Clever Geek Handbook
📜 ⬆️ ⬇️

Exergy

Exergy is the limiting (largest or smallest) value of energy that can be used (obtained or expended) in a thermodynamic process in a useful manner, taking into account the restrictions imposed by the laws of thermodynamics ; the maximum work that a macroscopic system can accomplish during a quasistatic transition from a given state to a state of equilibrium with the environment (the process exergy is positive), or the minimal work that needs to be spent on a quasistatic transition of a system from a state of equilibrium with the environment to a given state [1 ] (exergy of the process is negative [2] ).

The difference between the change in energy in the process and the exergy of the process, that is, that part of the energy that cannot be converted into exergy, is called anergy [3] . From the law of conservation of energy it follows that for any energy conversion, the sum of the exergy and anergy of the process remains unchanged [4] .

Comparing the exergy - the characteristic of an ideal quasistatic process [5] - with the energy received / expended in a real nonequilibrium process, a conclusion is drawn on the degree of thermodynamic perfection of the process.

Unlike energy, exergy and anergy depend not only on the parameters of the system, but also on environmental parameters and the characteristics of the process under consideration, that is, exergy and anergy are not parameters of the state of the system, but are parameters of the process performed by the system [6] , and we should talk about the process exergy and process anergy.

Quite often, if the state of the environment remains unchanged, exergy and anergy can be expressed in terms of the state functions of the system [7] , respectively, they behave as state functions, which they are conventionally assigned to in such situations [8] . Having met in the literature the phrases: “The energy of the system consists of exergy and anergy” [9] , “The second law of thermodynamics allows us to distinguish 2 forms of energy: anergy and exergy” [10] , “In an ideal reversible process, work equal to the loss of exergy will be obtained” [ 11] [12] , in which the terms system exergy and system anergy [11] [13] are used , we should recall the conventionality for assigning these thermodynamic quantities to state functions, that is, to the characteristics of the system, rather than the process [9] .

When the parameters of the working fluid are the same as those of the environment and the thermodynamic process is impossible, the exergy of the working fluid, considered as a conditional state function, is zero [14] . Exergy can only be obtained from sources with parameters different from the parameters of the environment, the exergy of which is always zero: no methods can make the environment do the work [15] .

For industrial installations, ambient air is usually taken as the environment. For installations operating in the open air, the temperature of which depends on the time of day and time of the year, it is necessary either to carry out calculations for different periods, or to take some average ambient temperature.

The concept of anergy as a conditional function of the state helps to realize the fact that objectively there is “useless” energy (the internal energy of the environment and the internal energy of systems in equilibrium with the environment). The transition of exergy to anergy accompanies any nonequilibrium process (energy dissipation). The reverse transition of anergy to exergy is impossible, therefore all attempts to use anergy in practice - to create a perpetual motion machine of the second kind - are doomed to failure [16] [17] [18] . Exergy requires natural resources and equipment. The implementation of technical processes requires exergy costs. Therefore, exergy always has a certain cost. The energy in the environment is practically unlimited, free, but its value is zero. Understanding the essence of anergy makes it possible, when solving practical problems, to exclude from consideration systems that operate based on the use of anergy [17] [19] .

Exergy Analysis

The fundamental idea of exergy analysis is to use an additional indicator, exergy, in addition to energy when analyzing technical systems: comparing actual work done with process exergy allows us to judge the energy efficiency in a heat engine [20] . The closer the energy indicators of a real nonequilibrium process to the process exergy, the more perfect the process and the more difficult it is to increase its efficiency.

An exergy analysis that takes into account losses from nonequilibrium processes in the system allows both a relative (see the Exergy efficiency section below ) and an absolute assessment of the degree of thermodynamic perfection of the technologies used in comparison with the analysis based on energy efficiency [21] [22] [23 ] [23 ] ] . Exergy analysis serves as a theoretical basis for energy conservation, since it makes it possible to simply and clearly determine the degree of process perfection and the sources of losses due to nonequilibrium in various installations, and exergy indicators can easily be associated with technical and economic ones. It is generally accepted that when choosing the basic principles of the process, it is possible to identify the sources of 40% of energy loss, while designing - another 40%. Thus, it is already impossible to influence about 80% of losses at the production stage. That is why exergy analysis is especially important at the stages of preliminary design and system design.

Exergy analysis does not exclude energy, based on the preparation of an energy balance, but supplements it. Exergy analysis naturally leads to the same results as the consideration of the problem by any other thermodynamic method, for example, using entropy ( entropy analysis ), but is more visual from an engineering point of view. One of the main advantages of the exergy method is that it allows one to judge the degree of perfection of the processes occurring inside the heat exchanger or chemical reactor by the external characteristic — the difference in exergy at the inlet and outlet of the apparatus [24] .

The terms “energy loss” and “loss of exergy” used in exergy analysis have fundamentally different contents: the first means the impossibility of using energy to achieve a specific goal, the second means the complete disappearance of exergy associated with energy dissipation (scattering).

