THERMODYNAMICS. 



267 



the same proportion whatever the substance used. Let ABCD (Fig. 

 153) be a number of heat reservoirs, arranged in descending order of 

 temperature, and let reversible engines 3, /3y, yd ... be set working 

 between the successive pairs. Let /3 go through a cycle, taking Q A 

 from A and yielding Q B to B. Let 167 go through a cycle, taking Q B 

 from B and yielding Q c to 0. Let yb go through a cycle, taking Q c from 

 C and yielding Q D to D and so on, each engine taking from its source 

 what its predecessor had yielded to it. The quantities of work yielded 

 will be Q A - Q B , Q B - Q c , Q c - Q D , &c., the heat being expressed in 

 mechanical measures. 



Now, adjust the temperatures so that the quantities of work given 

 up by the successive engines are equal, or so that 



Then we define the intervals of temperature as all equal. Or we may 



say that if a quantity of 



heat is sent down a succes- 



sion of temperature steps, 



the quantity lessening as 



it goes by reversible trans- 



formation into work, the 



steps are equal when the 



amount transformed in 



each step is the same. 



Though this defines equality 



of temperature interval, it 



still leaves it open to us to 



fix on any desired interval 



as 1, and to start from 



any desired zero point. 



We may represent this 

 process on the indicator 

 diagram. Drawing an iso- 

 thermal AB (Fig. 154) and 

 the adiabatics ACE, BDF, 

 the isothermals drawn so as to make the areas AD, CF, &c., equal, are 

 at equal intervals of temperature. 



We may also note that if BG, GL represent distances along which 

 the same amount of heat is taken in as along AB, the adiabatics through 

 G and L must form a series of quadrilaterals equal in area to AD. This, 

 of course, is merely equivalent to saying that the efficiency between given 

 limits is independent of the quantity of heat taken in. 



Efficiency expressed on the Absolute Scale. Any number of 



the engines a/3, $7, &c., may be joined together so as to work in concert, 

 and they will take heat from the source of the first, yielding heat to the 

 refrigerator of the last, transforming the difference to work. On the 

 whole, the intermediate reservoirs will be unaffected. Evidently the 

 process may be exactly reversed on putting in the work at the bottom, 

 so that the arrangement forms a compound reversible engine. 



If we keep to a given temperature of source indicated by O s , on a 

 scale at present arbitrary as to length of degree and zero, and if Q R be the 



FIG. 154. 



