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A thermodynamic cycle consists of a linked sequence of thermodynamic processes that involve transfer of heat and
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal t ...
into and out of the system, while varying pressure, temperature, and other
state variables A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of a ...
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 A heat pump is a device that can heat a building (or part of a building) by transferring thermal energy from the outside using a refrigeration cycle. Many heat pumps can also operate in the opposite direction, cooling the building by removing ...
. 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. During a closed cycle, the system returns to its original thermodynamic state of temperature and pressure. Process quantities (or path quantities), such as
heat 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 ...
and
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal t ...
are process dependent. For a cycle for which the system returns to its initial state the
first law of thermodynamics 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 amou ...
applies: :\Delta U = E_ - E_ = 0 The above states that there is no change of the internal energy (U) of the system over the cycle. E_ represents the total work and heat input during the cycle and E_ would be the total work and heat output during the cycle. The repeating nature of the process path allows for continuous operation, making the cycle an important concept in
thermodynamics 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 th ...
. Thermodynamic cycles are often represented mathematically as
quasistatic process In thermodynamics, a quasi-static process (also known as a quasi-equilibrium process; from the Latin ''quasi'', meaning ‘as if’), is a thermodynamic process that happens slowly enough for the system to remain in internal physical (but not ne ...
es in the modeling of the workings of an actual device.


Heat and work

Two primary classes of thermodynamic cycles are power cycles and heat pump cycles. Power cycles are cycles which convert some heat input into a
mechanical work In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force stre ...
output, while heat pump cycles transfer heat from low to high temperatures by using mechanical work as the input. Cycles composed entirely of quasistatic processes can operate as power or heat pump cycles by controlling the process direction. On a pressure–volume (PV) diagram or
temperature–entropy diagram In thermodynamics, a temperature–entropy (''T–s'') diagram is a thermodynamic diagram used to visualize changes to temperature () and specific entropy () during a thermodynamic process or cycle as the graph of a curve. It is a useful and ...
, the
clockwise and counterclockwise Two-dimensional rotation can occur in two possible directions. Clockwise motion (abbreviated CW) proceeds in the same direction as a clock's hands: from the top to the right, then down and then to the left, and back up to the top. The opposite s ...
directions indicate power and heat pump cycles, respectively.


Relationship to work

Because the net variation in state properties during a thermodynamic cycle is zero, it forms a closed loop on a
PV diagram PV may refer to: Places * Paceville, Malta * Puerto Vallarta, Mexico * Postal village, a settlement that has a post office United States * Palos Verdes Peninsula, California * Prescott Valley, Arizona * Prairie Village, Kansas Politics * P ...
. A PV diagram's ''Y'' axis shows pressure (''P'') and ''X'' axis shows volume (''V''). The area enclosed by the loop is the work (''W'') done by the process: : \text \qquad W = \oint P \ dV This work is equal to the balance of heat (Q) transferred into the system: : \text \qquad W = Q = Q_ - Q_ Equation (2) is consistent with the First Law; even though the internal energy changes during the course of the cyclic process, when the cyclic process finishes the system's internal energy is the same as the energy it had when the process began. If the cyclic process moves clockwise around the loop, then W will be positive, and it represents a heat engine. If it moves counterclockwise, then W will be negative, and it represents a
heat pump A heat pump is a device that can heat a building (or part of a building) by transferring thermal energy from the outside using a refrigeration cycle. Many heat pumps can also operate in the opposite direction, cooling the building by removing ...
.


A list of thermodynamic processes

The following processes are often used to describe different stages of a thermodynamic cycle: * Adiabatic : No energy transfer as heat (Q) during that part of the cycle would amount to δQ=0. Energy transfer is considered as work done by the system only. *
Isothermal In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature ''T'' of a system remains constant: Δ''T'' = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and ...
: The process is at a constant temperature during that part of the cycle (T=constant, δT=0). Energy transfer is considered as heat removed from or work done by the system. *
Isobaric Isobar may refer to: * Isobar (meteorology), a line connecting points of equal atmospheric pressure reduced to sea level on the maps. * Isobaric process In thermodynamics, an isobaric process is a type of thermodynamic process in which the pr ...
: Pressure in that part of the cycle will remain constant. (P=constant, δP=0). Energy transfer is considered as heat removed from or work done by the system. *
Isochoric Isochoric may refer to: *cell-transitive, in geometry *isochoric process In thermodynamics, an isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which ...
: The process is constant volume (V=constant, δV=0). Energy transfer is considered as heat removed from or work done by the system. *
Isentropic 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 ...
: The process is one of constant entropy (S=constant, δS=0). It is adiabatic (no heat nor mass exchange) and reversible. * Isenthalpic: process that proceeds without any change in enthalpy or specific enthalpy * Polytropic: process that obeys the relation: p V^ = C * Reversible:process where the net entropy production is zero: dS-\frac=0


