about two pounds of coal per hour per horse-power. Hence it is said that the steam-engine is a very inefficient machine, which the genius of the future inventor may improve till a pound of coal is made to yield six, eight, or ten times the power it now gives.
But, while the theory of thermodynamics asserts that the combustion of a pound of carbon yields an amount of heat equivalent to 11,116,800 foot-pounds of energy, it also asserts just as clearly and just as firmly that, under the conditions which exist upon this planet, heat can not be transformed into mechanical effect without wasting a considerable portion of the energy due to it. In other words, if a given quantity of heat be taken from a source, as a steam-boiler, and made to do work by means of any form of engine, a considerable portion of that heat must, from the very nature of things under existing conditions, be allowed to pass through the engine and raise the temperature of other bodies to no useful purpose. It is to the discussion upon which this conclusion is based that I propose to devote this article.
In a very valuable essay published in 1824, Carnot furnished us with a conception which is an exceedingly useful one in this investigation. It is that of an engine completely reversible in all its physical and mechanical agencies. A water-motor which could be driven backward by means of some source of power, and would then raise to a given level as much water as it would use from that level to develop the power required to run it backward, would be a reversible engine. It is plainly to be seen that such a motor would be a perfect motor, and also a perfect pump. A reversible heat-engine would be one which, running forward and performing a certain amount of work by means of a given amount of heat derived from a source, would, if run backward by the performance upon it of the same amount of work, restore to the source the same amount of heat.
A reversible engine in this sense is, of course, impossible in practice, but the theoretical deductions from the conception are in no way invalidated by this fact. Such a heat-engine would be a perfect engine in the sense that it would produce as much mechanical effect as could be produced by any heat-engine under the same conditions from the same quantity of heat. The proof of this proposition rests upon two assumptions that are supported by all past experience, and may, therefore, be regarded as physical axioms: 1. That a perpetual motion is impossible; 2. That it is impossible by means of inanimate material agency to derive mechanical effect from any portion of matter by cooling it below the temperature of surrounding objects.
A heat-engine when at work must carry heat from a body of high temperature (the source) to one of low temperature (the refrigerator), and experiment has proved that the amount of heat given to the refrigerator is always less than that taken from the source. Now, let there be two heat-engines, A and B, of which B is reversible, working between the same source and refrigerator. Let each take the same
