AVAILABLE AND UNAVAILABLE ENERGY

Consider the Carnot engine as a perfect mechanism. It takes heat-energy from a source at a temperature T₂°, and it gives up heat to a refrigerator at a temperature T₁°, T₂° being greater than T₁°. In the adiabatic expansion 1→2 the gas continues to expand until its temperature becomes equal to that of the refrigerator. It cannot, then, expand and do work any longer, and thus the proportion of the heat, Q₂, received from the source, which can be converted into work, depends on the difference of temperature T₂° − T₁°. The greater is this difference the greater will be the proportion of the heat-energy received which can be converted into work. If the engine were a perfect one, and if the gas were also a perfect one (that is a gas which would continue to expand according to the equation for the adiabatic expansion of gases), and if the refrigerator were absolutely cold, then all the heat energy received from the source could be converted into work.

We cannot produce a refrigerator of absolute temperature 0°, and therefore only a certain proportion of the heat which is received by the engine can be transformed into mechanical work. But this work can be used to reverse the action of the engine, and thus the same fraction of the total heat-energy which was given to the refrigerator can be taken from it and given back to the source. The perfect engine is therefore reversible without loss of available energy.

Now consider still the engine as a mechanism which takes heat from a source and gives it to a refrigerator, but let it be an actual engine. Instead of giving up a certain fraction of the heat received to the refrigerator—a fraction equal to Q₁ T₁°/T₂°, it gives up rather more, because it is not a perfect mechanism, that is, it generates friction, etc. Some of the heat received thus ceases to be available for the performance of work; and passes into the refrigerator. The fraction of the heat-energy which passes into the refrigerator in the perfectly reversible engine was unavailable energy in the conditions in which the mechanism worked, or was imagined to work, but in the actual engine this fraction is increased. If we divide the increase of unavailable energy by the temperature of the refrigerator, the product is the increase of entropy generated in the actual engine over that generated in the ideal engine. Because of this reduction of available energy the actual engine is an irreversible mechanism.

This is the connection between unavailable energy and entropy. In all transformations some fraction of the transforming energy becomes heat, and this heat flows by conduction and radiation into the surrounding bodies. In general this heat simply raises the temperature of the medium into which it flows, and becomes unavailable for further transformations. With every transformation that occurs some part of the energy involved becomes unavailable. Therefore although the sum of the available and unavailable energy of the Universe remains constant, the fraction of unavailable energy tends continually to a maximum.