280 



HEAT. 



bodies under such circumstances that they can neither part with heat 

 to, nor receive it from the outside, the entropy of the system cannot 

 diminish. In order to obtain the maximum work from the system, it 

 must evidently be brought to a condition of uniform temperature and 

 of uniform pressure, for if these are not uniform still more work may 

 be obtained by coming to uniformity. There will be some limiting 

 condition given as to pressure or volume. In coming to this, the best 

 course will be by adiabatic transformations, so that the final equals the 

 initial entropy, for if there is any gain, some of the energy which might 

 have been transformed has gone to increase the entropy of the system. 

 Now, if in the final state the entropy and some other quantity, say the 

 pressure, is given, the state of the system is determinate, and therefore 

 its intrinsic energy is determinate. Hence we may calculate the work 



done in any convenient method of passing from the initial to the final 

 state, in which we obey the condition of constant entropy. For instance, 

 we may first allow all the bodies to come to the standard pressure adia- 

 batically. We may then use a reversible engine to bring them to the 

 same temperature, first say working between the two coldest as source 

 and refrigerator ; then when they are at one temperature, working 

 between the next above as source, and these two as refrigerator, and 

 so on. 



We may represent the work obtained in the latter part of the process 

 on the entropy temperature diagram. Let us take the case of two 

 bodies only, at the same pressure but different temperatures. Let HAK 

 (Fig. ]61) represent the final pressure line for the hotter substance, AN 

 its temperature ; LBM the line for the same pressure of the colder sub- 

 stance, BN its temperature. If we turn the curve LBM round AB as 

 axis till BM is in the plane of the paper on the other side, lying ulong BH 

 and cutting HAK in H, evidently as the hotter body passes along AH, 

 giving up heat to a reversible engine with the colder as source, the latter 