An exergy analysis is most useful when thermal processes come to the fore [19] , for example, when analyzing energy-saving technologies and evaluating the heat engineering efficiency of a fuel technology. At the same time, not for every technical task there is a need for exergy analysis. So, when using energy for technological needs (evaporation, metal smelting, etc.), the exergy of the coolant is not of direct importance [9] . For the analysis of quasistatic processes, exergy analysis, taking into account losses from nonequilibrium, is naturally not used [25] .

Exergy Efficiency

Exergy efficiency is the ratio of actually completed work to its maximum possible value, that is, to the exergy of the process in question [26] [27] . If the usual energy efficiency shows the degree of useful energy use and allows you to compare heat engines by this indicator, then the exergy efficiency characterizes energy efficiency (thermodynamic process perfection) and answers questions about the theoretical possibility and practicality of increasing the efficiency of a heat engine: a relatively small value of energy efficiency may correspond to a value of exergy efficiency close to 100%, when a further increase in energy energetically efficiency can not be due to restrictions imposed by the laws of thermodynamics. A significant deviation of exergy efficiency from unity indicates the presence of fundamentally removable exergy losses, the reduction of which is possible with more rational processes and the use of more advanced equipment.

Exergy efficiency is applicable for the analysis of the perfection of any thermodynamic processes and any thermotechnical devices. So, we can talk about the exergy efficiency of the cycle, a combined installation for generating electricity and heat for the purpose of heating, heat exchanger, thermal insulation, etc. [28] . The exergy efficiency of equilibrium processes is 1.

Nonequilibrium as a source of work

Any thermal power plant (TEU), together with the environment, is considered by thermodynamics as an isolated system [29] . Within such a system, work can only be done when the system is not in equilibrium; in the case of the transition of the system to the state of equilibrium, it is impossible to obtain work in it (we are talking about complete equilibrium: mechanical, thermal, chemical, electrical, etc.) Thus, the possibility of obtaining work in the system is determined not by the energy reserve in it (energy isolated the system does not change during any processes), but the disequilibrium of the system, that is, the presence of a difference in pressure, temperature, electric potentials, etc.

As an example, consider a cylinder filled with compressed air at the same temperature as atmospheric. The system, consisting of atmospheric air (external environment) and air in the cylinder, is in thermal equilibrium, but there is no mechanical equilibrium in it, and this allows you to get work in this system using any air engine.

One more example. Let the system form the external environment and the body with high temperature. In the presence of mechanical equilibrium in such a system, there is no thermal equilibrium, which allows one to get work with the help of a heat engine that uses a body with a high temperature and an external medium as an energy receiver.

In both cases, the possibilities of getting work are exhausted when the system comes into a state of thermodynamic equilibrium. But the system can come to an equilibrium state without doing useful work: air from a cylinder can be released into the atmosphere simply by opening a tap; during thermal interaction with the external environment, the hot body cools by itself.

In the transition of a system from a nonequilibrium state to an equilibrium, useful work depends on the nature of such a transition. The greatest work will be in the case when there are no friction losses, and TEU duty cycles have maximum efficiency values.

Thus [30] [31] :

  • an isolated system is capable of producing work only if it is not in a state of thermodynamic equilibrium;
  • the system’s working capacity is exhausted and becomes zero when it reaches an equilibrium state;
  • the greatest possible work during the transition of the system from the initial nonequilibrium state to the final equilibrium state will be obtained when all the processes associated with the conversion of energy are quasistatic.

Types of Exergy

Exergy can be divided into the exergy of processes that are not characterized by entropy (mechanical, electrical, nuclear, etc.), equal to the change in energy (kinetic, for example) in these processes [32] [33] , and the thermodynamic exergy of processes characterized by entropy. For such processes, exergy is a measure of the technical operability of a thermodynamic system.

The following exergy components are distinguished [34] :

  • mechanical (deformation), depending on pressure;
  • thermal , temperature-dependent;
  • concentration , depending on the difference in the concentrations of substances in the system and in the environment;
  • reactionary , due to the possibility of chemical reactions between the substances of the system and the environment.

Thermodynamic exergy is divided into types of exergy either by the nature of thermodynamic processes (open and cyclic), or by the type of thermodynamic systems in which these processes occur. When classifying according to the nature of the process, they distinguish [33] :

  • thermomechanical exergy ( thermo- deformation exergy [34] , physical exergy [33] ), consisting of the mechanical and thermal components of exergy;
  • energy flow exergy [33] (heat flux exergy [35] , heat exergy [36] [37] , thermal exergy [38] );
  • chemical (zero) exergy [33] , consisting of the concentration and reaction components of exergy;
  • radiation exergy [33] .

