POSSIBLE EFFICIENCY OF HEAT-ENGINES. 833 



quantity, II, of heat from the source, and, if possible, let A derive 

 from this heat more work than 13. 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 back- 

 ward, 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 II of heat. The 

 two engines so coupled would then develop the mechanical effect W 

 W, Avhile no heat would be lost by the source. If A carries to the 

 refrigerator the same quantity of heat that B takes away, the mechan- 

 ical effect W W is developed without any change in external ob- 

 jects, without any consumption of energy. This would constitute a per- 

 petual 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, de- 

 rives as much mechanical effect from a given amount of heat as can be 

 derived by any heat-engine ichatever working between the same tem- 

 peratures. 



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 me- 

 chanical 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 work- 

 ing 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 conclu- 

 sion except through the perpetual motion, or the derivation of mechan- 

 ical effect from the heat of a body already cold. It has been some- 

 times claimed that the latter alternative was no impossibility, that 

 the expansion of a compressed gas, the expansion of a gas into a vacu- 

 um, 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 tempera- 

 ture than surrounding bodies. But to compress the gas, or produce 



TOL. XVII. 53 



