quantity, H, of heat from the source, and, if possible, let A derive from this heat more work than B. Let h be the quantity of heat carried to the refrigerator, and W' the mechanical effect developed by B when running forward. Let W' greater than W by hypothesis, be the mechanical effect developed by A. A may be used to run B backward, and, since B is perfectly reversible, will, in so doing, by the expenditure of the mechanical effect W, take from the refrigerator the amount h, and carry to the source the amount H of heat. The two engines so coupled would then develop the mechanical effect W'—W, while no heat would be lost by the source. If A carries to the refrigerator the same quantity of heat that B takes away, the mechanical effect W'—W is developed without any change in external objects, without any consumption of energy. This would constitute a perpetual motion, which, by the first axiom, is impossible. If A transfers to the refrigerator less heat than B takes away, the refrigerator will grow colder and colder, and, since for the purposes of this discussion all other bodies may be assumed to be at the same temperature as the source, this will present the case of a machine producing mechanical effect while taking heat from the coldest of surrounding bodies. This is contrary to the second axiom. Therefore, A can not do more work under the conditions named than B. The reversible engine, then, derives as much mechanical effect from a given amount of heat as can be derived by any heat-engine whatever working between the same temperatures.
It follows further that all reversible engines working between the same source and refrigerator, and taking from the source the same amount of heat, must yield the same mechanical effect; in other words, must have the same efficiency. No matter what the working substance, or in what way heat is made to yield mechanical effect, so long as the process is completely reversible, the same amount of mechanical effect will always be derived from the same heat taken from the source.
It may be well to emphasize a little the first conclusion, that no heat-engine whatever can be more efficient than a reversible engine. If the reasoning is correct, no form of heat-engine, whether using air, or gas, or a condensable vapor, or a liquid, or a solid, as the working substance, or using thermo-electric currents, or any other means of converting heat into mechanical effect, can be more efficient than any one of the reversible engines. There is no escaping this conclusion except through the perpetual motion, or the derivation of mechanical effect from the heat of a body already cold. It has been sometimes claimed that the latter alternative was no impossibility, that the expansion of a compressed gas, the expansion of a gas into a vacuum, or the diffusion of one gas into another, may perform work at the expense of its own heat, while being cooled down to a lower temperature than surrounding bodies. But to compress the gas, or produce
