Page:Popular Science Monthly Volume 76.djvu/243

Rh in which $$W$$ is expressed in joules and $$T$$ in degrees centigrade; and $$\phi$$ is expressed in terms of joules per degree. Thus one joule per degree is the degeneration involved in the conversion of one joule of work into heat at 1° C. on the absolute scale, or the amount involved in the conversion of 1,000 joules into heat at 1,000° C. on the absolute scale.

To convert an amount of work $$W$$ into heat at temperature $$T_{1}$$ involves $$W/T_{1}$$ units of degeneration, to convert the same amount of work into heat at temperature $$T_{2}$$ involves $$W/T_{2}$$ units of degeneration, and therefore to transfer an amount of heat equal to $$W$$ from temperature $$T_{1}$$ to temperature $$T_{2}$$ must involve an amount of degeneration equal to the excess of $$W/T_{2}$$ over $$W/T_{1}$$ or an amount equal to $$W(1/T_{2}-1/T_{1})$$, or $$H(1/T_{2}-1/T_{1})$$, where $$H$$ is the amount of heat transferred.

(a) The thermodynamic degeneration which accompanies a sweeping or irreversible process can not be directly repaired, nor can it be repaired by any means without compensation.

This is an entirely general statement of the second law of thermodynamics. The direct repair of the degeneration due to the sweeping process means the undoing of the havoc wrought by the process by allowing the sweep to perform itself backwards, an idea which is exactly as absurd as the idea of allowing a burned house to unburn itself. Following are several specialized statements of the second law of thermodynamics.

(b) Heat can not pass directly from a cold body to a hot body, nor can heat be transferred from a cold body to a hot body by any means without compensation.

(c) Heat can not be converted directly into work, nor can heat be converted into work by any means without compensation.

The direct conversion of heat into work would be the simple reverse of any of the ordinary sweeping processes which involve the degeneration of work into heat, that is, the direct conversion of work into heat would be to allow the sweeping process to perform itself backwards. For example, work is degenerated into heat in the bearing of a rotating shaft, and we all know that to reverse the motion of the shaft does not cause the bearing to grow cold and the heat so lost to appear as work helping to drive the shaft. That would be a rotary engine indeed! There is an important general theorem in thermodynamics to the effect that if two sweeping processes $$A$$ and $$B$$ involve the same amount of degeneration, and if either of the processes, say $$A$$, has been allowed to perform its sweep, then by a lever arrangement, as it were, the process