Using the provisional absolute scale as in dicated by a hydrogen thermometer, experi ment shows that the ideal efficiency, W/H, of a perfectly reversible engine, is roughly repre sented by the following equation in which W stands for the mechanical energy realized, H for the heat (measured in the equivalent foot pounds) leaving the high temperature source, T for the temperature of the source, and T' for the temperature of the cooler escape.
W T—T' H T This suggests a new definition for a tempera ture scale, namely, that numerical values of temperatures be so adjusted as to fulfil exactly the above formula. Since the formula only fixes a ratio between the temperatures T and Ta corresponding to a given efficiency, an in finite number of sets of numerical values for these temperatures could be found to satisfy the formula. But if it be decided that a definite numerical range, say 100 degrees, be comprised between the freezing and boiling points of water, only one set of values become pos sible. This decision makes the value of the freezing point very nearly + 273° Abs., and the value of the boiling point + 373° Abs. Lord Kelvin was the first to propose this thermodynamic wale. Theory shows that its indications would correspond exactly to a ther mometer containing a perfect gas. Hydrogen is not quite a perfect gas, for its molecules at tract each other slightly and they occupy an appreciable fraction of the space holding the gas. Hence there are small deviations of the hydrogen thermometer from the thermody namic scale, especially at low temperatures. In spite of these difficulties much progress in the realization of the thermodynamic scale has been achieved through ingenious mathematical considerations relating to two sets of experi mental observations: those made by Regnault on the expansion and on the increase of pres sure of hydrogen and other gases when heated, and those made by Joule and Kelvin on the temperature changes suffered by gases in pass ing through a porous plug. Nevertheless, the
thermodynamic scale offers us a theoretical ideal which is independent of the thermal prop erties of any particular substance, but is only related in a definite way to a fixed universal law.
When a small amount of heat is transferred from or to a gram of a substance, the heat transferred (measured in calories), divided by the average absolute temperature of the sub stance at the time of the transference is called the change of entropy of the substance. For convenience, the zero of entropy is generally taken to correspond to water at the freezing point and under the normal atmospheric pres sure. It may be shown that when two bodies at different temperatures are placed in con tact and their temperatures become equalized, the average entropy rises, for from the above definition of entropy, the heat leaving the hotter body must reduce its entropy less than it increases the entropy of the cooler body into which the heat enters. Consequently, as temperature equalizations are always going on, the average entropy of the universe is con stantly rising and tending toward a maximum. At the same time, for the same reason, the availability of the heat energy of the universe to be converted into mechanical energy is tend ing, toward zero, for this availability depends upon difference in temperature of sources and escapes,Und is destroyed by temperature equal ization resulting from conduction, radiation and mixing.