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14th Joint European Thermodynamics Conference
Budapest, May 21–25, 2017
THANATIA A THERMODYNAMIC THEORY TO ASSESS THE LOSS OF MINERAL
CAPITAL ON EARTH
1
Antonio Valero 1
Research Center for Energy Resources and Consumption (CIRCE Institute), University of Zaragoza
[email protected]
ABSTRACT
Introduction
The book Thanatia [1] opened a new thermodynamic vision of natural resources. I.e. the study of deterioration of planet Earth as a whole
thermodynamic system and a new way to study the rate of loss of mineral resources of the Planet using exergy analysis. It posed intriguing
theoretical problems. This paper is presented by invitation of JETC’17 organizers to open a deep discussion among thermodynamicists. First, I
sketch a summary of Thanatia theory, then its practical results and finally, I pose some questions.
One of the most important problems humanity is facing today is survival in an oversaturated and depleted planet, a “full world” in the words
of H. Daly [2]. In my view, a key way for understanding survival is understanding the Second Law. Ecological economists, social thinkers and
policy makers found this connection many years ago. They commonly use entropy-wording as metaphors, but are unable to put numbers in their
reasoning. Focusing on the idea of exergy rather than entropy could radically change such deficiency.
Exergy is a property of a system always relative to some associated reference state. As it is well known, exergy is the maximum work a system
can deliver when opposed with another big enough but real system, namely reservoir. The reservoir actually attracts our system to degradation or
entropy creation. Planet Earth is a Sunbathed ball floating in the Universe. During billions of years, Sun provided the energy needed to organize
Earth as it is. However, the Sun´s energy is radiated daily to the Universe whose temperature is around 2.73K. Only a tiny 0.024 % fraction of the
Sun´s radiation is stored by photosynthesis. This fraction plus the weathering effects on the crust and the internal heat on Earth allowed to create
and store all biological and mineral resources humanity has for its survival.
A physical observation of the Sun-Earth system allows to see many spontaneous processes like erosion, oxidation, mixing, cooling, melting,
evaporation and precipitation, mass transport, dispersion of materials and so on. There are also human-induced processes like extraction and use
of natural resources, solid, liquid and gas wasting, and climate change to say a few. With sufficient time, Sun and the internal heat of the planet´s
inner cores would provide the energy to restore in part such irreversible degradations. But the velocity of this degradation is different for
biological systems than for geological ones. Biological systems may be restored in decades or centuries, nonetheless geological resources are
non-renewable at human scale. In fact, natural processes behave cyclically, in contrast, human induced ones almost do not do. Nature has its pace
and cannot restore what humans hastily dispose. Human effects on this evolution are so high in magnitude that our era is now called the
Anthropocene [3].
Let´s now take Planet Earth as our system of thermodynamic study; the Universe acts as its attractor. Let´s suppose its initial state the
beginning of Anthropocene with a mature Earth plenty of natural resources. The human-made depletion of minerals and their dispersion as well
as that of ecosystems destruction gives no chance to Sun for restoring them and drives the planet to a greater entropic state. Let´s name the final
state Thanatia. Thanatia is like the ground of the ball Earth ready to fall down, a “dead state” of the planet Earth humans could be worried about.
(Thanatos in Greek means death). It is not a mere reference coordinate scheme but a real possibility of entropic degradation subject to Second
Law, and it is not an absolute end of the planet Earth but an epoch in its evolution.
Considering the exponential depletion of non-renewable natural resources it’s easy to extrapolate and imagine a planet without economically
available mineral deposits. It is not difficult to conceive such an evolution, no matter how much time is needed to achieve it. It would be a
tipping point where the global declining of marginal benefit of mining meets the increasing marginal cost of energy and its environmental impact
[3]. Once determined this dead state we may use it to assess the rate of exergy loss of our valuable mineral resources. Actually, any natural
resource distinct from Thanatia would have exergy that could be measured in kWh!
Thanatia composition
As explained, the atmosphere, hydrosphere and the earth crust, i.e. the Anthroposphere, evolve as a consequence of climate change, extraction
of minerals, topsoil degradation and pollution. Therefore a complete depleted planet can be imagined as the abiotic dead state our civilization is
predestined. This hypothesis becomes feasible when one knows that all minerals and fossil fuels ever existed constitute less than 0.01-0.001% of
the earth crust. Second, the complete combustion of Earth fossil fuels will only change the composition of current atmosphere in parts per million
of CO2 increase. Third, approximately 97% of hydrosphere appears as sea water, the other 3% is held as freshwater in glaciers and icecaps,
groundwater, lakes, rivers, soil, and in the atmosphere and biosphere. Only 0.33% of the total amount of freshwater is concentrated in lakes,
reservoirs and river systems. This small 0.33% part is in danger of being polluted. Also, as a consequence of climate change an important part of
ice caps will become diluted into the sea. Considering these numbers one can say that abiotic resources are deeply scarce in the planet.
