Abstract
So far the law of energy conservation, i.e. the first law of thermodynamics, has been discussed, that quantified the changeability of energy. However, this changeability is limited, so that thermal energy can not be converted completely into mechanical energy in a steady state process. The second law of thermodynamics can be applied to evaluate the constraints of energy conversion. In Chap. 15 a clockwise Carnot machine was introduced: A machine that operates between two thermal reservoirs in order to convert thermal energy into maximum mechanical work. Its efficiency in best case is given by the minimum and maximum temperature the machine is working in-between. This principle is essential to understand the thermodynamic idea of exergy as maximum working capability of any form of energy. The significance of the exergy is presented in this chapter.
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Notes
- 1.
The energy conservation principle claims, that energy must be constant.
- 2.
To keep the energy constant, anergy rises when exergy decreases!
- 3.
This balancing of exergy is usually performed with a constant environment.
- 4.
A thermal engine has been introduced as a clockwise thermodynamic cycle, that converts heat into work, see Chap. 15.
- 5.
In case the temperature at the cold end of the machine was below ambient temperature, there would be a heat flux from environment into the machine!
- 6.
The Energy-in-Exergy-and-Anergy-Decomposition-Machine must be a clockwise cycle!
- 7.
The second law of thermodynamics states, that heat always follows a temperature gradient form hot to cold.
- 8.
Thus, the thermodynamic mean temperature is constant as well. However, this is nontrivial if T is not constant, see Fig. 16.6.
- 9.
No matter, if the change of state runs reversibly or irreversibly!
- 10.
A closed system for example!
- 11.
To lift \(\dot{Q}\) against the temperature gradient!
- 12.
It has been shown in the previous section, that thermal energy can be utilised in a thermal engine to gain work.
- 13.
Due to the sign convention a power output is negative. Thus, in order to get a positive exergy, a minus sign is applied in the definition.
- 14.
Following the energy-in-is-balanced-by-energy-out principle under steady state conditions.
- 15.
Reversible and adiabatic means the change of state is isentropic!
- 16.
Due to the sign convention work release is negative. Hence, in order to get a positive exergy, a minus sign is applied in the definition.
- 17.
In Eq. 16.43\(v_{\text {env}}\) denotes the specific volume the fluid has under ambient conditions, i.e. at \(T_{\text {env}}\) and \(p_{\text {env}}\). It does not represent the specific volume of the environment!
- 18.
Mind, that the (env)-state is in rest!
- 19.
No entropy is generated, since \(\Delta T=0\) for the heat transfer!
- 20.
See Eq. 9.42.
- 21.
Applying the caloric equation for incompressible liquids.
- 22.
Water is treated as an incompressible liquid, so that \(v_{\text {env}}=v_{1}\).
- 23.
The system is adiabatic, so there is no exchange of exergy of heat! Furthermore, no electrical or mechanical work, that would be pure exergy, is transferred.
- 24.
Obviously, loss of exergy means a sink!
- 25.
Mind, that \(W_{12}\) is the work that passes the system boundary of the fluid inside the cylinder, whereas \(W_{\text {eff}}\) is the work that can effectively be utilised at the piston!
- 26.
Exergy loss reduces the exergy, so it is an outgoing flux! It is treated as a sink.
- 27.
Energy flux in is balanced by energy flux out.
- 28.
Entropy flux in is balanced by entropy flux out.
- 29.
Thus, it is the efficiency that is relevant to evaluate the engineer’s efforts!
- 30.
Named after Matthew Henry Phineas Riall Sankey, \(*\)9 November 1853 in Nenagh, Ireland, \(\dagger \)3 October 1925.
- 31.
In case of one-dimensional heat transfer!
- 32.
Bringing back the heat against the gradient requires a heat pump, i.e. a counterclockwise cycle, that consumes technical power!
- 33.
Exergy in is balanced by exergy out. Mind, that the exergy loss reduces the exergy of a system. Thus, it counts as outgoing exergy!
- 34.
The loss of exergy in part (b) has nothing to do with the loss of exergy in part (b), since the system boundary is different!
- 35.
Mind, that any change of state is polytropic! In this case it is adiabatic and frictional.
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Schmidt, A. (2019). Exergy . In: Technical Thermodynamics for Engineers. Springer, Cham. https://doi.org/10.1007/978-3-030-20397-9_16
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DOI: https://doi.org/10.1007/978-3-030-20397-9_16
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