Physical Constraints The Second Law Of Thermodynamics

The second law of thermodynamics is commonly known as the 'entropy law'. It states, in effect, that spontaneous processes in isolated systems always tend toward long-run thermodynamic equilibrium. In simple terms, it means that no energy transformation process that goes spontaneously in one direction can be reversed without some expenditure of available energy, or exergy. This applies, incidentally, to materials-recycling processes, a point emphasized (though somewhat misunderstood) by the late Nicholas Georgescu-Roegen (Georgescu-Roegen 1971).

The essence of the law is that every non-reversible process tends to increase the degree of disorder in the universe. Another way of saying it is that all processes tend to decrease gradients; for example, between high and low temperature regions, or between high and low concentrations of substances, densities, pressures, electric charges and so on. In other words, the universe is a great homogenizer. Many industrial processes, however, separate different substances or create greater temperature, density or pressure differences. The second law allows this to happen, locally, but subject to the rule that local order can only be increased at the cost of increasing global disorder. (Commonly this occurs by burning fossil fuels and dissipating the combustion products.)

In more precise technical language, the second law implies that there exists a non-decreasing function of thermodynamic state variables, known as entropy. This function is defined for every thermodynamic system and subsystem. The entropy for any subsystem reaches a maximum when that subsystem reaches thermodynamic equilibrium with its surroundings (the system).3 Similarly, there exists a measure of potentially available work (exergy) that is also defined and computable for all systems that are in local (internal) equilibrium. Energy is a conserved quantity. Exergy is not conserved; exergy is destroyed (lost) whenever a system performs physical work.

On the earth, where we live, thermodynamic equilibrium is a far distant static state of nature. Nevertheless, entropy is still a definable variable for every subsystem - such as a mass stream - although exergy is not defined for non-equilibrium situations. Changes in entropy can be calculated quantitatively for every 'event' in the physical world. In fact, it has been argued that the 'potential entropy' of products and waste residuals is a general - albeit imperfect - measure of potential environmental disturbance resulting from human economic activities (Ayres et al. 1993; Martinas and Ayres 1993).

However, in addition to the possibility of developing a general measure of potential harm to the environment, thermodynamic variables such as entropy and exergy also must satisfy explicit balance conditions. In particular, the exergy content of process inputs must be equal to the exergy lost in a process plus the exergy content of process outputs. Exergy lost in the process is converted into entropy. There is a balance equation for entropy, as well: the entropy of process inputs must also be equal to the entropy of process outputs minus the entropy generated within the process.

The above statements are probably not meaningful for most economists. They are included here only for the sake of completeness. In any case, computational details need not concern us here. All that really matters is that entropy and exergy balance conditions constitute effective constraints on possible process outcomes. If these conditions are violated - as in the case of the once sought-after 'perpetual motion machine' - the process or change cannot occur.

We note in passing that the simplest textbook version of the economic system, illustrated in Figure 5.1a, consists of two agents, namely a producer and a consumer, exchanging abstract goods and services for money and labor. More complex models can be constructed; for instance by adding agents such as producers of capital goods or central banks to create money (Figure 5.1c). But the system thus envisaged remains a sort of perpetual motion machine. The missing element, of course, is the fact that goods (unlike money or services) have a material basis; and real physical materials are not self-produced nor are they consumed, in the literal sense. Material goods are derived from raw materials, and converted first into useful goods and ultimately into waste residuals (Ayres and Kneese 1969). Entropy is created during this process.

A. Closed static production consumption system


Consumption of final goods and services

Wages, rents

B. Closed dynamic production consumption system

B. Closed dynamic production consumption system

C. Open static production consumption system

• i

Production of goods and services

Purchases M- -

Wages, rents


Production wastes mmmmmmmmmmmmmmmmma

Recycled materials


Consumption wastes

Consumption wastes

Recycled materials

Figure 5.1 Production-consumption systems

As a practical matter, all real, existing materials-transformation processes must satisfy the second-law conditions, by definition. However, industrial systems can be modeled without explicit attention to second-law constraints. Moreover, in constructing hypothetical future industrial systems (based, for instance, on the substitution of biomass for fossil fuels), or modeling processes (such as the carbon cycle or the nitrogen cycle) in the natural world, under altered conditions, it is important to take second-law constraints into account.

The second law also has immediate importance for modelers in regard to energy analysis. Since energy is conserved in all transformation processes (the first law of thermodynamics), there is no way to compare two energy conversion processes without talking about thermodynamic (exergy) efficiency. Exergy efficiency is a simple way of expressing second-law constraints.

To recapitulate: the importance of the two laws of thermodynamics for economics is that they constrain possible physical processes. In particular, all material-transformation processes must satisfy both first-law (mass balance) and second-law (exergy and entropy balance) conditions. Hence economic models with physical implications should reflect these constraints.

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  • Marco
    Is economic growth consistent with the second law of thermodynamics?
    8 years ago
  • kathrin
    What is the constraint of the second law of thermodynamics?
    7 years ago
    How law of thermodynamics harm environment?
    7 years ago
  • selma
    What are the physical effects of the second law of thermodynamics?
    10 days ago

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