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A Carnot heat engineis a theoretical engine that operates on the Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824. The Carnot engine model was graphically expanded by Benoît Paul Émile Clapeyron in 1834 and mathematically explored by Rudolf Clausius in 1857 from which the concept of entropy emerged.
Every thermodynamic system exists in a particular state. A thermodynamic cycle occurs when a system is taken through a series of different states, and finally returned to its initial state. In the process of going through this cycle, the system may perform work on its surroundings, thereby acting as a heat engine.
A heat engine acts by transferring energy from a warm region to a cool region of space and, in the process, converting some of that energy to mechanical work. The cycle may also be reversed. The system may be worked upon by an external force, and in the process, it can transfer thermal energy from a cooler system to a warmer one, thereby acting as a refrigerator or heat pump rather than a heat engine.
In the adjacent diagram, from Carnot's 1824 work, Reflections on the Motive Power of Fire ,there are "two bodies A and B, kept each at a constant temperature, that of A being higher than that of B. These two bodies to which we can give, or from which we can remove the heat without causing their temperatures to vary, exercise the functions of two unlimited reservoirs of caloric. We will call the first the furnace and the second the refrigerator.” Carnot then explains how we can obtain motive power, i.e., “work”, by carrying a certain quantity of heat from body A to body B. It also acts as a cooler and hence can also act as a Refrigerator.
The previous image shows the original piston-and-cylinder diagram used by Carnot in discussing his ideal engines. The figure at right shows a block diagram of a generic heat engine, such as the Carnot engine. In the diagram, the “working body” (system), a term introduced by Clausius in 1850, can be any fluid or vapor body through which heat Q can be introduced or transmitted to produce work. Carnot had postulated that the fluid body could be any substance capable of expansion, such as vapor of water, vapor of alcohol, vapor of mercury, a permanent gas, or air, etc. Although, in these early years, engines came in a number of configurations, typically QH was supplied by a boiler, wherein water was boiled over a furnace; QC was typically supplied by a stream of cold flowing water in the form of a condenser located on a separate part of the engine. The output work, W, represents the movement of the piston as it is used to turn a crank-arm, which in turn was typically used to power a pulley so as to lift water out of flooded salt mines. Carnot defined work as “weight lifted through a height”.
The Carnot cycle when acting as a heat engine consists of the following steps:
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 the same reservoirs.
This maximum efficiency is defined as above:
A corollary to Carnot's theorem states that: All reversible engines operating between the same heat reservoirs are equally efficient.
It is easily shown that the efficiency η is maximum when the entire cyclic process is a reversible process. This means the total entropy of the net system (the entropies of the hot furnace, the "working fluid" of the Heat engine, and the cold sink) remains constant when the "working fluid" completes one cycle and returns to its original state. (In the general case, the total entropy of this combined system would increase in a general irreversible process).
Since the "working fluid" comes back to the same state after one cycle, and entropy of the system is a state function; the change in entropy of the "working fluid" system is 0. Thus, it implies that the total entropy change of the furnace and sink is zero, for the process to be reversible and the efficiency of the engine to be maximum. This derivation is carried out in the next section.
The coefficient of performance (COP) of the heat engine is the reciprocal of its efficiency.
For a real heat engine, the total thermodynamic process is generally irreversible. The working fluid is brought back to its initial state after one cycle, and thus the change of entropy of the fluid system is 0, but the sum of the entropy changes in the hot and cold reservoir in this one cyclical process is greater than 0.
The internal energy of the fluid is also a state variable, so its total change in one cycle is 0. So the total work done by the system W, is equal to the heat put into the system minus the heat taken out .
For real engines, sections 1 and 3 of the Carnot Cycle; in which heat is absorbed by the "working fluid" from the hot reservoir, and released by it to the cold reservoir, respectively; no longer remain ideally reversible, and there is a temperature differential between the temperature of the reservoir and the temperature of the fluid while heat exchange takes place.
