Exergy efficiency (also known as the second-law efficiency or rational efficiency) computes the effectiveness of a system relative to its performance in reversible conditions. It is defined as the ratio of the thermal efficiency of an actual system compared to an idealized or reversible version of the system for heat engines. It can also be described as the ratio of the useful work output of the system to the reversible work output for work-consuming systems. For refrigerators and heat pumps, it is the ratio of the actual COP and reversible COP.
The reason the second-law efficiency is needed is because the first-law efficiencies fail to take into account an idealized version of the system for comparison. Using first-law efficiencies alone, can lead one to believe a system is more efficient than it is in reality. So, the second-law efficiencies are needed to gain a more realistic picture of a system's effectiveness. From the second law of thermodynamics it can be demonstrated that no system can ever be 100% efficient.
The exergy B balance of a process gives:
| (1) |
with exergy efficiency defined as:
| (2) |
For many engineering systems this can be rephrased as:
| (3) |
Where is the standard Gibbs (free) energy of reaction at temperature and pressure (also known as the standard Gibbs function change), is the net work output and is the mass flow rate of fuel.
In the same way the energy efficiency can be defined as:
| (4) |
Where is the standard enthalpy of reaction at temperature and pressure .
The destruction of exergy is closely related to the creation of entropy and as such any system containing highly irreversible processes will have a low energy efficiency. As an example the combustion process inside a power stations gas turbine is highly irreversible and approximately 25% of the exergy input will be destroyed here.
For fossil fuels the free enthalpy of reaction is usually only slightly less than the enthalpy of reaction so from equations ( 3 ) and ( 4 ) we can see that the energy efficiency will be correspondingly larger than the energy law efficiency. For example, a typical combined cycle power plant burning methane may have an energy efficiency of 55%, while its exergy efficiency will be 57%. A 100% exergy efficient methane fired power station would correspond to an energy efficiency of 98%.
This means that for many of the fuels we use, the maximum efficiency that can be achieved is >90%, however we are restricted to the Carnot efficiency in many situations as a heat engine is being used.
For any heat engine, the exergy efficiency compares a given cycle to a Carnot heat engine with the cold side temperature in equilibrium with the environment. Note that a Carnot engine is the most efficient heat engine possible, but not the most efficient device for creating work. Fuel cells, for instance, can theoretically reach much higher efficiencies than a Carnot engine; their energy source is not thermal energy and so their exergy efficiency does not compare them to a Carnot engine. [1] [2]
Neither the first nor the second law of thermodynamics includes a measure of the rate of energy transformation. When a measure of the maximal rate of energy transformation is included in the measure of second law efficiency it is known as second law efficiency under maximum power, and directly related to the maximum power principle (Gilliland 1978, p. 101).
A Carnot heat engine is a heat 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, work that led to the fundamental thermodynamic concept of entropy. The Carnot engine is the most efficient heat engine which is theoretically possible. The efficiency depends only upon the absolute temperatures of the hot and cold heat reservoirs between which it operates.
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication.
In thermodynamics and engineering, a heat engine is a system that converts heat to usable energy, particularly mechanical energy, which can then be used to do mechanical work. While originally conceived in the context of mechanical energy, the concept of the heat engine has been applied to various other kinds of energy, particularly electrical, since at least the late 19th century. The heat engine 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 higher 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 lower 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, and often described as the "father of thermodynamics". He published only one book, the Reflections on the Motive Power of Fire, in which he expressed the first successful theory of the maximum efficiency of heat engines and laid the foundations of the 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. Based on purely technical concerns, such as improving the performance of the steam engine, Sadi Carnot's intellect laid the groundwork for modern science technological designs, such as the automobile or jet engine.
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology.
The thermodynamic free energy is a concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in the free energy is the maximum amount of work that a thermodynamic system can perform in a process at constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful.
The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects, unless energy in some form is supplied to reverse the direction of heat flow. Another definition is: "Not all heat energy can be converted into work in a cyclic process."
