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## Thermodynamic cycleA A thermodynamic cycle is a closed loop on a P-V diagram. A P-V diagrams X axis shows volume (V) and Y axis shows pressure (P). The area enclosed by the loop is the work (W) done by the process: - .
This work is equal to the balance of heat (Q) transferred into the system: - .
Equation (2) makes a cyclic process similar to an isothermal process: even though the internal energy changes during the course of the cyclic process, when the cyclic process finishes the system's energy is the same as the energy it had when the process began. If the cyclic process moves clockwise around the loop, then it represents a heat engine, and W will be positive. If it moves counterclockwise then it represents a heat pump, and W will be negative. ## Additional recommended knowledge
## ClassesTwo primary classes of thermodynamic cycles are ## Thermodynamic 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 almost all motor vehicles. Power cycles can be divided according to the type of heat engine they seek to model. The most common cycles that model internal combustion engines are the Otto cycle, which models gasoline engines and the Diesel cycle, which models diesel engines. Cycles that model external combustion engines include the Brayton cycle, which models gas turbines, and the Rankine cycle, which models steam turbines. For example the pressure-volume mechanical work done in the heat engine cycle, consisting of 4 thermodynamic processes, is: If no volume change happens in process 4->1 and 2->3, equation (3) simplifies to: ## Thermodynamic heat pump and refrigeration cycleThermodynamic heat pump and refrigeration cycles are the models for heat pumps and refrigerators. The difference between the two is that heat pumps are intended to keep a place warm and refrigerators designed to cool it. 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 Linde-Hampson cycle. Regeneration in gas refrigeration allows for the liquefaction of gases. ## Types of thermodynamic cyclesA thermodynamic cycle can (ideally) be made out of 3 or more thermodynamic processes (typical 4). The processes can be any of these: - isothermal process (at constant temperature, maintained with heat added or removed from a heat source or sink)
- isobaric process (at constant pressure)
- isometric / isochoric process (at constant volume)
- adiabatic process (no heat is added or removed from the working fluid)
- isentropic process, reversible adiabatic process (no heat is added or removed from the working fluid - and the entropy is constant)
- isenthalpic process (the enthalpy is constant)
Some examples are as follows:
## Carnot cycleThe Carnot cycle is a cycle composed of the totally reversible processes of isentropic compression and expansion and isothermal heat addition and rejection. The thermal efficiency of a Carnot cycle depends only on the temperatures in Kelvin of the two reservoirs in which heat transfer takes place, and for a power cycle is: where and for a refrigerator the coefficient of performance is: 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. ## Ideal cycleAn ideal cycle is constructed out of: - TOP and BOTTOM of the loop: a pair of parallel
**isobaric**processes - LEFT and RIGHT of the loop: a pair of parallel
**isochoric**processes
## Otto cycleAn Otto cycle is constructed out of: - TOP and BOTTOM of the loop: a pair of quasi-parallel
**adiabatic**processes - LEFT and RIGHT sides of the loop: a pair of parallel
**isochoric**processes
The adiabatic processes are impermeable to heat: heat flows into the loop through the left pressurizing process and some of it flows back out through the right depressurizing process, and the heat which remains does the work. ## Stirling cycleA Stirling cycle is like an Otto cycle, except that the adiabats are replaced by isotherms. - 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 ## State Functions and EntropyIf - .
If entropy is defined as so that - ,
then it can be proven that for any cyclic process, ## Demonstration## Part 1Draw a rectangle on a P-V diagram, such that the top and bottom are horizontal isobaric processes and the left and right are vertical isochoric processes. Such a rectangle should be made really small, so that change in temperature can be averaged out, and so that the cycle will enclose an area Δarea. Let the top left corner be labeled A, then label the rest of the corners clockwise starting from A as ABCD.
Assume that the system is a monatomic gas. Then *W*_{AB}=*P*_{A}(*V*_{B}−*V*_{A})
Process BC: *W*_{BC}= 0
Process CD: *W*_{CD}=*P*_{C}(*V*_{A}−*V*_{C})
Process DA: *W*_{DA}= 0
Process ABCDA (cyclic): ## Part 2Any loop can be broken up into a rectangular grid of differential areas. The line integral of the entire loop is equal to the sum of the line integrals of each of the constituent differential areas. Let all these integrals be done clockwise. Then any pair of adjacent differential areas will be sharing a process as a common border, but one area will add that process in one direction while the adjacent area adds that process in the reverse direction, so that process is cancelled out. Therefore all processes internal to the loop cancel each other out (see Green's theorem), and the result of the summation is equal to the line integral of the contour of the loop:
Q.E.D. ## ConclusionThe fact that entropy is a state function is what puts entropy on the map (the P-V diagram). ## References- Halliday, Resnick & Walker.
*Fundamentals of Physics*, 5th edition. John Wiley & Sons, 1997. Chapter 21,*Entropy and the Second Law of Thermodynamics*.
## See also- Dual cycle
- Kalina cycle
- Organic Rankine Cycle
- Entropy
- Heat engine
Categories: Thermodynamic cycles | Thermodynamics |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Thermodynamic_cycle". A list of authors is available in Wikipedia. |