When classifying exergy types according to the type of thermodynamic systems, they proceed from the presence or absence of additional energy sources / receivers in these systems, in addition to the working fluid and the environment [39] [32] [40] [33] [41] :

  • exergy in the volume of the working fluid (exergy of matter in a closed volume [42] [33] , streamless exergy of the working fluid of constant mass, exergy of a motionless body, exergy of a closed system);
  • exergy in the flow of the working fluid (exergy of the flow [43] , exergy of the flow of matter [44] [33] , exergy of the flow of the working fluid [45] );
  • energy flow exergy in systems with additional energy sources / receivers.

For greater clarity, the classification of types of exergy with an indication of its components is presented in the table:

 

Exergy in volume

The volume of exergy is used to describe a single process of finite duration in the absence of sources of energy other than the environment with constant pressure P 0 and temperature T 0 . The uniqueness of the energy reservoir means that the process in question cannot be closed (cyclic). The volume exergy consists of thermomechanical exergy, chemical exergy (in batch reactors) and radiation exergy. For a thermodeformation system, exergy in the volume E x can be found by the formula [46]


Ex=(U-U0)-T0(S-S0)-P0(V0-V)=(H-H0)-T0(S-S0),{\ displaystyle E_ {x} = (U-U_ {0}) - T_ {0} (S-S_ {0}) - P_ {0} (V_ {0} -V) = (H-H_ {0} ) -T_ {0} (S-S_ {0}),}  (Exergy in volume and flow)

where U, H, S, and V are the internal energy, enthalpy, entropy, and volume of the working fluid, respectively, with values ​​without an index referring to its initial state, and values ​​with an index 0 to the final state. From this formula it follows that exergy in volume is a conditional function of the state of the system.

An example of a process in which only thermomechanical exergy is required is the expansion of compressed gas with pressure P 1 and temperature T 1 from a tank (gas cylinder) into the environment. For simplicity, we assume that the cylinder is filled with compressed air with the same temperature as atmospheric [47] . The P – V diagram shown in the figure below for slow (to maintain the process isothermal) bleeding of gas from a cylinder into the atmosphere corresponds to the case when thermal ( T = T 0 ) but not mechanical ( P > P 0 ) equilibrium occurs throughout the process between the system and the environment. In the final state 0, the working fluid in question has environmental parameters:

 

The only possible quasistatic process between states 1 and 0 in the presence of only one energy reservoir is the expansion of gas along the isotherm T 0 . In the diagram, the work of this process corresponds to the area of ​​the figure 1-0 — b — a — 1. The work corresponding to the area of ​​the rectangle a – c – 0 – b – a has been expended in displacing the medium and is not useful. Therefore, exergy - the maximum possible useful work equal to the difference between all the work done and the work spent on displacing the medium - corresponds to the area of ​​the figure 1-0-s-1.

For the image of both the direct (expansion) and reverse (compression) process, the same P – V diagram is used in the exergy analysis, bearing in mind that the compression exergy is negative.

Exergy in the stream

The flow exergy is used to describe an open stationary process of indefinite duration in the absence of energy sources other than the environment with constant pressure P 0 and temperature T 0 . Imagine a certain region limited by control surfaces (part of a heat engine or technological apparatus) in which some kind of physical and / or chemical transformation takes place. The stationary process assumes that a certain amount of a substance with pressure P 1 and temperature T 1 enters the system through one of the control surfaces, and the same amount of substance with pressure P 2 and temperature T 2 is discharged through another. The formula for calculating the exergy in a stream is given above, however, since we are talking about a stream, the quantities U, H, S, and V included in it mean specific (that is, referred to the unit mass of the working fluid) values ​​of internal energy, enthalpy, entropy, and volume of the working fluid. This equation does not include the exergy of the kinetic energy of the flow , which is equal to this energy itself, since this is easy to do if desired, but usually we are much more interested in what can be obtained by changing the parameters of the substance [42] .

Exergy in the flow is a conditional function of the state of the system [48] [49] . Under mechanical equilibrium of the body with the external environment, exergy in the flow and exergy in the volume are numerically equal [50] .

The notion of exergy in a flow is useful in those cases when a continuous flow of a working fluid is used in a heat power plant (water and its steam in steam turbine plants, air and combustion products in gas turbine plants and jet engines, etc.). The difference between the exergy values ​​at the input and output of the installation is equal to the sum of useful work and losses; knowing the actual value of useful work, one can find the value of the exergy efficiency of the installation. One of the ideas of the exergy analysis method is realized in this way — the ability to judge the losses inside the apparatus by the external characteristic — the difference in the values ​​of exergy at the entrance to the apparatus and at the exit from it [51] .

Energy Flow Exergy

The energy flow exergy (thermal exergy) is used to describe the process (both open and cyclic) in an open or closed system if, in addition to the environment with constant pressure P 0 and temperature T 0 , there are other sources (receivers) of energy. Thermal exergy depends on the nature of the process of energy supply to the system and even conditionally cannot be considered as a function of the state [16] [49] .

