810 TRANSACTIONS OF SECTION O. 



mechanical processes, returning ultimately to the standard condition of tempera- 

 ture, pressure, and volume, then the quantity of heat added to the hody is the 

 same as that which has been discharged from it; (2) No process can exist whereby 

 a given mechanical energy can increase its own quantity. On these indisputable 

 assumptions he bases his ideal cycle, which consists of four simple and easily 

 imagined operations, occurring within a cylinder behind a piston, so arranged that 

 during the C3"cle work can be done by the working fluid upon the piston or work 

 done by the piston on the working fluid. 



First Operation. — The given volume of the working fluid is to be imagined as 

 confined at its highest temperature and press\ire behind the piston, and heat is to 

 be added to keep the temperature constant, while the fluid expands, moving the 

 piston and doing work upon it. 



Second Operation. — ^The supply of heat is cut oft', and the working fluid expands 

 also during work on the piston, while its temperature falls to the lowest point 

 and its volume increases to its maximum. 



Third Operation. — The piston returns, compressing the working fluid, but 

 allowing the heat of compression to escape, so that the temperature remains 

 during the operation at its lowest point. 



Fourth Operation. — The piston compresses the working fluid, without allowing 

 any loss of heat, to such an extent that the temperature rises again to its highest 

 point, and the working fluid exists at the end of this operation at the same 

 volume, pressure, and temperature as at the beginning. 



This assumed series of operations would give a certain available work area, 

 the indicated power of the engine, inasmuch as the work done by the working 

 fluid would be greater than that done upon it. If however it be assumed that 

 in all the operations the direction of motion of the piston be reversed, then com- 

 pression without loss of heat would take place in the second operation ; further 

 compression, but with suiKcient heat loss to keep temperature constant, would 

 occur on the first operation ; the fourth operation would follow with exjiansion, and 

 tlie third operation would conclude also with expansion. The engine would be 

 reversed by beginning with the second operation, moving the piston backwards in 

 the order second, first, fourth, third. Carnot shows that this reverse operation 

 would be performed by exactly the same amount of work as was given out by the 

 direct operation, and that an amount of heat would be returned at the higher 

 temperature equal to that which was added in the first case. 



An engine which fulfils these conditions, Carnot states, will give the greatest 

 amount of work which can be obtained from a given quantity of heat falling 

 through a given temperature range. And it is evident that this must be so, 

 because, if we assume the existence of any engine under the same conditions 

 giving a greater amount of work from the same heat, then that engine could drive 

 a Carnot engine in the reverse direction in such proportion as to return to the 

 higher temperature a greater amount of heat than it abstracted, and so mechanical 

 energy could be obtained without any heat fall whatever. This marvellous 

 demonstration is obviously independent of the nature of the working fluid ; it 

 applies equally to all working substances, whether solid, liquid, or gaseous, whether 

 physical state changes or not. It at once gives a standard of the limit of 

 mechanical power which could possibly be obtained from a given amount of heat 

 and a given temperature fall. 



The Carnot cycle operations, as here given, are applicable either to the material 

 or to the dynamical theory of heat ; but Carnot originally stated that the whole of 

 the heat added in the first operation was to be discharged in the third. Under the 

 material or caloric theory, work was supposed to be done by the fact of fall in 

 temperature. Naturally, as the heat was material it could not be destroyed or 

 changed into mechanical energy. The production of mechanical energy was sup- 

 posed to be incidental to the fall of temperature, much in the same way as 

 mechanical energy was produced by the fall of water-level, and this analogy is 

 used throughout Carnot's work of 1824. 



Carnot thus succeeded in proposing a standard of efficiency which was 

 applicable to any heat engine, whatever the working fluid and whatever the 



