Page:Popular Science Monthly Volume 76.djvu/242

238 in equation (2), temperature $$T_{1}$$ being higher than temperature $$T_{2}$$. Therefore, since $$m_{1}$$ and $$m_{2}$$ depend only upon $$T_{1}$$ and $$T_{2}$$, respectively, it is permissible to adopt the equation

as the definition of the ratio $$T_{1}/T_{2}$$. This definition of temperature ratios is originally due to Lord Kelvin.

Another way to express the definition which is involved in equation (4) is to consider that the factor $$m_{1}$$ is the smaller the higher the temperature $$T_{1}$$ so that we may adopt $$k/m_{1}$$ as the measure of the temperature $$T_{1}$$ and $$k/m_{2}$$ as the measure of the temperature $$T_{2}$$, giving

where $$\phi$$ is an indeterminate constant. Therefore equations (2) and (3) may be written in the general form

where $$\phi$$ is the thermodynamic degeneration involved in the conversion of an amount of work W into heat at temperature T, and k is an indeterminate constant.

The ratio of two temperatures as defined by equation (4) is very nearly the same as the ratio of two temperatures as measured by the gas thermometer, and therefore gas thermometer temperatures may be used throughout this discussion without appreciable error.

Since the factor k in equation (7) is indeterminate, we may use as our unit of thermodynamic degeneration the amount which is involved in the conversion of one unit of work into heat at a temperature of one degree on the "absolute" scale; then the value of k is unity and equation (7) becomes