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Consequences of the Second Law

Validity of the Second Law

The Second Law of thermodynamics is one of the most basic laws of nature. Up until this moment no phenomena have been observed in the known universe which would be in conflict with the Second Law, so the law is considered to be valid for all known phenomena in nature. The Second Law says that any spontaneous process in a given system will go in the direction of more dispersal of matter, energy and directional movement: to more entropy of the system.

Visibility of Second Law consequences on global scale

Despite its basic importance the Second Law is rather invisible in most natural sciences and technologies. Usually natural phenomena and behaviour of technical systems can be explained in a way satisfactory for most purposes without using the somewhat elusive notions entropy and Second Law.

The reason why the notions entropy and the Second Law should play now a prominent part in environmental sciences is the scale of the human activities in the biosphere. Human behaviour has observable adverse effects on global scale, for example change of climate and decline of biodiversity. Human activities are not negligible anymore in comparison with the natural processes in the biosphere. Further expansion of human demand of resources and ecosystem services brings us in direct conflict with natural processes and ecosystems on global scale.

The magnitude of the human activities in relationship with the finite size of the biosphere, as a thermodynamic system, forces us to go to the basics of science and to apply the Second Law on environmental issues and sustainability of our society.

Principle of the Second Law

Each change in the universe is coupled to an energy conversion and an entropy effect. A basic formulation of the Second Law is:

With every change the entropy of the universe increases.

To understand the effect of the Second Law in the context of nuclear power and sustainable energy, a full comprehension of the notion entropy is not necessary. The Second Law can be formulated in different ways. Selfevidently all correct formulations are based on the same principle:

dispersion of matter and randomizing of oriented energy flows by any spontaneous process.

In respect of processes of everydays practice and in the context of nuclear power and sustainable energy the following formulation is useful:

In a system without energy input from the outside and without material exchange with its surroundings any spontaneous process will increase the entropy (randomness of matter and energy) of the system and decrease its quality and usefulness.

Probability and the Second Law

In a given system, consisting of a certain amount of materials in a certain volume at a certain pressure and containing a certain amount of energy, the distribution of particles and energy quanta will end up in the most probable distribution by spontaneous processes. Examples are the dispersion of a scent in a closed room and the levelling of the temperatures in a closed room with a cup of hot tea.

Any deviation from the most probable situation will require dedicated effort and useful (directional) energy. The farther the desirable situation deviates from the most probable situation, the more dedicated effort and useful energy is required to reach that situation. In other words: the more specific the properties of the desirable ordered material are, the less probable is the end situation from a probababilistic viewpoint and consequently the more useful energy has to be invested to fabricate the ordered material from raw materials.

Heat engines

Heat engines are machines for conversion of heat into mechanical and electric energy, such as steam and gas turbines and car engines. From the Second Law follows that heat cannot be converted fully into mechanical and electric energy. The heat generated in the heat source flows through the heat engine to the surrounding at a lower temperature. A part of this heat flow can be conveted into mechanical energy. The conversion efficiency is mainly determined by the temperature difference between the heat source and the surroundings of the heat engine. This context of the Second Law is the best known among technicians and scientists.

A nuclear power station is a heat engine with a nuclear heated boiler. Generally the net conversion efficiency is around 32-34%. That means that 66-68% of the generated heat in the nuclear reactor is discharged as waste heat into the environment.

Separation processes

Separation processes are a common and essential part of industrial activities needed for production of the ordered materials used in the economic system, such as steel, medicines, electronic components and prepared food. A consequence of the Second Law with respect of separation processes is:

• The separation of a mixture of different chemical species never goes to completion. Consequently it is not possible to separate a mixture into its pure constituents without losses.

• The amount of useful energy required for separation increases with the number of chemical species in the mixture and with the desired purity of the separated constituents.

The limitations of separation processes has far reaching consequences for the potential of nuclear power [more i42, i43].

Coupled systems

An important consequence of the Second Law is that the conversion of a given amount of potential energy into useful energy, say by fission of 1 kg uranium, generates more entropy than can be compensated for by the generated amount of useful energy. More entropy means more mess and uselessness.

