Page:Popular Science Monthly Volume 76.djvu/241

Rh by the transfer of heat from a given high temperature T1 to a given low temperature T2 is proportional to the quantity of heat transferred. Consider a steady flow of heat from temperature T1 to temperature T2 constituting a steady sweep, a sweep which remains entirely unchanged in character in successive intervals of time. Any result of this sweep must be proportional to the lapse of time, and therefore the degeneration which takes place in a given interval of time is proportional to the time; but the quantity of heat transferred is also proportional to the time, therefore, the amount of degeneration is proportional to the quantity of heat transferred from temperature T1 to temperature T2.

The definition of the ratio of two temperatures previously given was understood to be a provisional definition. We are now in a position to propose a definition of the ratio of two temperatures which is independent of the physical properties of any particular substance. This definition will remain somewhat vague, however, until the action of the steam engine is discussed in the later sections of this article. According to proposition (a) above, the thermodynamic degeneration which is involved in the conversion of work into heat at a given temperature is proportional to the amount of work so converted and the proportionality factor depends upon the temperature only. Therefore, we may write

where $$\phi$$ is the degeneration involved in the conversion of an amount of work W into heat at temperature T1 and $$\phi$$ is the degeneration involved in the conversion of an amount of work W into heat at temperature T2, and m1 and m2 are factors which depend only upon T1 and T''2, respectively. The amount of work W having been converted into heat at temperature T1; imagine the heat to flow to a lower temperature T2, thus involving an additional amount of degeneration according to proposition (b) above. The conversion of work W into heat at temperature T2 and the subsequent flow of this heat to a lower temperature T2 gives the same result as would be produced by the conversion of the work into heat at the lower temperature directly. Therefore the lower the temperature at which work is converted into heat the greater the amount of degeneration involved. That is to say, the factor m2 in equation (3) is larger in value than the factor m1