As an example of calculating exergy, we consider the simplest case — heating (curve 2–1) or cooling (curve 1–2) of a working fluid of constant mass, both the initial and final temperatures of the working fluid above the ambient temperature T u :

 

In the figure, T is the temperature, T u is the ambient temperature, S is the entropy. The process excursion can be found by isolating the elementary (infinitesimal) change in the entropy dS and performing integration for the entire temperature range. The process exergy corresponds to the area of ​​the figure T u –2–1 – S – T u under the heating / cooling curve [52] . The exergies of heating and cooling are numerically equal, but differ in signs: the exergy of heating is negative, while the exergy of the cooling process is positive.

Real TEU cycles are connected with the supply and removal of energy at a variable temperature. An example is the cycle of a boiler unit, in which gaseous products of fuel combustion serve as an energy source. In a boiler unit, they are cooled at constant pressure, giving energy to water and water vapor, from the combustion temperature T to (in the limit) the ambient temperature T 0 [50] :

 

The operating cycle of the installation on the T – S diagram is a curved triangle 0–1–2–0: the working fluid receives energy from the combustion products along the 0–1 curve, and the quasistatic transition from point 1 to the T 0 isotherm should occur along the ideal adiabat 1– 2, and the working fluid can quasistatically give energy to the environment only through the 2–0 isotherm. Any other cycle of the working fluid when using combustion products as a heater cannot be quasistatic [50] .

Chemical Exergy

Chemical (zero) exergy is associated with establishing the equality of chemical potentials between the corresponding components of the substance and the environment and is measured by the amount of useful energy that can be obtained in the quasistatic process of achieving chemical (concentration and reaction) equilibrium of the working fluid with the environment with constant pressure P 0 and temperature T 0 [53] . In the processes of separation, mixing, and dissolution of substances that are not accompanied by chemical transformations, the main component is the concentration component of chemical exergy, and in chemical reactors the reaction component [54] .

The term zero exergy [55] [56] , sometimes used in domestic literature, is intended to emphasize that the value of process exergy is measured from the initial (zero) state, characterized by environmental parameters [55] [57] .

In technical thermodynamics, the main attention is paid to the chemical exergy of the fuel used in thermal power plants (in particular, internal combustion engines). Finding the exact value of chemical exergy is very time consuming. Approximately accept [58] :


Ex=0.95Hu,{\ displaystyle E_ {x} = 0.95H_ {u},}  (for gaseous fuels)
Ex=1.064Hu,{\ displaystyle E_ {x} = 1.064H_ {u},}  (for diesel fuel)
Ex=1.067Hu,{\ displaystyle E_ {x} = 1.067H_ {u},}  (for gasoline)
Ex=1.039Hu.{\ displaystyle E_ {x} = 1.039H_ {u}.}  (for kerosene)

Here E x is the chemical exergy of the fuel; H u is the lowest energy of fuel combustion (the amount of energy released during the combustion of a unit mass of fuel, minus the energy spent on the evaporation of water generated during the combustion of fuel).

Radiation Exergy

The exergy of radiation depends on only one environmental parameter - its temperature T 0 - and is determined by the amount of useful energy that can be obtained from radiation with temperature T in the quasistatic process of bringing this radiation into equilibrium with the environment. To, without losing the rigor of the conclusions, to make the presentation more visual and to simplify the terminology, we will talk about a radiation receiver (working fluid) that is in equilibrium with the environment. The exergy density of the absorbed radiation for a completely black working fluid with temperature T 0 is calculated by the formula [59]


ex=α3(3Tfour+T0four-fourT0T3),{\ displaystyle e_ {x} = {\ frac {\ alpha} {3}} (3T ^ {4} + {T_ {0}} ^ {4} -4T_ {0} T ^ {3}),}  (Exergy density of absorbed_radiation)

and the exergy power per unit surface of the working fluid is found by the formula [59]


exf=αc12(3Tfour+T0four-fourT0T3).{\ displaystyle e_ {xf} = {\ frac {\ alpha c} {12}} (3T ^ {4} + {T_ {0}} ^ {4} -4T_ {0} T ^ {3}).}  (Exergy power of absorbed radiation per unit surface of the radiation receiver)

Here e x is the radiation exergy density, J / m 3 ; e xf — radiation exergy power per unit surface area of ​​the working fluid, W / m 2 ; α is the radiation constant (7.5657 · 10 −16 J · m −3 · K −4 ); c is the speed of light in vacuum (2.9979 · 10 8 m / s). For a gray working fluid, the values ​​found by the above formulas are multiplied by the degree of blackness of the absorbing surface of the body.

The radiation exergy has a zero value at T = T 0 and increases with a deviation of T from T 0 towards both high and low temperatures, while maintaining a positive value. The energy and exergy of radiation are always different in magnitude, with the exception of one point corresponding to the temperature T = 0.63 T 0 . At T > 0.63 T 0, the exergy of radiation is less than its energy, and at T <0.63 T 0, the exergy of radiation is greater than its energy [60] .

For monochromatic coherent radiation (for example, a laser beam), the exergy of radiation is equal to its energy [18] .

