Seguin, when he assumed that the work done by an expanding heated body was the equivalent of the heat which it loses, and Mayer, when he went to work on the hypothesis that the amount of heat produced in compressing a gas is equivalent to the work done in compres sion, violated this principle, so that their conclusions were logically untrustwor thy. It is easily demonstrable on the conservation principle that Carnot's re versible engine is the most perfect pos sible engine, and that consequently all reversible engines working between the same temperatures have the same ef ficiency. For a small difference of tem perature the efficiency is a function only of the temperature, and this efficiency, divided by the difference of tempera tures, is called Carnot's function. Thom son, defining temperature as the recipro cal of Carnot's function, has construct ed a scale of temperature absolutely independent of the nature of the ther mometric substance. Hence if t is the temperature measured according to this absolute scale of the source of heat, and t' that of the refrigerator or condenser, the efficiency may be expressed by the t—t' fraction — . Now the efficiency is de
fined as the ratio of the work done to the heat supplied expressed in dynami cal measure. Hence, if W is the work done, H the heat supplied to the engine, and h the heat given out to the condenser, all expressed in dynamical measure we have W t—t' W =- H – h h t' whence H t or, in a reversible engine, the heat re jected is to the heat received as the abso lute temperature of the refrigerator is to the absolute temperature of the boiler. From the first of these equations it is evident that the heat supplied cannot be wholly transformed into work unless the refrigerator is at absolute zero of tem perature, a practical impossibility. Con sequently, in a material system only a part of the intrinsic energy is available for work, and this available portion or entropy is continually diminishing be cause of the universal tendency of heat to diffuse itself, and reduce the system to a uniform temperature, when of course no work can be produced. This is Thom son's principle of the dissipation of en ergy.