Thermodynamic cycle

During a closed cycle, the system returns to its original thermodynamic state of temperature and pressure. Process quantities (or path quantities), such as heat and work are process dependent. For a cycle for which the system returns to its initial state the first law of thermodynamics applies:

${\displaystyle \mathrm{\Delta }U=E_{in}-E_{out}=0}$

The above states that there is no change of the internal energy (${\displaystyle U}$) of the system over the cycle. ${\displaystyle E_{in}}$ represents the total work and heat input during the cycle and ${\displaystyle E_{out}}$ 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. Thermodynamic cycles are often represented mathematically as quasistatic processes 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 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, the clockwise and counterclockwise 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 P-V diagram. A P-V diagram is often labelled with pressure (P) on the y-axis and volume (V) on the x-axis. The area enclosed by the loop is the net work (${\displaystyle W_{net}}$) done by the processes, i.e. the cycle:

${\displaystyle \text{(1)}{W}_{net}=\oint PdV}$

This work is equal to the net heat (Q) transferred into and out of the system:

${\displaystyle \text{(2)}{W}_{net}=Q_{net}=Q_{in}-Q_{out}}$

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 ${\displaystyle W_{net}}$ will be positive, the cyclic machine will transform part of the heat exchanged into work and it represents a heat engine. If it moves counterclockwise, then ${\displaystyle W_{net}}$ will be negative, the cyclic machine will require work to absorb heat at a low temperature and reject it at a higher temperature and it represents a heat pump.

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 (${\displaystyle Q}$) during that part of the cycle (${\displaystyle \delta Q=0}$). Energy transfer is considered as work done by the system only.
• Isothermal : The process is at a constant temperature during that part of the cycle (${\displaystyle T=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}}$, ${\displaystyle dT=0}$). Energy transfer is considered as heat removed from or work done by the system.
• Isobaric : Pressure in that part of the cycle will remain constant. (${\displaystyle P=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}}$, ${\displaystyle dP=0}$). Energy transfer is considered as heat removed from or work done by the system.
• Isochoric : The process is constant volume (${\displaystyle V=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}}$, ${\displaystyle dV=0}$). Energy transfer is considered as heat removed from the system, as the work done by the system is zero.
• Isentropic : The process is one of constant entropy (${\displaystyle S=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}}$, ${\displaystyle dS=0}$). It is adiabatic (no heat nor mass exchange) and reversible.
• Isenthalpic : The process that proceeds without any change in enthalpy or specific enthalpy.
• Polytropic : The process that obeys the relation ${\displaystyle P{V}^n=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}}$.
• Reversible : The process where the net entropy production is zero; ${\displaystyle dS-\frac{\delta Q}{T}=0}$.

Example: The Otto cycle

The Otto Cycle is an example of a reversible thermodynamic cycle.

• 1→2: Isentropic / adiabatic expansion: Constant entropy (s), Decrease in pressure (P), Increase in volume (v), Decrease in temperature (T)
• 2→3: Isochoric 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 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, the Rankine cycle, 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 output from the ideal Stirling cycle (net work out), consisting of 4 thermodynamic processes, is:

${\displaystyle \text{(3)}{W}_{\mathrm{n}\mathrm{e}\mathrm{t}}=W_{1\to 2}+W_{2\to 3}+W_{3\to 4}+W_{4\to 1}}$

${\displaystyle W_{1\to 2}={\int }_{V_1}^{V_2}PdV,\text{negative, work done on system}}$

${\displaystyle W_{2\to 3}={\int }_{V_2}^{V_3}PdV,\text{zero work since }{V}_2=V_3}$

${\displaystyle W_{3\to 4}={\int }_{V_3}^{V_4}PdV,\text{positive, work done by system}}$

${\displaystyle W_{4\to 1}={\int }_{V_4}^{V_1}PdV,\text{zero work since }{V}_4=V_1}$

For the ideal Stirling cycle, no volume change happens in process 4-1 and 2-3, thus equation (3) simplifies to:

${\displaystyle \text{(4)}{W}_{\mathrm{n}\mathrm{e}\mathrm{t}}=W_{1\to 2}+W_{3\to 4}}$

Heat pump cycles

Thermodynamic heat pump cycles are the models for household heat pumps 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. Multiple compression and expansion cycles allow gas refrigeration systems to liquify gases.