Lowering the entropy of a given amount of matter (here called system A), equivalent to an increase of the usefulness of the system, is only possible if simultaneously in another amount of matter (system B) the entropy increases with a larger amount: the sum of both entropy changes jointly is a net increase, in other words a net increase of mess and uselessness. The useful energy generated in system B makes possible the increased usefulness of system A. Systems A and B are thermodynamically coupled systems.

An example of coupled systems is an electrolysis plant to produce aluminum as system A, powered by the electricity from a nuclear power station as system B.

Ordered materials: reliability and energy investments

How well is a given material or piece of equipment suited to perform a given task, and what is the mean time between failures? These questions refer to the functionality and reliability of materials and constructions. Functionality has to do with the specific properties of a piece of equipment and the materials it is made from. Reliability has to do with the predictability of the behaviour of the equipment and materials under operational conditions of wear, stress and corrosion.

Upgrading an amount of a raw material into a useful substance or a piece of equipment implies lowering the entropy of that amount of raw material. To produce useful materials and objects from raw materials as found in nature dedicated effort and energy is needed. An object is better useful when it is better suited to perform a specialistic task. The more specialistic the task, the higher the quality standards are required of materials, design and craftsmanship for production of the material or object, and consequently the higher energy input. A higher usefulness, or quality, requires higher investments of useful energy and human skill. This observation follows directly from the Second Law.

Mineral energy sources are not sustainable

Mineral energy resources – fossil fuels, uranium and deuterium/lithium for fusion – are recovered from the accessible part of the earth’s crust, within the biosphere. Burning fuels, fissioning uranium and fusing deuterium + tritium are basically spontaneous processes, once started, which can go on as long as fuel is available. The entropy generation inevitably coupled to the these spontaneous processes and the generation of useful energy from these sources, occurs within the biosphere.

From the Second Law follows that the generated amount of useful energy from mineral energy sources is insufficient to compensate for its coupled entropy generation, even if all useful energy would applied to that purpose. As a result the entropy of the biosphere increases constantly by using mineral energy sources. For that reason no mineral energy source can be sustainable, by definition. As the biosphere is a finite system, an unlimited increase of man-made entropy will irrevocably lead to environmental disasters, endangering human society [more i40].

Declining thermodynamic quality of mineral resources

A second effect accelerates the entropy generation associated with the energy production in the biosphere, even if the demand of useful energy would remain constant: the declining thermodynamic quality with time of the remaining mineral resources. Lower thermodynamic quality results in a higher entropy generation per unit delivered useful energy. The easiest reoverable resources are exploited first, so the remaining resources are harder to exploit. Harder means higher requirements of useful energy and ordered materials per unit recovered mineral.

These developments are observable in the fossil fuel recovery from the crust: deeper wells at more remote and harsh locations are needed, the recovery of oil from tar sands consumes at least half of its energy content, recovery of gas from shales (fracking) consumes a substantial part of its energy content and cause extensive damage to ecosystems. Coal mining meets similar problems. The average uranium ore grade declines and the the mining companies have to dig deeper. The easy oil, gas and coal, having a high thermodynamic quality, are getting depleted. Exploitation of increasingly lower-quality resources is the trend.

Sustainable energy supply has to be based on an energy source outside of the biosphere, so the associated entropy generation stays outside of the biosphere. Man has one: the sun [more i44].

Photosynthesis in the biosphere, spontaneous order from chaos?

Plants grow spontaneously. Via the photosynthesis carbondioxide from the air, water and dissolved minerals in the water are fixed into highly sophisticated biomolecules. From chaotic materials highly ordered materials with very specific properties are synthesized. As pointed out above ordered materials have low entropy. Apparently order from chaos in a spontaneous process. Is photosynthesis a violation of the Second Law?

Of course not. The biosphere with its photosynthesis is thermodynamically coupled to the sun. The sun emits useful energy in a unidirectional flow, which green plants utilize to increase the usefulness of chaotic matter. The entropy generation on the sun is far greater than the entropy reduction in the biosphere, so the Second Law is obeyed.

Photosynthesis may seem a spontaneous process from a human point of view, for no human intervention is needed. From a thermodynamic viewpoint photosynthesis is the opposite of a spontaneous process, for it requires the input of high-quality directional energy (solar radiation) and proceeds under the influence of an ordering principle (DNA of the living cells).