Carnot cycle
The Carnot cycle is a cycle of particular importance in thermodynamics. He is a purely theoretical process. Its importance is that it indicates the optimum that can be surpassed by any particular cycle in which the working gas moves between the same temperatures. The determined from the working temperatures Carnot efficiency ( Carnot factor) specifies which portion of the supplied heat can be converted into a maximum mechanical work. By this shall all the others, the special machinery adjusted comparable processes measured, such as the Otto cycle as a comparison process for the gasoline engine or the Clausius- Rankine cycle as a comparison process for the steam power plant.
The process was developed by the French officer, engineer and physicist Nicolas Léonard Sadi Carnot. Historically Carnot reasoned considerations, the scientific field of thermodynamics.
Description
The end of the Carnot cycle can be thought of as that a gas alternately with a heat reservoir of constant high temperature ( to absorb heat ) and a cold reservoir with constant lower temperature ( for releasing heat ) is in contact with it alternately by applying mechanical work is compressed and expanded again with the release of mechanical work. The difference between recorded and heat given corresponds to the reversible case, the area enclosed by the cycle in the Ts diagram surface. It is exactly equal to the total recovered mechanical work. The gas obtained after the complete run of the process returns to the initial state, that is, all state variables, such as temperature T, pressure p, volume V and internal energy U are so again as large as at the beginning of the process. The process is conceivable as an ideal heat engine (clockwise in the Ts diagram ) or as an ideal heat pump or refrigerating machine (counterclockwise ). The recovered thermal power process technical work can be used in the heat pump process without loss to the the thermal power process to the cold heat reservoir ( environment ) of heat given off - heat reservoir hot in this - together with converted into thermal drive the heat pump is ( rectangular area ) again " hochzupumpen ". Because of this reversibility of the process is known to be reversible. The process could be realized with a periodically operating machinery only under particularly great effort and only approximated. With respect to a process with gases: there is no compressor and no expansion machine, which allow in one pass the heat transfer, so that the temperature is constant. Regarding the process with wet steam: While there are wet steam turbines, but no compressor, compress the wet steam to liquid. In addition, occur in all machines and in all flow processes on friction losses.
Representation in the T- S diagram
The Carnot cycle consists of two isothermal and two isentropic state changes, which form a rectangle in the TS diagram. The entropy is a reversible process, with the heat supplied to the absolute temperature and linked by the equation:
Gradually dissolved:
The cycle consists of the following sub-processes:
1 change of state ( 1 → 2): Isothermal compression
In contact with the cold heat reservoir to the working gas at constant temperature ( isothermal) an amount of heat is removed. This leads to a reduction of the volume V1 to V2.
Since in an isothermal process for an ideal gas is true for the change in internal energy, follows the first law. Thus results for the amount of heat removed by integration
The value for the amount of heat is negative, that is, the heat is withdrawn from the system.
Second change of state ( 2 → 3): Isentropic compression (adiabatic and frictionless )
The gas is insulated and compressed isentropically by mechanical working, thereby transferred to the higher temperature level TI.
3 Change in condition ( 3 → 4 ): Isothermal expansion
In contact with the hot heat reservoir, the gas expands at constant temperature TI. It is the same as above, that is,. Thus the amount of heat supplied is described by:
4 Change in condition ( 4 → 1): Isentropic expansion (adiabatic and frictionless )
The gas expands under isentropic performance of mechanical work until the output condition is reached with respect to pressure, volume and temperature.
The efficiency
The first law of thermodynamics is
After passing through the cycle all state variables reach in the system, including the internal energy of its initial value, (). The useful work is calculated from:
For the Carnot cycle is thus obtained:
The Carnot efficiency is the ratio of actual output to labor supplied heat:
Perpetual motion of the second kind
In all four stages of the process is converted to mechanical energy. The total mechanical energy recovered after passage through the cycle depends only on the fed and amount of heat removed. The obtained mechanical work corresponds to the green highlighted area in the TS diagram.
At temperatures other than 0 K, the Carnot efficiency is always less than 1 Since it after the third law of thermodynamics is not possible to reach the absolute zero of temperature, there is no real ( cyclically operating ) machine that merely deprives a reservoir of heat and this completely appropriate in the work. A machine that efficiency would greater than the Carnot efficiency at given temperatures of the heat reservoirs, called a perpetual motion machine of the second kind Ultimately, this might be through with the derived work again the reverse process as a refrigerator, and it could then be generated as a greater amount of heat used in the heat engine process.
Exergy is defined in thermodynamics as the fraction of thermal energy that can be used as a work. Accordingly, the Carnot efficiency can also be expressed by:
The non- convertible into labor share of thermal energy is called anergy.
Representation of the process with an ideal gas pV diagram
In the case of an ideal gas as the working fluid, the specific volume change work can represent manageable. The individual works that are to be applied for state changes, are here under the assumption that they are positive ( ), presented and provided later in accounting with the appropriate sign:
- 2-3: isentropic compression, the following applies:
- 3-4: isothermal expansion:
- 4-1: isentropic expansion
Work of the Carnot cycle
The overall operation of the process is obtained with the convention that out of the system continuous heat and work with a negative sign - be provided to ():
Carnot efficiency
The thermal efficiency as the ratio of benefits to costs is therefore