Example: The Otto cycle

The
Otto Cycle An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines. The Otto cycle is a description of what hap ...
is an example of a reversible thermodynamic cycle. *1→2:
Isentropic 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 ...
/ adiabatic expansion: Constant entropy (s), Decrease in
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
(P), Increase in
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). Th ...
(v), Decrease in
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
(T) *2→3:
Isochoric Isochoric may refer to: *cell-transitive, in geometry *isochoric process In thermodynamics, an isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which ...
cooling: Constant volume(v), Decrease in pressure (P), Decrease in entropy (S), Decrease in temperature (T) *3→4: Isentropic / adiabatic compression: Constant entropy (s), Increase in pressure (P), Decrease in volume (v), Increase in temperature (T) *4→1: Isochoric heating: Constant volume (v), Increase in pressure (P), Increase in entropy (S), Increase in temperature (T)


Power cycles

Thermodynamic power cycles are the basis for the operation of heat engines, which supply most of the world's electric power and run the vast majority of motor vehicles. Power cycles can be organized into two categories: real cycles and ideal cycles. Cycles encountered in real world devices (real cycles) are difficult to analyze because of the presence of complicating effects (friction), and the absence of sufficient time for the establishment of equilibrium conditions. For the purpose of analysis and design, idealized models (ideal cycles) are created; these ideal models allow engineers to study the effects of major parameters that dominate the cycle without having to spend significant time working out intricate details present in the real cycle model. Power cycles can also be divided according to the type of heat engine they seek to model. The most common cycles used to model
internal combustion engine An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal c ...
s are the
Otto cycle An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines. The Otto cycle is a description of what hap ...
, which models
gasoline engine A petrol engine (gasoline engine in American English) is an internal combustion engine designed to run on petrol (gasoline). Petrol engines can often be adapted to also run on fuels such as liquefied petroleum gas and ethanol blends (such as ''E ...
s, and the
Diesel cycle The Diesel cycle is a combustion process of a reciprocating internal combustion engine. In it, fuel is ignited by heat generated during the compression of air in the combustion chamber, into which fuel is then injected. This is in contrast to ign ...
, which models
diesel engine The diesel engine, named after Rudolf Diesel, is an internal combustion engine in which ignition of the fuel is caused by the elevated temperature of the air in the cylinder due to mechanical compression; thus, the diesel engine is a so-ca ...
s. Cycles that model external combustion engines include the
Brayton cycle The Brayton cycle is a thermodynamic cycle that describes the operation of certain heat engines that have air or some other gas as their working fluid. The original Brayton engines used a piston compressor and piston expander, but modern gas tu ...
, which models
gas turbine A gas turbine, also called a combustion turbine, is a type of continuous flow internal combustion engine. The main parts common to all gas turbine engines form the power-producing part (known as the gas generator or core) and are, in the directio ...
s, the
Rankine cycle The Rankine cycle is an idealized thermodynamic cycle describing the process by which certain heat engines, such as steam turbines or reciprocating steam engines, allow mechanical work to be extracted from a fluid as it moves between a heat sourc ...
, which models steam turbines, the Stirling cycle, which models hot air engines, and the Ericsson cycle, which also models hot air engines. For example :--the pressure-volume
mechanical work In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force stre ...
output from the ideal Stirling cycle (net work out), consisting of 4 thermodynamic processes, is: : \text \qquad W_ = W_ + W_ + W_ + W_ : W_ = \int_^ P \, dV, \, \, \text : W_ = \int_^ P \, dV, \, \, \text V_2 = V_3 : W_ = \int_^ P \, dV, \, \, \text : W_ = \int_^ P \, dV, \, \, \text V_4 = V_1 For the ideal Stirling cycle, no volume change happens in process 4-1 and 2-3, thus equation (3) simplifies to: : \text \qquad W_ = W_ + W_


