Exergy refers to the portion of the total energy of a system that can perform work when placed in the thermodynamic (thermal, mechanical and chemical ) equilibrium with its surroundings. Exergy is a potential between at least two states, one of which is usually the ambient condition.

Exergy is in contrast to the energy not conserved quantity, that is, in contrast to energy, exergy can be destroyed. Together with the concept of anergy can be so that the two laws of thermodynamics describe:

  • 6.1 Calculation of number of strokes
  • 6.2 Calculation of work


Exergy losses occur in heat transfer, for example. When energy flows in the form of heat into the environment from a poorly insulated hot water pipe, it can not be used to do work. It applies the principle of conservation of energy: The pipe and the surrounding area together have the same amount of energy as before the start of the heat transfer. In this respect, the term " energy loss " is misleading.

The second law of thermodynamics ( entropy) restricts the first law regarding one of the possible energy conversions. For example, if in a heat-insulated ( adiabatic ) mixing chamber two substances with different temperatures are mixed together, so can be used in the energy balance equation no losses seen, the total energy in the system remains the same. Nevertheless there are thermodynamic losses because this process is produced by entropy. Before having the system containing the two substances, the exergy that may utilize a heat engine in the temperature balance between the material. After this is no longer possible because of the universality of the second law, this exergy was destroyed. There remains only the exergy, which owns the entire system from the environment.

Examples of exergetic losses are:

  • Heat transport at a finite temperature difference
  • Friction
  • Mixture
  • Chemical reactions.

See also: Carnotisierung to keep energy losses low.


The Exergiekonzept provides a tool with which on the one hand, the maximum useful work a system or material stream can be calculated. On the other hand, actual losses can be calculated. For engineering problems, it may be a help, especially if the Exergiekonzept is linked to economic variables - thermo -economic methods.

In the literature one often reads sweeping the context:

Wherein anergy denotes the non-usable part of the energy. This relationship then apparently leads to a contradiction when processes run below ambient temperature ( chillers ): below the ambient temperature, the exergy of a system increases with decreasing temperature, because the temperature difference could be used to the environment in order to run a heat engine and as useful work to. win However, the internal energy of the system decreases with decreasing temperature. It is therefore in an appropriate system pressure possible that the physical exergy of a system below the ambient temperature is greater than its (internal ) energy, which would then mean that the anergy would be negative. The relationship is true, however, when taking into account that the energy consisting of the two portions from the vicinity in this case flows into the system. Exergy is a potential which now owns the area across the system. Nevertheless, it is reasonable and customary to assign the exergy of the system.


The exergy of a system or material stream Esys is composed of the inner exergy A, the chemical exergy Echem, the kinetic exergy and potential exergy Ekin Epot. The latter terms correspond to the kinetic and potential energy:

Or mass-specific

Internal exergy of a closed system

Determine the exergy can be One of a closed system as follows:

Specific value

The specific value of exergy is the average exergy per unit mass.

Absolute value

In the calculation equations for the exergy T u is the mass of specific internal energy, h is the mass specific enthalpy, S is the mass-specific entropy, p is the pressure, the temperature, t is the time v is the mass specific volume and m represents the mass. The index 0 characterizes the state of the system or material stream at ambient pressure and ambient temperature ( in thermal and mechanical equilibrium).


The exergy of a system can be changed by the transportation of associated material and energy flows Exergieströmen over the system limit or the exergy destruction in the system. Exergiebilanzgleichung the closed system is therefore:

And for an open system:

The exergy destruction caused by irreversibilities in the process. The relationship between the exergy destruction and entropy generation is

Exergieberechnung in compressed air systems

In the compressed air and pneumatics as well as in other engineering disciplines, there is a need to evaluate plant parts and components quality, eg by energy losses and efficiencies are given. It seems plausible at first to describe the current state of the compressed air at a specific point in the system to make use of the thermodynamic variables of the internal energy U ( closed system) or the enthalpy H ( open system). Although both variables result from the energy content is correct, the usability of this energy, however, no statement can be made because the energy gradient from the environment in two sizes is not considered. This is also reflected in the fact that both U so only H are functions of temperature as well. The pressure in the current state has no control. In particular, since the pressure as the driving variable for performance of mechanical work in pneumatics but relevant, a statement is with U and H on the benefits of the energy content hardly possible.

Remedied by using the exergy balance as size. For the calculation of Exergiegehalts in a state of measurable quantities three values ​​are needed: the absolute pressure Pa, the temperature Ta and the corresponding flow rate Qa. Using this data, the exergy calculated as:

The index 0 denotes the ambient condition, the value of cp is the specific heat capacity, R is the ideal gas constant and the density. The product of flow rate and density is the mass flow. Consequently, it can optionally be replaced by a known mass flow or the product of the standard volume flow and standard density.

Through the exergy of all important events in the causal chain can be captured:

  • Pressure changes occurring
  • Temperature changes
  • Changes of the mass flow (eg through leakage)

A state can be a certain point in the effect chain, eg the final state of the compressed air after compression. The comparison of two states allows the calculation of the exergy loss between two states. Substituting this in percentage relative to the output energy, we obtain the percentage exergy loss at each station the results chain. A graphical representation of the losses can be carried out for example in the form of a Sankey diagram ( right).

Thus, e.g. the exergy of compressed air are calculated in state 2 after compression. With p2 = 7.3 bar; T2 = 80 ° C ( = 353K ); the standard volume flow Q2N = 10m3/min ( = 0.167 m3 / s) and the standard density of 1,185 kg/m3 results in an exergy of 39.3 kW. Behind the aftercooler in state 3 is the pressure on p3 = 7.0 bar and dropped the temperature to T3 = 25 ° C (= 298 K ). The volume flow is preserved. Therefore, now results in a 36.4 kW of exergy. Based on the input power of 63.6 kW, this represents an exergy loss of 4.6 % in the aftercooler.

The exergy thus provides a clear and comprehensible measure to assess quality compressed air systems to identify losses and to provide a basis of comparison for the evaluation of plants and plant parts.

Example: Calculation of exergy in a bicycle tire

A bicycle tire is to be inflated bar with a hand pump in accordance with the sketch from an external pressure of 1 to 4 bar. It is to determine the minimum required to work alongside the number of pump strokes. This work is also the energy contained by the inflation of the tire, as only a reversible process, the work is to be applied at a minimum. This means that an isothermal compression must be assumed, ie a process that would be theoretically frictionless and can only be realized in an infinitely long time to avoid heating.

Calculation of the number of strokes

Calculation of working

To calculate the work we imagine a pump that is so large that the compression process can be done with a single stroke. Then the entire mass is at the beginning in the system plus tire pump included at ambient condition. With the stroke volume is now compressed to the tire. Without friction and with ( infinite) amount of time can reversible isothermal run the operation.

The real applied work is much greater due to the finite time for compression, where the air is heated and consequently a higher back pressure is overcome, and by friction losses in the valve and the piston, especially by the so-called dead space in the pump. You may well be twice that.

Difference between exergy and free enthalpy

Exergy is not to be confused with the free enthalpy G. This is merely a state function which describes the state of a material with a specific composition at a given temperature and pressure. It is independent of the environmental parameters such as ambient temperature, pressure and humidity, for example. Exergy other hand, depends on ambient temperature, pressure and composition very well, since it represents mechanical work, which can be obtained in a suitable machine, if one [ of a given temperature and pressure ] cools the substance according to ambient temperature and pressure / warms / relaxed / compacted etc. exergy is therefore a relative size and thus no state function. The exergy of a material stream can be determined as the difference between the Gibbs free energy in a given state and the free energy at ambient temperature and pressure.