Note 70 — Chapter XX · THE IRREVERSIBILITY OF TIME

It is important to understand the precise significance of the principle of entropy. Keeping in mind the fact that the principle refers to probabilities and not to absolute certainties, we may express its general formulation as follows: For all changes of a system the total entropy either is increased (irreversible changes) or else remains constant (reversible changes). At first sight it might appear as though the transformation of heat into work in the steam engine, or the withdrawal of heat from a colder body and its transfer to a warmer one, as in the case of refrigerating machines, would constitute flagrant violations of the principle. But, as a matter of fact, such is not the case. For, with the steam engine, the unnatural change exhibited by the transformation of heat into work is counterbalanced by a natural change illustrated by the fall of heat from generator to condenser. In fine, the total entropy thus remains constant (in a perfectly reversible cycle, for instance in a Carnot cycle), or else suffers an increase. Again, with the refrigerating machine, the unnatural passage of heat from the cold to the warmer body is compensated by a natural transformation; this is represented by the transformation into heat of the mechanical work performed on the apparatus. So once again the total entropy is increased, or, at best, remains constant. Still more striking cases, where the principle would appear to be at fault, are illustrated by the endothermic reactions in chemistry. Contrary to what we should expect, they absorb heat so that low-grade heat energy is transformed into higher-grade chemical energy; but here again compensating influences are at work. We cannot dwell further on these points. The reader who is interested in studying them must consult some standard work on thermodynamics.