During heat transfer from the hot reservoir at to the fluid, the fluid would have a slightly lower temperature than , and the process for the fluid may not necessarily remain isothermal. Let be the total entropy change of the fluid in the process of intake of heat.
where the temperature of the fluid T is always slightly lesser than , in this process.
So, one would get
Similarly, at the time of heat injection from the fluid to the cold reservoir one would have, for the magnitude of total entropy change of the fluid in the process of expelling heat:
where, during this process of transfer of heat to the cold reservoir, the temperature of the fluid T is always slightly greater than .
We have only considered the magnitude of the entropy change here. Since the total change of entropy of the fluid system for the cyclic process is 0, we must have
The previous three equations combine to give:
Equations ( 2 ) and ( 7 ) combine to give
where is the efficiency of the real engine, and is the efficiency of the Carnot engine working between the same two reservoirs at the temperatures and . For the Carnot engine, the entire process is 'reversible', and Equation ( 7 ) is an equality.
Hence, the efficiency of the real engine is always less than the ideal Carnot engine.
Equation (7) signifies that the total entropy of the total system (the two reservoirs + fluid) increases for the real engine, because the entropy gain of the cold reservoir as flows into it at the fixed temperature , is greater than the entropy loss of the hot reservoir as leaves it at its fixed temperature . The inequality in Equation ( 7 ) is essentially the statement of the Clausius theorem.
According to the second theorem, "The efficiency of the Carnot engine is independent of the nature of the working substance".
An adiabatic process occurs without transfer of heat or mass of substances between a thermodynamic system and its surroundings. In an adiabatic process, energy is transferred to the surroundings only as work. The adiabatic process provides a conceptual basis for the theory used to expound the first law of thermodynamics, and as such it is a key concept in thermodynamics.
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 igniting the fuel-air mixture with a spark plug as in the Otto cycle (four-stroke/petrol) engine. Diesel engines are used in aircraft, automobiles, power generation, diesel-electric locomotives, and both surface ships and submarines.
In statistical mechanics, entropy is an extensive property of a thermodynamic system. It is closely related to the number Ω of microscopic configurations that are consistent with the macroscopic quantities that characterize the system. Entropy expresses the number Ω of different configurations that a system defined by macroscopic variables could assume. Under the assumption that each microstate is equally probable, the entropy is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant kB. Formally,
In thermodynamics and engineering, a heat engine is a system that converts heat or thermal energy—and chemical energy—to mechanical energy, which can then be used to do mechanical work. It does this by bringing a working substance from a higher state temperature to a lower state temperature. A heat source generates thermal energy that brings the working substance to the high temperature state. The working substance generates work in the working body of the engine while transferring heat to the colder sink until it reaches a low temperature state. During this process some of the thermal energy is converted into work by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity, but it usually is a gas or liquid. During this process, some heat is normally lost to the surroundings and is not converted to work. Also, some energy is unusable because of friction and drag.
Sous-lieutenantNicolas Léonard Sadi Carnot was a French mechanical engineer in the French Army, military scientist and physicist, often described as the "father of thermodynamics." Like Copernicus, he published only one book, the Reflections on the Motive Power of Fire, in which he expressed, at the age of 27 years, the first successful theory of the maximum efficiency of heat engines. In this work he laid the foundations of an entirely new discipline, thermodynamics. Carnot's work attracted little attention during his lifetime, but it was later used by Rudolf Clausius and Lord Kelvin to formalize the second law of thermodynamics and define the concept of entropy.
The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. Isolated systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy.
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.
Carnot's theorem, developed in 1824 by Nicolas Léonard Sadi Carnot, also called Carnot's rule, is a principle that specifies limits on the maximum efficiency any heat engine can obtain. The efficiency of a Carnot engine depends solely on the temperatures of the hot and cold reservoirs.
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 transfer of heat or matter. Such an idealized process is useful in engineering as a model of and basis of comparison for real processes.