Historical background

In 1889, Louis Georges Guy introduced the concept of technical operability - the maximum technical work that a system can perform when moving from a given state to a state of equilibrium with the environment, and Aurel Stodola (1898) brought a methodology for analyzing processes in a stream beyond the bounds of a pure theory and applied he introduced the concept of free technical enthalpy for heat engineering calculations. The Guy – Stodola theorem states that the energy loss in a system due to the nonequilibrium processes occurring in it is equal to the product of the ambient temperature and the change in the entropy of the system [24] . The term “exergy” was proposed in 1955 by Zoran Rant (1904–1972) [61] .

Notes

  1. ↑ Erofeev V.L. et al., Heat Engineering, 2008 .
  2. ↑ A negative sign of exergy means that the work is done due to the energy of the external environment ( Burdakov V.P. et al. , Thermodynamics, part 2, p. 118).
  3. ↑ Rem G. D., Technical Thermodynamics, 1977 , p. 165.
  4. ↑ Rem G. D., Technical Thermodynamics, 1977 , p. 166.
  5. ↑ How to describe the transition between nonequilibrium and equilibrium states of a system using equilibrium thermodynamics? To this end, they use the principle of local equilibrium, which underlies the classical nonequilibrium thermodynamics . А именно, неравновесное состояние полагают локально — во времени и/или пространстве — равновесным, и переход между интересующими нас состояниями рассматривают как равновесный процесс. С тем, чтобы избежать когнитивного диссонанса от фразеологических оборотов типа: «равновесный процесса перехода из неравновесного состояния…», термин « равновесный процесс » в данной статье заменён на рассматриваемое в качестве его синонима словосочетание « квазистатический процесс ».
  6. ↑ Барилович B. A., Смирнов Ю. А., Основы технической термодинамики, 2014 , с. 76.
  7. ↑ Это всегда можно сделать для адиабатных и изобарных процессов ( Исаев С. И. , Курс химической термодинамики, 1986, с. 108).
  8. ↑ Коновалов В. И., Техническая термодинамика, 2005 , с. 156.
  9. ↑ 1 2 3 Алексеев Г. Н., Энергия и энтропия, 1978 , с. 161.
  10. ↑ Эрдман С. В., Изд-во ТПУ, 2006 , с. 34.
  11. ↑ 1 2 Казаков и др., 2013 , с. sixteen.
  12. ↑ Луканин П. В., Технологические энергоносители предприятий, 2009 , с. 15.
  13. ↑ Луканин П. В., Технологические энергоносители предприятий, 2009 , с. 14—15.
  14. ↑ Мазур Л. С., Техническая термодинамика и теплотехника, 2003 , с. 42.
  15. ↑ Мазур Л. С., Техническая термодинамика и теплотехника, 2003 , с. 43.
  16. ↑ 1 2 Барилович B. A., Смирнов Ю. А., Основы технической термодинамики, 2014 , с. 48.
  17. ↑ 1 2 Мазур Л. С., Техническая термодинамика и теплотехника, 2003 , с. 46.
  18. ↑ 1 2 Бродянский В. М. и др., Эксергетический метод и его приложения, 1988 , с. 51.
  19. ↑ 1 2 Сажин Б. С. и др., Эксергетический анализ работы промышленных установок, 2000 , с. 13-14.
  20. ↑ Исаев С. И., Курс химической термодинамики, 1986 , с. 108.
  21. ↑ Бродянский В. М. и др., Эксергетический метод и его приложения, 1988 .
  22. ↑ Бродянский В. М., Эксергетический метод термодинамического анализа, 1973 .
