Abstract
In this chapter the causality between process variables and the change of state variables of a thermodynamic system is derived. The first section introduces the principle of equivalence between work and heat—an essential prerequisite in order to formulate the energy conservation principle known as first law of thermodynamics. Finally, the first law of thermodynamics is applied for closed respectively open systems as well as for thermodynamic cycles. Anyhow, thermodynamic cycles play an important role in the following chapters.
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Notes
- 1.
To be more precise, it should be the same change of internal energy that can be observed. If a real fluid changes its aggregate state, the temperature for instance can even be constant, though its internal energy changes.
- 2.
As mentioned before, real fluids do not necessarily heat up, since so-called latent heat causes a phase change!
- 3.
It is the energy that remains constant, not the specific energy!
- 4.
Under these premises the entire work is purely composed of volume work! Areas in a p, V-diagram represent volume work respectively pressure work in open systems.
- 5.
This obviously depends on the temperature of the environment!
- 6.
Changes of kinetic as well as potential energies are ignored, see Sect. 11.2.2. However, if these effects are not neglected, the conclusion would be the same, since due to the addition of all sequential changes of state, they disappear anyway!
- 7.
Mind, that the p, V-diagram shows the volume work. Volume work is identical with the entire work, in case there is no dissipation and changes of outer energies are ignored!
- 8.
However, if the centre of gravity is fixed, neither potential nor kinetic energy vary. As a consequence they are ignored in Eq. 11.5 for systems at rest!
- 9.
It is known from experience, e.g. with an air-pump, that it takes a larger effort to achieve the same result, for instance compressing to the same volume, in case there is friction than if the process runs reversibly.
- 10.
U indicates the voltage potential!
- 11.
Once again, in this equation U denotes the voltage potential and not the internal energy U!
- 12.
Change of outer energies can be ignored, since the system is at rest in states (1) and (2) and the vertical position of the centre of gravity does not vary.
- 13.
No dissipation, no mechanical work due to horizontal cylinder.
- 14.
The dissipation always consumes energy. This energy has to be supplied!
- 15.
So we do not just have to rely on our experience, that work with friction requires a larger effort than work without friction.
- 16.
This will be covered discussed in Sect. 13.5!
- 17.
As we have seen in case 2, the same amount of work in reversible/irreversible operation does not lead to the same compression rate. In irreversible operation the compression stops before reaching the final position. Obviously, in order to reach the same compression ratio further work needs to be supplied.
- 18.
A quasi-static change of state is assumed.
- 19.
As mentioned explicitly in the problem description.
- 20.
Work for lifting the centre of gravity of the gas shall be ignored according to the problem description!
- 21.
Homogeneous means free of any imperfections. Hence, there is no dissipation, see Sect. 14.4 for details.
- 22.
As long as the piston itself moves frictionless, see Example 7.24!
- 23.
Since the temperature of the piston does not change. It has ambient temperature in states (1) and (2).
- 24.
In fact, the gas from state (1) to state (2) has been replaced! Its chemical composition has changed.
- 25.
For a laminar flow the pressure drop is \(\Delta p=\rho \frac{c^{2}}{2}\lambda \frac{l}{d}\) with \(\lambda =\frac{64\eta }{\rho c d}\). The combination brings \(\Delta p=\frac{32u\eta l}{d^2}\). The specific dissipation is \(\psi =\frac{\Delta p}{\rho }=\frac{32u\eta l}{\rho d^2}\), the entire dissipation is \(\Psi =\psi m_{\text {total}}\).
- 26.
Heat is not transferred once for instance but continuously. Hence, a heat flux is relevant instead of an amount of heat.
- 27.
Technical work is always related to open systems!
- 28.
Energy is constant, not specific energy!
- 29.
Mass as an extensive state value represents the size of a system.
- 30.
Sure, both can also disappear!
- 31.
However, some state values have a vivid physical meaning, others are regarded as more or less artificial.
- 32.
Once again, energy shall be represented by energy-bubbles, so that the energy conservation principle actually means counting bubbles.
- 33.
Thus, the kinetic energy of the inflow is ignored!
- 34.
Potential as well as kinetic energy of the gas are neglected, see Example 7.24!
- 35.
The volume change lifts the piston. Thus, work is released to increase the piston’s potential energy.
- 36.
Mind, that there is no dissipation since the state of state needs to run very slowly, see Sect. 9.2.5!
- 37.
Thus, the kinetic energy of the inflow is ignored!
- 38.
Potential as well as kinetic energy of the gas are neglected, see Example 7.24!
- 39.
The potential energy of the piston is reduced and supplied to the gas.
- 40.
Mind, that there is no dissipation since the state of state needs to run very slowly, see Sect. 9.2.5!
- 41.
This is due to the energetic state of a system does not vary by time in steady state!
- 42.
Mind, that arrows pointing into the system are energy fluxes in, while arrows pointing out of the system represent energy fluxes out. Anyhow, a mass flux carries enthalpy, potential and kinetic energy.
- 43.
In steady state!
- 44.
Caloric equations of state indicate how the change of a caloric state value can be calculated. Remember, that caloric state values, such as specific enthalpy or specific internal energy, can not be measured, but must be calculated.
- 45.
The technical work then is positive.
- 46.
The technical work then is negative.
- 47.
According to Eq. 11.21 lifting or accelerating the centre of gravity requires mechanical work!
- 48.
The moving coordinate system represents the single particle, while the fixed coordinate system represents the energy balance as given by Eq. 11.198.
- 49.
Volume work only occurs in closed systems! However, both, volume and pressure work, satisfy the physical definition of work, i.e. force times distance.
- 50.
This is well known from everyday experience: Systems with friction require a larger effort than frictionless systems!
- 51.
Mind, as documented in Fig. 11.29, technical work only crosses the system boundary, if there is a mechanical shaft, electrical wires or any other possibility to carry energy in form of work into or out of the system. This is not the case—the presented example purely is a passive tube section!
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Schmidt, A. (2019). First Law of Thermodynamics. In: Technical Thermodynamics for Engineers. Springer, Cham. https://doi.org/10.1007/978-3-030-20397-9_11
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DOI: https://doi.org/10.1007/978-3-030-20397-9_11
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