THERMODYNAMICS. 265 



of steam will suffice to start evaporation, which will continue until all 

 the water has become steam at 100. At any point we may restore 

 equilibrium by holding the piston while we restore the infinitesimal load 

 removed ; and at any point we may reverse the motion and condense the 

 steam by adding an extra infinitesimal load so that the pressure is just 

 over 1 atmosphere. As another illustration, consider a quantity of ice 

 and water under atmospheric pressure at 0, Keep the surrounding 

 temperature and the proportion of the two remains unchanged. But 

 lower the temperature ever so little below and the ice increases ; raise 

 it ever so little above and the water increases. The change from 

 water to ice or ice to water may be reversed by indefinitely small 

 temperature changes. 



Examples of Irreversible Processes. We may contrast with 

 these the case in which water at 100 is under a piston with a load of, 

 say, half an atmosphere. Evaporation with expansion will ensue, and 

 the piston will ultimately rise about twice as far as in the previous case, 

 and will then be in equilibrium. But an indefinitely small increase of 

 load will now only lead to an indefinitely small compression, and not to 

 a reversal of the whole process. Clearly, too, the process is very far 

 from reversible at intermediate points. Or suppose that a lump of ice is 

 thrown into water at 10. The ice will melt, but no known process will 

 suffice to make the water at 10 change back to ice. 



"We conclude, then, that in Carnot's reversible cycle the machinery 

 must be free from friction, the working substance must never differ 

 appreciably in temperature and pressure from its surroundings, and that 

 the process must be indefinitely slow. 



Efficiency Of an Engine. The fraction of the heat received from 

 the source which an engine converts into work is termed the efficiency of 

 the engine. 



It is convenient to denote any quantity of heat in calories by H, and 

 its work equivalent by Q = JH when J is the mechanical equivalent of 

 1 calory. 



If an engine receives H units of heat from the source and produces 

 W units of work its efficiency is 



We shall now prove that 



All reversible engines working- between two given tempera- 

 tures and taking- in equal quantities of heat from the source 

 are equally efficient. 



If possible, suppose that one reversible engine A is more efficient 

 between a given source and refrigerator than another reversible engine 

 B. Sending B through a cycle, let it take S of heat from the source and 

 give up R to the refrigerator producing W of work. Or, in reverse 

 working, when W of work is done on it per cycle, it will take R from 

 the refrigerator and give S to the source. Now, by hypothesis, for every 

 quantity of heat S which A receives from the source, it produces more 

 than W of work, say W'. Allow A to work forwards, and out of every 

 quantity W of work which it yields, take W to work B backwards 

 through a complete cycle. Then on the Avhole the source will neither 