  23. ↑ Шаргут Я., Петела Р., Эксергия, 1968 .
  24. ↑ 1 2 Сажин Б. С. и др., Эксергетический анализ работы промышленных установок, 2000 , с. 6.
  25. ↑ Бурдаков В. П. и др., Термодинамика, ч. 2, 2009 , с. 120.
  26. ↑ Бурдаков В. П. и др., Термодинамика, ч. 2, 2009 , с. 118.
  27. ↑ Модификация этой дефиниции на случай отрицательных значенийэксергии выполняется элементарно.
  28. ↑ Александров А. А., Термодинамические основы циклов теплоэнергетических установок, 2004 , с. 71.
  29. ↑ В зависимости от контекста далее под системой подразумевается либо подсистема «рабочее тело», либо, как в данном подразделе, рабочее тело + источники/приёмники энергии + окружающая среда.
  30. ↑ Коновалов В. И., Техническая термодинамика, 2005 , с. 154.
  31. ↑ Арнольд Л. В. и др., Техническая термодинамика и теплопередача, 1979 , с. 128.
  32. ↑ 1 2 Мазур Л. С., Техническая термодинамика и теплотехника, 2003 , с. 47.
  33. ↑ 1 2 3 4 5 6 7 8 9 Чечеткин А. В., Занемонец Н. А., Теплотехника, 1986 , с. 73.
  34. ↑ 1 2 Мазур Л. С., Техническая термодинамика и теплотехника, 2003 , с. 48.
  35. ↑ Чечеткин А. В., Занемонец Н. А., Теплотехника, 1986 , с. 76.
  36. ↑ Кириллин В. А. и др., Техническая термодинамика, 2008 , с. 115.
  37. ↑ Александров А. А., Термодинамические основы циклов теплоэнергетических установок, 2004 , с. 68.
  38. ↑ Коновалов В. И., Техническая термодинамика, 2005 , с. 160.
  39. ↑ Александров Н. Е. и др., Основы теории тепловых процессов и машин, ч. 2, 2012 , с. 67.
  40. ↑ Арнольд Л. В. и др., Техническая термодинамика и теплопередача, 1979 , с. 129.
  41. ↑ Коновалов В. И., Техническая термодинамика, 2005 , с. 154, 160, 276.
  42. ↑ 1 2 Александров А. А., Термодинамические основы циклов теплоэнергетических установок, 2004 , с. 67.
  43. ↑ Казаков и др., 2013 , с. 22.
  44. ↑ Александров А. А., Термодинамические основы циклов теплоэнергетических установок, 2004 , с. 136.
  45. ↑ Кириллин В. А. и др., Техническая термодинамика, 2008 , с. 306.
  46. ↑ Кириллин В. А. и др., Техническая термодинамика, 2008 , с. 302.
  47. ↑ Кириллин В. А. и др., Техническая термодинамика, 2008 , с. 111-112.
  48. ↑ Казаков и др., 2013 , с. 24.
  49. ↑ 1 2 Физическая энциклопедия, т. 5, 1998 , с. 500.
  50. ↑ 1 2 3 Коновалов В. И., Техническая термодинамика, 2005 , с. 161.
  51. ↑ Кириллин В. А. и др., Техническая термодинамика, 2008 , с. 304.
  52. ↑ Александров А. А., Термодинамические основы циклов теплоэнергетических установок, 2004 , с. 69.
  53. ↑ Сажин Б. С. и др., Эксергетический анализ работы промышленных установок, 2000 , с. 17-18.
  54. ↑ Чечеткин А. В., Занемонец Н. А., Теплотехника, 1986 , с. 74.
  55. ↑ 1 2 Александров Н. Е. и др., Основы теории тепловых процессов и машин, ч. 2, 2012 , с. 68.
  56. ↑ Сажин Б. С. и др., Эксергетический анализ работы промышленных установок, 2000 , с. 17.
  57. ↑ Шаргут Я., Петела Р., Эксергия, 1968 , с. 47.
  58. ↑ Александров Н. Е. и др., Основы теории тепловых процессов и машин, ч. 2, 2012 , с. 75.
  59. ↑ 1 2 Шаргут Я., Петела Р., Эксергия, 1968 , с. 233.
  60. ↑ Мазур Л. С., Техническая термодинамика и теплотехника, 2003 , с. 67.
  61. ↑ Рант, 1965 .