Heat pump cycles

Thermodynamic heat pump cycles are the
model A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models c ...
s for household
heat pump A heat pump is a device that can heat a building (or part of a building) by transferring thermal energy from the outside using a refrigeration cycle. Many heat pumps can also operate in the opposite direction, cooling the building by removing ...
s and refrigerators. There is no difference between the two except the purpose of the refrigerator is to cool a very small space while the household heat pump is intended to warm or cool a house. Both work by moving heat from a cold space to a warm space. The most common refrigeration cycle is the vapor compression cycle, which models systems using refrigerants that change phase. The absorption refrigeration cycle is an alternative that absorbs the refrigerant in a liquid solution rather than evaporating it. Gas refrigeration cycles include the reversed Brayton cycle and the
Hampson–Linde cycle The Hampson–Linde cycle is a process for the liquefaction of gases, especially for air separation. William Hampson and Carl von Linde independently filed for patents of the cycle in 1895: Hampson on 23 May 1895 and Linde on 5 June 1895. The Ha ...
. Multiple compression and expansion cycles allow gas refrigeration systems to liquify gases.


Modeling real systems

Thermodynamic cycles may be used to model real devices and systems, typically by making a series of assumptions.Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: an engineering approach. Boston: McGraw-Hill. pp. 452. . simplifying assumptions are often necessary to reduce the problem to a more manageable form. For example, as shown in the figure, devices such a
gas turbine A gas turbine, also called a combustion turbine, is a type of continuous flow internal combustion engine. The main parts common to all gas turbine engines form the power-producing part (known as the gas generator or core) and are, in the directio ...
or jet engine can be modeled as a
Brayton cycle The Brayton cycle is a thermodynamic cycle that describes the operation of certain heat engines that have air or some other gas as their working fluid. The original Brayton engines used a piston compressor and piston expander, but modern gas tu ...
. The actual device is made up of a series of stages, each of which is itself modeled as an idealized thermodynamic process. Although each stage which acts on the working fluid is a complex real device, they may be modelled as idealized processes which approximate their real behavior. If energy is added by means other than combustion, then a further assumption is that the exhaust gases would be passed from the exhaust to a heat exchanger that would sink the waste heat to the environment and the working gas would be reused at the inlet stage. The difference between an idealized cycle and actual performance may be significant. For example, the following images illustrate the differences in work output predicted by an ideal Stirling cycle and the actual performance of a Stirling engine: As the net work output for a cycle is represented by the interior of the cycle, there is a significant difference between the predicted work output of the ideal cycle and the actual work output shown by a real engine. It may also be observed that the real individual processes diverge from their idealized counterparts; e.g., isochoric expansion (process 1-2) occurs with some actual volume change.


Well-known thermodynamic cycles

In practice, simple idealized thermodynamic cycles are usually made out of four thermodynamic processes. Any thermodynamic processes may be used. However, when idealized cycles are modeled, often processes where one state variable is kept constant are used, such as an isothermal process (constant temperature),
isobaric process In thermodynamics, an isobaric process is a type of thermodynamic process in which the pressure of the system stays constant: Δ''P'' = 0. The heat transferred to the system does work, but also changes the internal energy (''U'') of t ...
(constant pressure),
isochoric process In thermodynamics, an isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which the volume of the closed system undergoing such a process remains constant. ...
(constant volume), isentropic process (constant entropy), or an
isenthalpic process An isenthalpic process or isoenthalpic process is a process that proceeds without any change in enthalpy, ''H''; or specific enthalpy, ''h''. Overview If a steady-state, steady-flow process is analysed using a control volume, everything outside ...
(constant enthalpy). Often
adiabatic process In thermodynamics, an adiabatic process (Greek: ''adiábatos'', "impassable") is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal proces ...
es are also used, where no heat is exchanged. Some example thermodynamic cycles and their constituent processes are as follows:


Ideal cycle

An ideal cycle is simple to analyze and consists of: # TOP (A) and BOTTOM (C) of the loop: a pair of parallel isobaric processes # RIGHT (B) and LEFT (D) of the loop: a pair of parallel isochoric processes If the working substance is a perfect gas, U is only a function of T for a closed system since its internal pressure vanishes. Therefore, the internal energy changes of a perfect gas undergoing various processes connecting initial state a to final state b are always given by the formula \Delta U= \int_^ C_ dT Assuming that C_ is constant, \Delta U= C_ \Delta T for any process undergone by a perfect gas. Under this set of assumptions, for processes A and C we have W = p \Delta v and Q = C_ \Delta T , whereas for processes B and D we have W = 0 and Q = \Delta U = C_ \Delta T . The total work done per cycle is W_ = p_A (v_2 - v_1) + p_C(v_4-v_3) = p_A (v_2 - v_1) + p_C (v_1 - v_2) = (p_A - p_C) (v_2 - v_1) , which is just the area of the rectangle. If the total heat flow per cycle is required, this is easily obtained. Since \Delta U_ = Q_ - W_ = 0, we have Q_ = W_. Thus, the total heat flow per cycle is calculated without knowing the heat capacities and temperature changes for each step (although this information would be needed to assess the
thermodynamic efficiency In thermodynamics, the thermal efficiency (\eta_) is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, steam turbine, steam engine, boiler, furnace, refrigerator, ACs etc. For a ...
of the cycle).


Carnot cycle

The Carnot cycle is a cycle composed of the totally reversible processes of
isentropic 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 ...
compression and expansion and
isothermal In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature ''T'' of a system remains constant: Δ''T'' = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and ...
heat addition and rejection. The
thermal efficiency In thermodynamics, the thermal efficiency (\eta_) is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, steam turbine, steam engine, boiler, furnace, refrigerator, ACs etc. For a ...
of a Carnot cycle depends only on the absolute temperatures of the two reservoirs in which heat transfer takes place, and for a power cycle is: :\eta=1-\frac where is the lowest cycle temperature and the highest. For Carnot power cycles the coefficient of performance for a
heat pump A heat pump is a device that can heat a building (or part of a building) by transferring thermal energy from the outside using a refrigeration cycle. Many heat pumps can also operate in the opposite direction, cooling the building by removing ...
is: :\ COP = 1+\frac and for a refrigerator the coefficient of performance is: :\ COP = \frac The second law of thermodynamics limits the efficiency and COP for all cyclic devices to levels at or below the Carnot efficiency. The Stirling cycle and Ericsson cycle are two other reversible cycles that use regeneration to obtain isothermal heat transfer.


Stirling cycle

A Stirling cycle is like an Otto cycle, except that the adiabats are replaced by isotherms. It is also the same as an Ericsson cycle with the isobaric processes substituted for constant volume processes. # TOP and BOTTOM of the loop: a pair of quasi-parallel isothermal processes # LEFT and RIGHT sides of the loop: a pair of parallel isochoric processes Heat flows into the loop through the top isotherm and the left isochore, and some of this heat flows back out through the bottom isotherm and the right isochore, but most of the heat flow is through the pair of isotherms. This makes sense since all the work done by the cycle is done by the pair of isothermal processes, which are described by ''Q=W''. This suggests that all the net heat comes in through the top isotherm. In fact, all of the heat which comes in through the left isochore comes out through the right isochore: since the top isotherm is all at the same warmer temperature T_H and the bottom isotherm is all at the same cooler temperature T_C , and since change in energy for an isochore is proportional to change in temperature, then all of the heat coming in through the left isochore is cancelled out exactly by the heat going out the right isochore.


State functions and entropy

If ''Z'' is a state function then the balance of ''Z'' remains unchanged during a cyclic process: : \oint dZ = 0 . Entropy is a state function and is defined in an absolute sense through the Third Law of Thermodynamics as : S = \int_0^T where a reversible path is chosen from absolute zero to the final state, so that for an isothermal reversible process : \Delta S = . In general, for any cyclic process the state points can be connected by reversible paths, so that : \oint dS = \oint = 0 meaning that the net entropy change of the working fluid over a cycle is zero.


See also

* Entropy *
Economizer Economizers (US and Oxford spelling), or economisers (UK), are mechanical devices intended to reduce energy consumption, or to perform useful function such as preheating a fluid. The term economizer is used for other purposes as well. Boiler, po ...
* Thermogravitational cycle


References


Further reading

* Halliday, Resnick & Walker. ''Fundamentals of Physics'', 5th edition. John Wiley & Sons, 1997. Chapter 21, ''Entropy and the Second Law of Thermodynamics''. * Çengel, Yunus A., and Michael A. Boles. ''Thermodynamics: An Engineering Approach'', 7th ed. New York: McGraw-Hill, 2011. Print. * Hill and Peterson. "Mechanics and Thermodynamics of Propulsion", 2nd ed. Prentice Hall, 1991. 760 pp.


External links

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