class="citation journal cs1">Al-Raeei, Marwan (2025-06-04). <a rel="nofollow" class="external text" href="https://doi.org/10.1063/5.0271867">"Integrating artificial intelligence into thermodynamics: A new paradigm for sustainable future"</a>. <i>AIP Advances</i>. <b>15</b> (6): 060701. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F5.0271867">10.1063/5.0271867</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2158-3226">2158-3226</a>.</cite></span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

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</div>

<ul><li><i>Physics for Scientists and Engineers - with Modern Physics</i> (6th Edition), P. A. Tipler, G. Mosca, Freeman, 2008, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-7167-8964-7</bdi></li>

<li><i>Encyclopaedia of Physics</i> (2nd Edition), <a href="Rita_G._Lerner" title="Rita G. Lerner">R.G. Lerner</a>, G.L. Trigg, VHC publishers, 1991, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>3-527-26954-1</bdi> (Verlagsgesellschaft), <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-89573-752-3</bdi> (VHC Inc.)</li>

<li><i>McGraw Hill Encyclopaedia of Physics</i> (2nd Edition), C.B. Parker, 1994, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-07-051400-3</bdi></li>

<li><i>Physics with Modern Applications</i>, L.H. Greenberg, Holt-Saunders International W.B. Saunders and Co, 1978, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-7216-4247-0</bdi></li>

<li><i>Essential Principles of Physics</i>, P.M. Whelan, M.J. Hodgeson, 2nd Edition, 1978, John Murray, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-7195-3382-1</bdi></li>

<li><i>Thermodynamics, From Concepts to Applications</i> (2nd Edition), A. Shavit, C. Gutfinger, CRC Press (Taylor and Francis Group, USA), 2009, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9781420073683</bdi></li>

<li><i>Chemical Thermodynamics</i>, D.J.G. Ives, University Chemistry, Macdonald Technical and Scientific, 1971, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-356-03736-3</bdi></li>

<li><i>Elements of Statistical Thermodynamics</i> (2nd Edition), L.K. Nash, Principles of Chemistry, Addison-Wesley, 1974, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-201-05229-6</bdi></li>

<li><i>Statistical Physics</i> (2nd Edition), F. Mandl, Manchester Physics, John Wiley & Sons, 2008, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780471915331</bdi></li></ul>

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</style></div><div role="navigation" class="navbox" aria-labelledby="Thermodynamic_cycles210" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Thermodynamic_cycles210" style="font-size:114%;margin:0 4em"><a href="Thermodynamic_cycle" title="Thermodynamic cycle">Thermodynamic cycles</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="External_combustion_engine" title="External combustion engine">External<br>combustion / thermal</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Without phase change<br>(<a href="Hot_air_engine" title="Hot air engine">hot air engines</a>)</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Brayton_cycle#Reverse_Brayton_cycle" title="Brayton cycle">Bell Coleman</a></li>

<li><a href="Brayton_cycle" title="Brayton cycle">Brayton/Joule</a></li>

<li><a href="Carnot_cycle" title="Carnot cycle">Carnot</a></li>

<li><a href="Ericsson_cycle" title="Ericsson cycle">Ericsson</a></li>

<li><a href="Stirling_cycle" title="Stirling cycle">Stirling</a></li>

<li><a href="Pseudo_Stirling_cycle" title="Pseudo Stirling cycle">Stirling (pseudo/adiabatic)</a></li>

<li><a href="Stoddard_cycle" class="mw-redirect" title="Stoddard cycle">Stoddard</a></li>

<li><a href="Manson_engine" title="Manson engine">Manson</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">With phase change</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Kalina_cycle" title="Kalina cycle">Kalina</a></li>

<li><a href="Hygroscopic_cycle" title="Hygroscopic cycle">Hygroscopic</a></li>

<li><a href="Rankine_cycle" title="Rankine cycle">Rankine</a> (<a href="Organic_Rankine_cycle" title="Organic Rankine cycle">Organic Rankine</a>)</li>

<li><a href="Regenerative_cycle" class="mw-redirect" title="Regenerative cycle">Regenerative</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Internal_combustion_engine" title="Internal combustion engine">Internal <br>combustion / thermal</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Atkinson_cycle" title="Atkinson cycle">Atkinson</a></li>

<li><a href="Brayton_cycle" title="Brayton cycle">Brayton/Joule</a></li>

<li><a href="Diesel_cycle" title="Diesel cycle">Diesel</a></li>

<li><a href="Expander_cycle" title="Expander cycle">Expander</a></li>

<li><a href="Gas-generator_cycle" title="Gas-generator cycle">Gas-generator</a></li>

<li><a href="Homogeneous_charge_compression_ignition" title="Homogeneous charge compression ignition">Homogeneous charge compression ignition</a></li>

<li><a href="Humphrey_cycle" title="Humphrey cycle">Humphrey</a></li>

<li><a href="Lenoir_cycle" title="Lenoir cycle">Lenoir</a></li>

<li><a href="Miller_cycle" title="Miller cycle">Miller</a></li>

<li><a href="Scuderi_cycle" title="Scuderi cycle">Scuderi</a></li>

<li><a href="Staged_combustion_cycle" title="Staged combustion cycle">Staged combustion</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mixed</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Combined_cycle" class="mw-redirect" title="Combined cycle">Combined</a></li>

<li><a href="Mixed/dual_cycle" title="Mixed/dual cycle">Mixed/dual</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Heat_pump_and_refrigeration_cycle" title="Heat pump and refrigeration cycle">Refrigeration</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Hampson%E2%80%93Linde_cycle" title="Hampson–Linde cycle">Hampson–Linde</a></li>

<li><a href="Kleemenko_cycle" title="Kleemenko cycle">Kleemenko</a></li>

<li><a href="Pulse_tube_refrigerator" title="Pulse tube refrigerator">Pulse tube</a></li>

<li><a href="Regenerative_cooling" title="Regenerative cooling">Regenerative cooling</a></li>

<li><a href="Transcritical_cycle" title="Transcritical cycle">Transcritical</a></li>

<li><a href="Absorption_refrigerator" title="Absorption refrigerator">Vapor absorption</a></li>

<li><a href="Vapor-compression_refrigeration" title="Vapor-compression refrigeration">Vapor-compression</a></li>

<li><a href="Siemens_cycle" title="Siemens cycle">Siemens</a></li>

<li><a href="Vuilleumier_cycle" title="Vuilleumier cycle">Vuilleumier</a></li>

<li><a href="Ionocaloric_refrigeration" title="Ionocaloric refrigeration">Ionocaloric</a></li></ul>

</div></td></tr></tbody></table></div>

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