Page:Popular Science Monthly Volume 17.djvu/858

838 the absolute scale we wish to determine. We have as above T$$-$$t : T :: H$$-$$h : H, and T$$-$$t : T :: H$$-$$h' : h, if h is the heat rejected at the temperature t. Hence T$$-$$t : T$$-$$t :: H$$-$$h : H$$-$$h. But H$$-$$h is the heat converted into work by an engine working between the temperatures T and t, and is proportional to the area B C D A. Also H$$-$$h is the heat converted into work by an engine working between the temperatures T and t', and is proportional to the area B C m n. Therefore T$$-$$t : T$$-$$t :: area B C B A : area B C m n; or 180° : T$$-$$t' :: area B C B A : area B C m n.

Having the data for constructing the isothermal and adiabatic lines, the areas B C B A and B C m n can be computed, and hence t' determined. The divisions of an absolute scale so constructed are found to correspond very closely with the divisions of the air-thermometer, and to differ but little from the divisions of the Fahrenheit scale. We are led, then, to the conclusion that to convert all the energy of a given amount of heat into mechanical effect, a refrigerator at a temperature of 491 Fahrenheit degrees below the melting-point of ice, or 459° below zero Fahr., is necessary.

Let us recapitulate briefly the points of this argument.

1. It is impossible for any heat-engine, of whatever construction, to convert into mechanical effect a larger proportion of the heat derived from a given source than can be done under the same conditions by a reversible engine. This proposition can not be denied without involving a denial of two physical axioms which are founded upon the results of all past experience, viz.: That the perpetual motion is impossible, and that "it is impossible by means of inanimate material agency to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of surrounding objects."

2. That all reversible engines, whatever the working substance, have the same efficiency; that is, taking from the source the same quantity of heat H, they will transfer to the refrigerator the same quantity h, and convert into mechanical effect the same quantity H$$-$$h. Hence whatever results are derived from a discussion of any one form of reversible engine will be true of all others.

3. If a scale of temperature be constructed such that the temperature of the source is to the temperature of the refrigerator of a reversible engine as the heat derived from the source is to the heat given to the refrigerator, the scale divisions will differ but little from the divisions of the scales in common use. The efficiency of an engine

will then  $$=$$ 1 $$-$$ 

4. Upon such a scale, if there are, as in the Fahrenheit scale, 180 between the freezing and the boiling points of water, the former point would be numbered 491·4 and the latter 671·4. The