Page:Reflections on the Motive Power of Heat.djvu/113

Rh by means of the law demonstrated above. The heat set free by compression, according to the theorem of page 81, ought to be represented by an expression of the form

&emsp;&emsp; s = A + B log v,

s being this heat, v the volume of the gas after compression, A and B arbitrary constants dependent on the primitive volume of the gas, on its pressure, and on the units chosen.

The specific heat varying with the volume according to the law just demonstrated, should be represented by an expression of the form

&emsp;&emsp; z = A' + B' log v,

A'  and B'  being the different arbitrary constants of A and B.

The increase of temperature acquired by the gas, as the effect of compression, is proportional to the ratio $$\tfrac{s}{z}$$ or to the relation $$\tfrac{A + B \log v}{A' + B' \log v}.$$ It can be represented by this ratio itself; thus, calling it t, we shall have

&emsp;&emsp; t = $$\tfrac{A + B \log v}{A' + B' \log v}.$$

If the original volume of the gas is 1, and the original temperature zero, we shall have at the