An isothermal process is a change of a system, in which the temperature remains constant: ΔT =0. This typically occurs when a system is in contact with an outside thermal reservoir, and the change in the system will occur slowly enough to allow the system to continue to adjust to the temperature of the reservoir through heat exchange. In contrast, an adiabatic process is where a system exchanges no heat with its surroundings (Q = 0). In other words, in an isothermal process, the value ΔT = 0 and therefore the change in internal energy ΔU = 0 but Q ≠ 0, while in an adiabatic process, ΔT ≠ 0 but Q = 0.
The Rankine cycle is a model used to predict the performance of steam turbine systems. It was also used to study the performance of reciprocating steam engines. The Rankine cycle is an idealized thermodynamic cycle of a heat engine that converts heat into mechanical work while undergoing phase change. It is an idealized cycle in which friction losses in each of the four components are neglected. The heat is supplied externally to a closed loop, which usually uses water as the working fluid. It is named after William John Macquorn Rankine, a Scottish polymath and Glasgow University professor.
A thermodynamic cycle consists of a linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables 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. At every point in the cycle, the system is in thermodynamic equilibrium, so the cycle is reversible.
In thermodynamics, the thermal efficiency is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, a steam turbine or a steam engine, a boiler, furnace, or a refrigerator for example. For a heat engine, thermal efficiency is the fraction of the energy added by heat that is converted to net work output. In the case of a refrigeration or heat pump cycle, thermal efficiency is the ratio of net heat output for heating, or removal for cooling, to energy input.
Entropy is a property of thermodynamical systems. The term entropy was introduced by Rudolf Clausius who named it from the Greek word τρoπή, "transformation". He considered transfers of energy as heat and work between bodies of matter, taking temperature into account. Bodies of radiation are also covered by the same kind of reasoning.
In aircraft and rocket design, overall propulsive efficiency is the efficiency with which the energy contained in a vehicle's propellant is converted into kinetic energy of the vehicle, to accelerate it, or to replace losses due to aerodynamic drag or gravity. It can also be described as the proportion of the mechanical energy actually used to propel the aircraft. It is always less than one, because conservation of momentum requires that the exhaust have some of the kinetic energy, and the propulsive mechanism is never perfectly efficient. Overall propulsive efficiency is greatly dependent on air density and airspeed.
The Carnot cycle is a theoretical ideal thermodynamic cycle proposed by French physicist Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. It provides an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of work to the system. It is not an actual thermodynamic cycle but is a theoretical construct.
Thermodynamic heat pump cycles or refrigeration cycles are the conceptual and mathematical models for heat pumps and refrigerators. A heat pump is a mechanical system that allows for the transference of heat from one location at a lower temperature to another location at a higher temperature. Thus a heat pump may be thought of as a "heater" if the objective is to warm the heat sink, or a "refrigerator" if the objective is to cool the heat source. In either case, the operating principles are identical. Heat is moved from a cold place to a warm place.
A photo-Carnot engine is a Carnot cycle engine in which the working medium is a photon inside a cavity with perfectly reflecting walls. Radiation is the working fluid, and the piston is driven by radiation pressure.
In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter. The mechanisms include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or isochoric mechanical work done by the surroundings on the system of interest; or Joule heating by an electric current driven through the system of interest by an external system; or a combination of these. When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system. Thermal conduction occurs by the stochastic (random) motion of microscopic particles. In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field. The definition of heat transfer does not require that the process be in any sense smooth. For example, a bolt of lightning may transfer heat to a body.
Endoreversible thermodynamics is a subset of irreversible thermodynamics aimed at making more realistic assumptions about heat transfer than are typically made in reversible thermodynamics. It gives an upper bound on the energy that can be derived from a real process that is lower than that predicted by Carnot for a Carnot cycle, and accommodates the exergy destruction occurring as heat is transferred irreversibly.