Abstract
Entropy is the physical measure of disorder. According to the Second Law of Thermodynamics it grows whenever something happens in the world. This shows up in the room of a playing child, on the desk of a working scientist, and in all natural and technical energy conversion processes. The growth of entropy determines the Arrow of Time. It prevents a Perpetuum Mobile of the Second Kind, which would be a cyclically operating machine that does nothing other than perform physical work and cool down a heat reservoir, such as the environment. All attempts to construct such a machine and establish an energetic fool’s paradise have failed and will fail. Furthermore, entropy production, inevitably coupled to energy conversion, is associated with exergy destruction and the emission of heat and particles. Model calculations of the Heat Equivalents of Noxious Substances show how sufficiently large energy inputs into pollution control processes, such as denitrification, desulfurization, carbon dioxide capture and storage (CCS), and nuclear waste disposal, can convert the emissions of material pollutants into heat emissions. The latter, however, accelerate the approach to the Heat Barrier, beyond which climate changes are expected even without the Anthropogenic Greenhouse Effect (AGE). The physics, cause, and consequences of the AGE are explained.
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Notes
- 1.
The total mass of the oceans is 1.4 ×1021 kg [1]. The energy content of the ocean layer between 0- and 700-m depth is estimated to be about 1023 J [ 2]. This is more than 230 times world energy consumption in 2004. But only a small fraction of that could be used permanently by ocean thermal energy conversion. In ocean thermal energy conversion the Sun is the source that puts the energy into the ocean and maintains the temperature difference between the surface and deeper water layers.
- 2.
Nevertheless, even university professors outside the natural sciences, with the best of intentions, ask for public funding of proposals to convert the quantum-mechanical zero-point oscillations of the vacuum into electricity. The energy quanta of these oscillations would constitute a “heat reservoir” at the zero of absolute temperature, and the machine that would convert their energy into work would be the ultimate perpetual motion machine of the second kind. The promoters of such a machine are part of the “vacuum field energy” movement. They believe that the Casimir force from the field fluctuations of the vacuum can be converted into work performed by a cyclically operating machine without any energy input. As “proof” they show videos of machines, of course always connected to the public grid, where one watt meter shows a small electricity input and another watt meter shows a huge electricity output. The suggestion to charge batteries with the net electricity output, sell them, become rich and famous, and build the new vacuum field power system all over the world is met with indignation.
- 3.
Someone might have a somewhat more sophisticated proposal: With the help of a freezing machine let us create a many-body system in its ground state of minimum internal energy at the absolute zero of temperature and let it serve as the receiving reservoir with T 0 = 0 K for a heat engine; then this engine will convert all the heat from a finite temperature reservoir completely into work W, because the Carnot efficiency of (3.1) is unity in this case. This proposal is of no help either. One would have to expend at least the same amount of exergy to cool down the reservoir to T ≈ 0 K as one would gain by letting a machine work between it and, say, the ocean. This is because even the tiniest amount of absorbed heat δQ 0 would lift the many-body system out of its ground state into any one of its many exited states of equal energy which become accessible to it by the absorption of δQ 0; this raises the temperature of the system to some finite value, and all further operations of the heat engine would further raise the temperature until it is back to that of the ocean, and the efficiency in (3.1) becomes zero. If one could gain more exergy in the process of heating up the low-temperature reservoir than one had invested in cooling it down, one could reinvest part of it in cooling down the reservoir anew and continue the cycles of net exergy generation. This would be another impossible perpetual motion machine of the second kind.
- 4.
Although Liouville’s theorem in classical mechanics and Boltzmann’s H theorem in its quantum-mechanical generalization make the postulate of equal a priori probabilities mathematically very plausible, its basis is experience. And no experience whatsoever has ever contradicted this postulate and the conclusions derived from it.
- 5.
Stopping the mixing and letting one ball drop out is like taking a snapshot of the ball’s position during the mixing process. The mechanical ball mixing is statistically equivalent to the thermal mixing of gas particles in equilibrium within an isolated box.
- 6.
This correlated motion cannot be broken up by the statistical oscillations of the metal atoms. Since there is no scattering of the paired electrons, the electrical resistance vanishes.
- 7.
Quantum mechanically the many-body state of an ideal gas in a box of volume V is only characterized by the quantized values of the momenta p i in (3.2). But for a single particle the quantum-mechanical density of states, that is, the number of states in a tiny energy range, is also proportional to V. Thus, the classical and the quantum-mechanical Ω(E) both grow with V N. They only differ in the counting of states occupied by identical particles.
- 8.
From a macroscopic point of view a “random distribution” appears as a “uniform distribution.”
- 9.
The following passages until the end of this subsection are translated excerpts from Arne Stahl’s article “Entropiebilanzen und Rohstoffverbrauch”[8].
- 10.
In the opposite limit τ ≫ t exp, where equilibrium is achieved very slowly compared with experimental times, one can also treat the system as if it were in equilibrium while one observes its behavior.
- 11.
Recently, one has also begun to discuss an arrow of time associated with self-organization. A broad analysis of the physical basis of the direction of time is given in [10].
- 12.
If chemical reactions occur, one gets \({\sigma }_{S} = {\sigma }_{S,\mathrm{dis}} + {\sigma }_{S,\mathrm{chem}}\) in (3.18). The entropy production densities σ S, dis and σ S, chem are positive separately because σ S, dis is given by products of vectorial currents and forces, which cannot interfere with the scalar currents and forces that make up σ S, chem; see also the Appendix.
- 13.
Süddeutsche Zeitung, 7/8 August 2010, p. 20.
- 14.
The absorption bands of a given gas are saturated if – because of its atmospheric concentration – there is a rather low likelihood that an additional molecule in this spectral region will absorb further radiation. This molecule is overshadowed, so to speak, by the other molecules of the same gas [27].
- 15.
Low deuterium levels suggest particularly high temperatures, whereas high deuterium levels indicate low temperatures.
- 16.
The complete oxidation of 1 t of carbon results in 3.67 t of CO2.
- 17.
All the factors that determine the climate in the “urban heat islands” are described in [22] (pp. 339–343).
- 18.
In (2.54) the index “rev” has been omitted for the sake of simplicity.
- 19.
Such statements can be even heard from people with a Ph.D. degree in physics. Furthermore, at an international physics conference on energy and the environment in the early 1990s, an invited speaker from a well-known institution of a country that is a member of the United Nations Security Council gave a talk in which he claimed to have mathematically disproven the second law of thermodynamics. This was printed without any critical comment in the report on the conference, published by a physics journal.
- 20.
These identifications are mathematically not unique, but they are the ones that satisfy physical criteria such as Galilean invariance.
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Kümmel, R. (2011). Entropy. In: The Second Law of Economics. The Frontiers Collection. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9365-6_3
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