Literature

  • Ehrenfest-Afanassjewa T. Zur Axiomatisierung des zweiten Hauptsatzes der Thermodynamik (нем.) // Zeitschrift für Physik. — 1925. — Vol. 33, Nr. 1 . — P. 933–945.
  • Ehrenfest-Afanassjewa T. Berichtigung zu der Arbeit: Zur Axiomatisierung des zweiten Hauptsatzes der Thermodynamik (нем.) // Zeitschrift für Physik. — 1925. — Vol. 34, Nr. 1 . — P. 638.
  • Ehrenfest-Afanassjewa T. Die Grundlagen der Thermodynamik. — Leiden: EJ Brill, 1956. — XII + 131 с.
  • Fowler RH, Guggenheim EA Statistical Thermodynamics: A Version of Statistical mechanics for Students of Physics and Chemistry. — Cambridge: University Press, 1939. — 693 с.
  • Hatsopoulos GN, Keenan JH Principles of General Thermodynamics. — N. Y. e. a.: John Wiley & Sons, Inc., 1965. — XLII + 788 p.
  • Александров А. А. Термодинамические основы циклов теплоэнергетических установок. — М. : Изд-во МЭИ, 2004. — 159 с. — ISBN 5-7046-1094-3 .
  • Александров Н. Е., Богданов А. И., Костин К. И. и др. Основы теории тепловых процессов и машин. Часть I / Под ред. Н. И. Прокопенко. - 4th ed. (электронное). — М. : Бином. Лаборатория знаний, 2012. — 561 с. — ISBN 978-5-9963-0833-0 .
  • Александров Н. Е., Богданов А. И., Костин К. И. и др. Основы теории тепловых процессов и машин. Часть I / Под ред. Н. И. Прокопенко. - 4th ed. (электронное). — М. : Бином. Лаборатория знаний, 2012. — 572 с. — ISBN 978-5-9963-0834-7 .
  • Алексеев Г. Н. Энергия и энтропия. — М. : Знание, 1978. — 192 с. — (Жизнь замечательных идей).
  • Андрющенко А. И. Основы технической термодинамики реальных процессов. — М. : Высшая школа, 1967. — 268 с.
  • Арнольд Л. В., Михайловский Г. А., Селиверстов В. М. Техническая термодинамика и теплопередача / Под. общ. ed. В. И. Крутова. - 2nd ed., Revised. — М. : Высшая школа, 1979. — 445 с.
  • Архаров А. М., Исаев С. И., Кожинов И. А. и др. Теплотехника / Под. общ. ed. В. И. Крутова. — М. : Машиностроение, 1986. — 432 с.
  • Афанасьева-Эренфест Т. А. Необратимость, односторонность и второе начало термодинамики (рус.) // Журнал прикладной физики. — 1928. — Vol. 5, № 3–4 . — P. 3—30.
  • Барилович B. A., Смирнов Ю. А. Основы технической термодинамики и теории тепло- и массообмена. — М. : ИНФРА-М, 2014. — 432 с. — (Высшее образование: Бакалавриат). — ISBN 978-5-16-005771-2 .
  • Бахшиева Л. Т., Кондауров Б. П., Захарова А. А., Салтыкова В. С. Техническая термодинамика и теплотехника / Под ред. проф А. А. Захаровой. - 2nd ed., Rev. — М. : Академия, 2008. — 272 с. - (Higher vocational education). — ISBN 978-5-7695-4999-1 .
  • Белоконь Н. И. Термодинамика. — М. : Госэнергоиздат, 1954. — 416 с.
  • Белоконь Н. И. Основные принципы термодинамики. — М. : Недра, 1968. — 112 с.
  • Бродянский В. М. Эксергетический метод термодинамического анализа. — М. : Энергия, 1973. — 296 с.
  • Бродянский В. М., Фратшер В., Михалек К. Эксергетический метод и его приложения. — М. : Энергоатомиздат, 1988. — 288 с.
  • Бурдаков В. П. , Дзюбенко Б. В., Меснянкин С. Ю., Михайлова Т. В. Термодинамика. Часть 2. Специальный курс. — М. : Дрофа, 2009. — 362 с. — (Высшее образование. Современный учебник). — ISBN 978-5-358-06140-8 .
  • Бэр Г. Д. Техническая термодинамика. — М. : Мир, 1977. — 519 с.
  • Вукалович М. П., Новиков И. И. Термодинамика. — М. : Машиностроение, 1972. — 671 с.
  • Гельфер Я. М. История и методология термодинамики и статистической физики. - 2nd ed., Revised. and add. — М. : Высшая школа, 1981. — 536 с.
  • Глаголев К. В., Морозов А. Н. Физическая термодинамика. - 2nd ed., Rev. — М. : Изд-во МГТУ им. Н. Э. Баумана, 2007. — 270 с. — (Физика в техническом университете). — ISBN 978-5-7038-3026-0 .
  • Грассман П. Эксергия и диаграмма потоков энергии, пригодной для технического использования (рус.) // Вопросы термодинамического анализа (эксергетический метод). — М.: Мир, 1965, с. 28—43.
  • Гухман А. А. Об основаниях термодинамики. — Алма-Ата: Изд-во АН КазССР, 1947. — 106 с.
  • Гухман А. А. Об основаниях термодинамики. — М. : Энергоатомиздат, 1986. — 384 с.
  • Гухман А. А. Об основаниях термодинамики. - 2nd ed., Rev. — М. : Изд-во ЛКИ, 2010. — 384 с. — ISBN 978-5-382-01105-9 .
  • Ерофеев В. Л., Семенов П. Д., Пряхин А. С. Теплотехника. — М. : Академкнига, 2008. — 488 с. — (Учебник для вузов). — ISBN 978-5-94628-331-1 .
  • Зоммерфельд А. Термодинамика и статистическая физика / Пер. с нем.. — М. : Изд-во иностр. лит-ры, 1955. — 480 с.