In thermodynamics, 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 that any heat engine can obtain.
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 net transfer of heat or matter. Such an idealized process is useful in engineering as a model of and basis of comparison for real processes. This process is idealized because reversible processes do not occur in reality; thinking of a process as both adiabatic and reversible would show that the initial and final entropies are the same, thus, the reason it is called isentropic. Thermodynamic processes are named based on the effect they would have on the system. Even though in reality it is not necessarily possible to carry out an isentropic process, some may be approximated as such.
A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are not thermodynamic systems. A wall of a thermodynamic system may be purely notional, when it is described as being 'permeable' to all matter, all radiation, and all forces. A state of a thermodynamic system can be fully described in several different ways, by several different sets of thermodynamic state variables.
The Rankine cycle is an idealized thermodynamic cycle describing the process by which certain heat engines, such as steam turbines or reciprocating steam engines, allow mechanical work to be extracted from a fluid as it moves between a heat source and heat sink. The Rankine cycle is named after William John Macquorn Rankine, a Scottish polymath professor at Glasgow University.
In thermodynamics, the exergy of a system is the maximum useful work possible during a process that brings the system into equilibrium with a heat reservoir, reaching maximum entropy. When the surroundings are the reservoir, exergy is the potential of a system to cause a change as it achieves equilibrium with its environment. Exergy is the energy that is available to be used. After the system and surroundings reach equilibrium, the exergy is zero. Determining exergy was also the first goal of thermodynamics. The term "exergy" was coined in 1956 by Zoran Rant (1904–1972) by using the Greek ex and ergon meaning "from work", but the concept had been earlier developed by J Willard Gibbs in 1873.
A thermodynamic cycle consists of linked sequences 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. If at every point in the cycle the system is in thermodynamic equilibrium, the cycle is reversible. Whether carried out reversible or irreversibly, the net entropy change of the system is zero, as entropy is a state function.
The maximum power principle or Lotka's principle has been proposed as the fourth principle of energetics in open system thermodynamics, where an example of an open system is a biological cell. According to Howard T. Odum, "The maximum power principle can be stated: During self-organization, system designs develop and prevail that maximize power intake, energy transformation, and those uses that reinforce production and efficiency."
In thermodynamics, the thermal efficiency is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, steam turbine, steam engine, boiler, furnace, refrigerator, ACs etc.
In aerospace engineering, concerning aircraft, rocket and spacecraft design, overall propulsion system efficiency is the efficiency with which the energy contained in a vehicle's fuel is converted into kinetic energy of the vehicle, to accelerate it, or to replace losses due to aerodynamic drag or gravity. Mathematically, it is represented as , where is the cycle efficiency and is the propulsive efficiency.
A Carnot cycle is an ideal thermodynamic cycle proposed by French physicist Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. By Carnot's theorem, it provides an upper limit on the efficiency of any classical thermodynamic engine during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference through the application of work to the system.
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.
Entropy production is the amount of entropy which is produced in any irreversible processes such as heat and mass transfer processes including motion of bodies, heat exchange, fluid flow, substances expanding or mixing, anelastic deformation of solids, and any irreversible thermodynamic cycle, including thermal machines such as power plants, heat engines, refrigerators, heat pumps, and air conditioners.
The Carnot method is an allocation procedure for dividing up fuel input (primary energy, end energy) in joint production processes that generate two or more energy products in one process (e.g. cogeneration or trigeneration). It is also suited to allocate other streams such as CO2-emissions or variable costs. The potential to provide physical work (exergy) is used as the distribution key. For heat this potential can be assessed the Carnot efficiency. Thus, the Carnot method is a form of an exergetic allocation method. It uses mean heat grid temperatures at the output of the process as a calculation basis. The Carnot method's advantage is that no external reference values are required to allocate the input to the different output streams; only endogenous process parameters are needed. Thus, the allocation results remain unbiased of assumptions or external reference values that are open for discussion.