Accordingly, Thanatia is a not-so-difficult-to-imagine a state of the Anthroposphere where all mineral deposits would have been mined, and
their materials and fertile soils thereof dispersed throughout the crust. Also, all fossil fuels were combusted, thus inducing the corresponding
changes in the atmosphere and hydrosphere.
14th Joint European Thermodynamics Conference
Budapest, May 21–25, 2017
Then the theory would be ready to assess - with sufficient data – the exergy of mineral deposits, fertile soils, ice caps, rivers, wastes, clouds or
the pristine atmosphere as abiotic resources clearly distinguishable from a resource-exhausted planet, even if they have fuzzy boundaries and illdefined intensive properties. Also, even if the social collapse would come before reaching Thanatia, from a physical point of view the complete
depletion hypothesis is realistic for the assessment of the loss of Mineral Capital on Earth and other aplications.
Consequently, Thanatia must have a defined composition of the upper continental crust, the hydrosphere, and the atmosphere. For the upper
continental crust, we proposed an improved model based on the mineralogical composition of the Russian geologist Grigor’ev [4]. The resulting
crust is composed of nearly 300 minerals. A crust depleted of mineral deposits but full of common rocks containing those minerals in their
cortical concentration.
The exhausted atmosphere would occur once all conventional fossil fuel reserves would have been depleted with an atmospheric injection of
about 2000 Gt C [5]. Accordingly, this atmosphere will reach a carbon dioxide content of 683 ppm, a mean surface temperature of 17 ºC (a peak
carbon dioxide induced warming of 3.7 ºC above pre-industrial temperatures), a pressure of 1.021 bar and a composition, on a volume basis of
78.8% N2, 20.92% O2, 0.93% Ar and 0.0015% of trace gases.
Considering that saline water accounts for 97% of the whole hydrosphere and considering that climate change could induce a partial or even
total melting of the poles which contain most of the remaining 3% of freshwater, the exhausted hydrosphere is assumed to have the current
chemical composition of the oceans at the average temperature of around 17 ºC [5].
It is important to distinguish Thanatia from a conventional reference environment -RE-. A conventional RE like that from Szargut [6]
contains one substance and only one per element (to the extent of 85 elements) with their lowest chemical potential compatible with the Earth
crust. Thus for silicon is SiO2, not the abundant silicates. However Thanatia adapts better to geological-anthropological reality. The Earth crust
is mainly composed by silicates and the conversion of a silicate into SiO2 has a substandard slow kinetics and its reaction exergy has an
insignificant practical value. On the contrary, Thanatia is composed of ordinary rocks, saline water and air containing the CO2 originated by the
combustion of all reserves of fossil fuels. What is important in Thanatia is valuing those mineral deposits that constitute the endowment
humankind has for its development rather than its dead-end exergy.
Besides that, the concentration factor is another important difference. Declining ore grades of minerals are a critical issue in determining their
increasing extraction exergy. In a business as usual trend, humankind would need to exploit common rocks with their highest extraction exergy.
For instance, when cheap bauxite (aluminum hydroxides) to produce alumina would be depleted, aluminum silicates would need to be mined as
substitutes. In such case, those silicates richer in Al, like anorthite (CaAl2Si2O6), sillimanite (Al2SiO5), or kaolinite (Al4Si4O10(OH)8) would
be used thereafter. The concentration factor is another difference. In a conventional RE it is of minor importance because the element´s
representative substance is chosen as the most stable one within a reasonable abundance in the Earth’s crust instead of the more abundant even
though less stable. Also, when considering reversible processes for exergy calculations, the concentration exergy is negligible in comparison with
chemical exergy. All we know the huge work is needed to concentrate and beneficiate a mineral in comparison with its exergy gain. Therefore for
avoiding confusions we consider Thanatia as a practical baseline reference.
What to measure?
Simply –or not so simply- the annual rate of materials dispersion. This includes minerals extraction, the loss of fertile soils, air pollution,
contamination of rivers and aquifers, poles melting, waste accumulation, and ecosystems destruction. All these phenomena are deeply related
with entropy generation. As Lindley [7] says: “These abiotic economic resources are, basic¬ally, so scarce in the planet that a condition of
coming close to Thanatia is a very realistic prospect, now that “the race for what´s left” is under way.
Dispersion is deeply more comprehensive and critical than climate change. In fact and from an Anthropocene perspective, the aging of the
Planet could be assessed by measuring the annual rate of materials dispersion. From an anthropic view materials dispersion is even more critical
than energy irreversibility, because as long as the Sun shines every day at an hour well established there will be no fear, as a society, of energy
shortages.
The dispersion of the gases that produce climate change; the dispersion of pollutants in aquifers and rivers, the melting of poles diluting in the
saline ocean; the dispersion of human wastes, either biological or geological; the entropic mixture of scarce materials in alloys impossible to
recycle; the multi-component devices of single use and throw, are the phenomena of the dispersion.
Developed tools
In my speech I will explain the concepts of exergy resource, exergy cost, exergy replacement cost, thermodynamic rarity, composed rarity,
rareness intensity, recoverability, recyclability and Spiral Economy.