  • Исаев С. И. Курс химической термодинамики. — 2-е изд.. — М. : Высшая школа, 1986. — 272 с.
  • Казаков В. Г., Луканин П. В., Смирнова О. С. Эксергетические методы оценки эффективности теплотехнологических установок. - SPb. : Санкт-Петербург. state технол. ун-т растительных полимеров, 2013. — 63 с. — ISBN 978-5-91646-051-3 .
  • Кириллин В. А. , Сычев В. В., Шейндлин А. Е. Техническая термодинамика. - 5th ed., Revised. and add. - M .: Publishing House дом МЭИ, 2008. — 496 с. — ISBN 978-5-383-00263-6 .
  • Коновалов В. И. Техническая термодинамика. — Иваново: Иван. state энерг. ун-т, 2005. — 620 с. — ISBN 5-89482-360-9 .
  • Латыпов Р. Ш., Шарафиев Р. Г. Техническая термодинамика и энерготехнология химических производств. — М. : Энергоатомиздат, 1998. — 344 с. — ISBN 5-283-03178-0 .
  • Луканин П. В. Технологические энергоносители предприятий (Низкотемпературные энергоносители). - SPb. : Санкт-Петербург. state технол. ун-т растительных полимеров, 2009. — 117 с. — ISBN 5-230-14392-4 .
  • Мазур Л. С. Техническая термодинамика и теплотехника. — М. : Гэотар-мед, 2003. — 351 с. — (XXI век). — ISBN 5-9231-0271-4 .
  • Николаев Г. П., Лойко А. Э. Техническая термодинамика. — Екатеринбург: УрФУ, 2013. — 227 с.
  • Новиков И. И. Термодинамика. — М. : Машиностроение, 1984. — 592 с.
  • Путилов К. А. Термодинамика / Отв. ed. М. Х. Карапетьянц. — М. : Наука, 1971. — 376 с.
  • Рант З. Эксергия — новый термин для обозначения «технической работоспособности» (рус.) // Вопросы термодинамического анализа (эксергетический метод). — М.: Мир, 1965. — С. 11—14 .
  • Сажин Б. С., Булеков А. П., Сажин В. Б. Эксергетический анализ работы промышленных установок. - M .: Moscow state. Textile University, 2000 .-- 297 p.
  • Самсонов А. И. Эксергетический анализ работы тепловых машин. Противоречия и неточности в учебниках по технической термодинамике. Кораблестроение океанотехника вопросы экономики. Выпуск 25. — Владивосток, 2002. — С. 21—22.
  • Сапожников С. З., Китанин Э. Л. Техническая термодинамика и теплопередача . - SPb. : Изд-во СПбГТУ, 1999. — 319 с. — ISBN 5-7422-0098-6 . Архивная копия от 10 января 2017 на Wayback Machine
  • Свиридонов М. Н. Развитие понятия энтропии в работах Т. А. Афанасьевой-Эренфест (рус.) // История и методология естественных наук. Выпуск X. Физика. — Издательство МГУ, 1971. — P. 112—129.
  • Sivukhin D.V. General course of physics. T. II. Термодинамика и молекулярная физика. - 5th ed., Rev. — М. : ФИЗМАТЛИТ, 2005. — 544 с. — ISBN 5-9221-0601-5 .
  • Фаулер Р. , Гуггенгейм Э. Статистическая термодинамика / Под. ed. В. Г. Левича. — М. : Издательство иностранной литературы, 1949. — 612 с.
  • Физическая энциклопедия / Гл. ed. А. М. Прохоров . — М. : Советская энциклопедия, 1988. — Т. 1: Ааронова — Длинные. — 704 с.
  • Физическая энциклопедия / Гл. ed. А. М. Прохоров . — М. : Советская энциклопедия, 1988. — Т. 1: Ааронова — Длинные. — 704 с.
  • Физическая энциклопедия / Гл. ed. А. М. Прохоров . — М. : Советская энциклопедия, 1990. — Т. 2: Добротность — Магнитооптика. — 704 с. — ISBN 5-85270-061-4 .
  • Физическая энциклопедия / Гл. ed. А. М. Прохоров . — М. : Большая Российская энциклопедия , 1994. — Т. 4: Пойнтинга—Робертсона эффект — Стримеры. — 704 с. — ISBN 5-85270-087-8 .
  • Физическая энциклопедия / Гл. ed. А. М. Прохоров . — М. : Большая Российская энциклопедия , 1998. — Т. 5. — 760 с. — ISBN 5-85270-101-7 .
  • Чечеткин А. В., Занемонец Н. А. Теплотехника. — М. : Высшая школа, 1986. — 344 с.
  • Шаргут Я., Петела Р. Эксергия / Пер. from polish. — М. : Энергия, 1968. — 280 с.
  • Эксергетический метод и его приложения. Ed. Бродянского В. М. — М. : Мир, 1967. — 248 с.
  • Энергия и эксергия. Ed.Brodyansky V.M. - M .: Mir, 1968 .-- 192 p.
  • Erdman S.V. Technical thermodynamics and heat engineering. - Tomsk: TPU Publishing House, 2006 .-- 420 p.
  • Yastrzhembsky A.S. Technical Thermodynamics. - 8th ed., Revised. and add. - M .: Gosenergoizdat, 1960 .-- 496 p.
  • Yastrzhembsky A.S. Thermodynamics and the history of its development. - M. — L .: Energy, 1966. - 669 p.
Источник — https://ru.wikipedia.org/w/index.php?title=Эксергия&oldid=101545673


More articles:

  • Hepatitis
  • Violetov, Ivan Timofeevich
  • Classical Political Economy
  • Cuadrilla de Anyana
  • Selenocysteine ​​- Wikipedia
  • Rezhan
  • Bryanovo (Orhei district)
  • Budei (Orhei District)
  • Getlovo
  • Izvory (Orhei district)

All articles

Clever Geek | 2019