Page:Popular Science Monthly Volume 76.djvu/242

in equation (2), temperature $T_{1}$ being higher^[1] 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

$T_{1}/T_{2}=m_{2}/m_{1}T$

(4)

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

$m_{1}=k/T_{1}$	(5)
and
$m_{2}=k/T_{2}$	(6)

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

$\phi =kW/T$

(7)

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.^[2]

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

$\phi =W/T$

(8)

1. The idea of higher and lower temperature is not dependent upon any method of measuring temperature. When a substance receives heat definite observable effects are produced, and when these effects are produced by placing one substance in contact with another substance, the other substance is known to give heat to the given substance and its temperature is known to be higher than the temperature of the given substance. Does not one know that a stove is hotter than the floor, for example, when one spills water partly on the stove and partly on the floor?
2. One of the most important discussions in elementary thermodynamics is that which establishes this fact. See Art. 58 of Franklin and MacNutt's "Elementary Theory of Heat" for a very simple discussion of this matter.