A Carnot cycle is an idealized
thermodynamic cycle performed by a
Carnot heat engine, consisting of the following steps: to illustrate the work done. 1-to-2 (isothermal expansion), 2-to-3 (adiabatic expansion), 3-to-4 (isothermal compression), 4-to-1 (adiabatic compression). In this case, since it is a
reversible thermodynamic cycle (no net change in the system and its surroundings per cycle) \frac{Q_\text{H}}{T_\text{H}} = - \frac{Q_\text{C}}{T_\text{C}}. This is true as
QC and
TC are both smaller in magnitude and in fact are in the same ratio as
QH/
TH.
Pressure–volume graph When a Carnot cycle is plotted on a
pressure–volume diagram (), the isothermal stages follow the isotherm lines for the working fluid, the adiabatic stages move between isotherms, and the area bounded by the complete cycle path represents the total work that can be done during one cycle. From point 1 to 2 and point 3 to 4 the temperature is constant (isothermal process). Heat transfer from point 4 to 1 and point 2 to 3 are equal to zero (adiabatic process).
Temperature-entropy graph A Carnot cycle plotted on a
Temperature-entropy diagram () is rather simple. Isothermic paths are horizontal, adiabatic paths are vertical. The area enclosed by the cycle is the amount of heat energy extracted from the hot reservoir but not delivered to the cold reservoir, which has been converted into work. Defining , the heat energy injected into the engine is and the heat energy extracted from the engine is , which is the portion of the injected energy that is unavailable to do work. The engine is reversibly transporting entropy from the hot reservoir to the cold reservoir.
Efficiency The efficiency
η is defined to be: {{NumBlk|:|\eta=\frac{W}{Q_\text{H}}=\frac{Q_\text{H}-Q_\text{C}}{Q_\text{H}}=1-\frac{T_\text{C}}{T_\text{H}} |}} where • is the work done by the engine system (energy exiting the system as work), •
QC > 0 is the heat taken from the engine system (heat energy leaving the system), •
QH > 0 is the heat put into the engine system (heat energy entering the system), •
TC is the
absolute temperature of the cold reservoir, and •
TH is the absolute temperature of the hot reservoir. This is the Carnot heat engine working efficiency definition as the fraction of the work done by the engine system to the thermal energy received by the system from the hot reservoir per cycle. This thermal energy is the cycle initiator.
Reversed Carnot cycle A Carnot heat-engine cycle described is a totally reversible cycle. That is, all the processes that compose it can be reversed, in which case it becomes the Carnot
heat pump and refrigeration cycle. This time, the cycle remains exactly the same except that the directions of any heat and work interactions are reversed. Heat is absorbed from the low-temperature reservoir, heat is rejected to a high-temperature reservoir, and a work input is required to accomplish all this. The
P–
V diagram of the reversed Carnot cycle is the same as for the Carnot heat-engine cycle except that the directions of the processes are reversed.
Carnot's theorem It can be seen from the above diagram that for any cycle operating between temperatures
TH and
TC, none can exceed the efficiency of a Carnot cycle. '''Carnot's theorem'
is a formal statement of this fact: No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between those same reservoirs.'' Thus, Equation gives the maximum efficiency possible for any engine using the corresponding temperatures. A corollary to Carnot's theorem states that:
All reversible engines operating between the same heat reservoirs are equally efficient. Rearranging the right side of the equation gives what may be a more easily understood form of the equation, namely that the theoretical maximum efficiency of a heat engine equals the difference in temperature between the hot and cold reservoir divided by the absolute temperature of the hot reservoir. Looking at this formula an interesting fact becomes apparent: Lowering the temperature of the cold reservoir will have more effect on the ceiling efficiency of a heat engine than raising the temperature of the hot reservoir by the same amount. In the real world, this may be difficult to achieve since the cold reservoir is often an existing ambient temperature. In
mesoscopic heat engines, work per cycle of operation in general fluctuates due to thermal noise. If the cycle is performed quasi-statically, the fluctuations vanish even on the mesoscale. However, if the cycle is performed faster than the relaxation time of the working medium, the fluctuations of work are inevitable. Nevertheless, when work and heat fluctuations are counted, an exact equality relates the exponential average of work performed by any heat engine to the heat transfer from the hotter heat bath.
Efficiency of real heat engines Carnot realized that, in reality, it is not possible to build a
thermodynamically reversible engine. So, real heat engines are even less efficient than indicated by Equation . In addition, real engines that operate along the Carnot cycle style (isothermal expansion / adiabatic expansion / isothermal compression / adiabatic compression) are rare. Nevertheless, Equation is extremely useful for determining the maximum efficiency that could ever be expected for a given set of thermal reservoirs. This can help illustrate, for example, why a
reheater or a
regenerator can improve the thermal efficiency of steam power plants by increasing the value of
TH and why the thermal efficiency of combined-cycle power plants (which incorporate gas turbines operating at even higher temperatures) exceeds that of conventional steam plants. The first prototype of the
diesel engine was based on the principles of the Carnot cycle. == As a macroscopic construct ==