The concept of thermodynamic rarity (kWh) is quite useful to establish the level of criticality of minerals since it measures its geological
scarcity plus the exergy needed to convert the ore into a metal. Also, the more rare components has a given apparatus the greater its composed
rarity. For instance, in a common smartphone the epoxy resin of its base plate is coated with a gold foil. Its circuitry can contain Cu; Au; As; Ga;
Cd; Pb; Ni; Pd; Hg; Mn; Li; Be; Br; Ag; Zn and Ta in addition to adhesives and coatings. Their screen contains tin-indium oxide and lithium is
the main component of batteries. These constituents add to those of the charger, frame, packaging and so on. Therefore the composed rarity of a
mobile phone is extremely high and considering the number of sold units each year, the sustainability of mobile phone technologies are in serious
threat. I will present a graph with a number of critical tech devices.
The indicators of rarity, recoverability and recyclability allow to compare in kWh the discussion of what is rare, recoverable or recyclable,
then guiding technology and society into a greater conservation of scarce mineral resources. They allow to measure and compare the possibilities
of recycling against the alternative of extracting more minerals. In fact, the rate of Global Aggregated Rarity of all extracted minerals is plainly
14th Joint European Thermodynamics Conference
Budapest, May 21–25, 2017
the rate of Loss of Mineral Capital in the planet caused by our wasteful use of our mineral endowment. Also recoverability and recyclability pose
the attention on what difficult is to close material cycles. From a Physics point of view, Circular Economy does not exist, but Spiral Economy.
Conclusions
The thermodynamic rarity concept adds two values: conservation (through the exergy replacement costs) and process efficiencies (through
real embodied exergies). While the latter are widely recognized, the first is ignored by society mainly due to a lack of knowledge and indicators.
Yet both indicators, exergy replacement costs and embodied exergy costs, are equally required for a rational management of resources. This is
because conservation means, in fact, avoided replacement. Indeed, one can associate a cost of replacement to each and every act of conservation,
whether relating to mineral resources or any natural resource in general. The cost of replacement acts as a mind barrier which prevents further
deliberate destructions. The more irreplaceable an object is, the stronger the desire to conserve. Therefore taking into account replacement costs
in addition to embodied costs is a way of converting into energy values the debt left for future generations.
Essentially Thanatia could become the end of the Anthropocene era. It sheds light to see our current civilization in a countdown way to the
end, and provides a wisdom for Humankind Aging. It is something like the hourglass, in which degradation, deterioration and dispersion of
materials is like the sand falling to the bottom till nothing to fall. And that is the greatness of the Second Law.
In CIRCE we are assessing the rarity, recoverability and recyclability of ores, metals appliances and technologies. The field is so extended
that researchers are invited to contribute.
But many new questions have appeared like, discussions about fundamentals, refining models, how to get mineral information, assessing and
compiling rarities, or even a discussion whether Thanatia is a thermodynamic theory or an environmental theory integrating thermodynamics for
the understanding of the Loss of Mineral Capital on Earth. Is Thanatia post-normal science? According to Funtowicz and Ravetz [9], post-normal
science represents a novel approach for the use of science on issues where ‘facts are uncertain, values in dispute, stakes high and decisions
urgent’. Kay described “post-normal science as a process that recognizes the potential for gaps in knowledge and understanding that cannot be
resolved in ways other than revolutionary science”[10]. We will here humbly present some of our results.
REFERENCES
[1] Valero, A.; Valero, D.A. Thanatia: The Destiny of the Earth’s Mineral Resources; World Scientific Publishing: Singapore, 2014.
[2] Daly, H. Economics for a Full World. June 2015 in http://www.greattransition.org/images/Daly-Economics-for-a-Full-World.pdf
(Accessed, Feb, 2017)
[3] Crutzen, P. J. (2002). Geology of Mankind, Nature 415, 6867, pp 23.
[4] Grigor’ev, N.A. The average mineral composition of the upper continental crust. Ural. Geol. J., vol. 3, pp. 3–21. 2000. (In Russian)
[5] Valero, A.; Agudelo, A.; Valero, D.A. The crepuscular planet. A model for the exhausted atmosphere and hydrosphere. Energy, vol. 36, pp.
3745–3753, 2011.
[6] Szargut, J., Chemical exergies of the elements. Appl. Energy, vol. 32, pp. 269–286, 1989.
[7] Lindley, M., An Introduction to the Thanatia Concept: An Account, for Economists and Laymen, of Assessing Thermodynamically the
Depletion of Nonrenewable Natural Resources in This and the Next Century. To be publ. in New Society Publishers.(2017)
[8] Lozano, M.; Valero, A. Theory of the exergetic cost. Energy, vol. 18, pp. 939–960, 1993.
[9] Funtowicz, S. O. and Ravetz, J. R.: A New Scientific Methodology for Global Environmental Issues, in Costanza, R. (ed.), Ecological
Economics: The Science and Management of Sustainability: pp. 137–152. New York: Columbia University Press. 1991.
[10] https://en.wikipedia.org/wiki/Post-normal_science