92 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



where the elastic forces do a work = ^JF; strictly speaking, d'Q is 

 not differential of Q the heat supply. 



(3) Two gases (i) and (2) thermally connected, are maintained 

 at same temperature but different pressure and change adiabat- 

 ically while experiencing change of volumes; then it can be shown 

 that for this finite change, 5i+5 2 = constant, that is for the two 

 gases the sum of the final entropies = 5'i 1 + k S l 2 1 = 6*1 4- 6*2 = sum 

 of their initial entropies. No other change is effected in any 

 other bodies but in these two gases; here emphasis is laid on 

 preposition in-, for the work done may be the lifting or lowering 

 of a load and such change of location in rigid bodies involves 

 no change of inner energy. Changes of density in external bodies 

 can be also avoided by having the two gas tanks located in a 

 vacuum. 



(4) A similar proposition can be established for a system of any 

 number of gases by successively treating the gases in pairs as above. 

 The theorem then reads: "If the gas system as a whole possesses 

 the same entropy in two different states then the system can be 

 brought from one state to the other in a reversible manner without 

 changes .remaining in other bodies." 



(5) We know that the expansion of an ideal gas without doing 

 external work and receiving any heat supply is an irreversible 

 process. The consequence is that the entropy of this gas increases. 

 It follows at once that " it is impossible to diminish the entnopy 

 of an rdeal gas without changes remaining in other bodies." 



(6) The same result obtains for a system of any number of 

 ideal gases. Consequently "there exists in the whole of Nature 

 no means (be they of the mechanical, thermal, chemical or electrical 

 sort) of diminishing the entropy of a system of ideal gases, without 

 changes remaining in other bodies." 



(7) " If a system of ideal gases has changed to another state (pos- 

 sibly in an entirely unknown way) without changes remaining 

 in other bodies, then the final entropy can certainly not be smaller, 

 it can only be greater than or equal to the initial condition. In 



