Page:Scientific Papers of Josiah Willard Gibbs.djvu/46

10 general character, which shows an important advantage on the side of the entropy-temperature diagram. In thermodynamic problems, heat received at one temperature is by no means the equivalent of the same amount of heat received at another temperature. For example, a supply of a million calories at 150c is a very different thing from a supply of a million calories at 50c. But no such distinction exists in regard to work. This is a result of the general law, that heat can only pass from a hotter to a colder body, while work can be transferred by mechanical means from one fluid to any other, whatever may be the pressures. Hence, in thermodynamic problems, it is generally necessary to distinguish between the quantities of heat received or given out by the body at different temperatures, while as far as work is concerned, it is generally sufficient to ascertain the total amount performed. If, then, several heat-areas and one work-area enter into the problem, it is evidently more important that the former should be simple in form, than that the latter should be so. Moreover, in the very common case of a circuit, the work-area is bounded entirely by the path, and the form of the isometrics and the line of no pressure are of no especial consequence.

It is worthy of notice that the simplest form of a perfect thermodynamics engine, so often described in treatises on thermodynamics, is represented in the entropy-temperature diagram by a figure of extreme simplicity, viz: a rectangle of which the sides are parallel to the co-ordinate axes. Thus in figure 3, the circuit $$ABCD$$ may represent the series of states through which the fluid is made to pass in such an engine, the included area representing the work done, while the area $$ABFE$$ represents the heat received from the heater at the highest temperature $$AE$$, and the area $$CDEF$$ represents the heat transmitted to the cooler at the lowest temperature $$DE$$.

There is another form of the perfect thermodynamic engine, viz. one with a perfect regenerator as defined by Rankine, ''Phil. Trans.,'' vol. 144, p. 140, the representation of which becomes peculiarly simple in the entropy-temperature diagram. The circuit consists of two equal straight lines $$AB$$ and $$CD$$ (fig. 4) parallel to the axis of abscissas, and two precisely similar curves of any form $$BC$$ and $$AD$$.