THERMODYNAMICS. 271 



work forward, driving a reversible engine backward. If the first is more 

 efficient it can get more work from a given quantity of heat. Put it so 

 that it will be able to drive the reversible one at such rate that the revers- 

 ible restores to the source the heat taken out and there is a balance of work 

 over, which can only come from the refrigerator. If this is arranged to 

 be the coldest body of the system the result is contrary to the Second Law. 



Water-Wheel Analogue of the Reversible Engine. The reader may be 

 aided in understanding and remembering the foregoing theory of the 

 reversible heat engine by considering an analogous case of energy tran- 

 formation. 



Let us suppose that we have two reservoirs of water at different 

 levels, and that we wish to transform the potential energy of the water in 

 the higher by means of a water-wheel, allowing the water to fall in the 

 wheel from one reservoir to the other. Evidently we cannot get all the 

 potential energy transformed by the wheel. We put in so much at the 

 top and take out a smaller quantity at the bottom. If the wheel works 

 very slowly, receiving the water at the level of the surface of the higher 

 reservoir, and parting with it at the level of the surface of the lower one, 

 and if there is no leakage and no friction, then the whole of the potential 

 energy lost will be usefully transformed by the wheel, and no wheel 

 between the same levels could be more efficient. We see at once that 

 the conditions of maximum efficiency and reversibility coincide. It is 

 obvious that it is impossible to get mechanical effect out of the lower 

 reservoir if that is already in the lowest available position the analogue 

 of the Second Law of Thermodynamics. The total potential energy of a 

 mass of water in the upper reservoir is the work which would be done in 

 lifting it from the absolute zero of level the centre of the earth. 



If then we define 



Efficiency = Work got out 

 Energy put in 



the denominator is very nearly the same for the same mass of water at 

 different places, and the efficiency is very nearly proportional to the 

 difference in height, in feet, between the two reservoirs. But the height 

 in feet does not give an absolute scale of efficiency, for, as gravity varies, 

 the work for a fall of one foot depends to some extent on the situation of 

 the wheel. This is analogous to the gas scale of temperature. We may 

 get an absolute scale by discarding the length measure of difference of 

 level and substituting for it a work measure. Dividing up the distance 

 between the centre of the earth and the level of the higher reservoir into 

 steps, so adjusted that a reversible wheel in each step will give the same 

 amount of work from the passage of the same quantity of water, we may 

 define these steps as having equal differences of level. Now the efficiency 

 of any wheel becomes 



No. of steps occupied by wheel. 



Total No. of steps from centre of earth to higher level, 

 or if n = No. of steps from centre of earth to higher level 



and n' = the No. from centre of earth to lower level. 



-ncc. n ri 

 Lmciency = 



