Rejoinder to the "Gibbs-Function Problem" Discussion Different spproaehesto G are used, here, for the samecomposite system. Contrary to Tykodi's claim made above, however, our results (1) stand. and He writes AGmrn,,,e = AGrublt AGWII.- G,., = AGMILS, then improperly discards this last term also, to get AG,,,,,,e = 0, offering in justification only thst "it is customary to to treat the container as thermodynamically inert.. ." Has Tykodi been mislead by Pippard (21, whom he cites later on? Pippard writes (p 44) that "the free energy" [ F = U - T S I A] is "not a meaningful concept" for a composite of subsystems unless T is uniform, though it may then "be arbitrarily [our emphases] defined as ZP,,"and comments similarly for T, P, and G. We believe that Pippard deals with the matter too briefly and that had he gone further he would have seen that the free and Gibbs energies, F, and G,, of the parts of a eomposite system can be formulated so that the sums F a n d G are meaningful, when there are thermal or mechanical constraints such that some or all of the parts can be simultaneously in equilibrium with more than one thermobarostatic reservoir. In any ease, we will now demon= 0 is incorrect here. strate that Tykodi's AGWaII As we have shown (I), AG follows naturally for the entire composite system when it is realized that the process is after all of a type to which the G criterion can he applied; the PippardTykodi assumption of additivity then demands, however, a special form for Gwelh,even if they are ideally rigid. One simply applies the Gibbs recipe G = U - T S P V t o the total system and process under discussion. This system is in contact with the same thermobarostatic bath at all times, is in (metastable) mechanical equilibrium with it throughout, and is in- thermal eouilihrium with it both initiallv and finallv. These ~ conrlitinna nre hit more than sufficient (the necesserv condi- .n.~ tionj we have called ~avborodntie( 1 ) ) to justify expecting that AG should be negative fur the strongly irreversible process. HPcause there are here no changes in external volume, no work is done against the pressure exerted by the surroundings, and the PVof the definition of G plays only a nominal albeit important bookkeeping role. It is entirely irrelevant that the pressure within is nonuniform: the entire system is nonetheless a suitable thermodynamic object, and obeys the appropriate general rules. Since Uand S are additive in the parts of the system, while PVis constant, we then have AG = (AUsubsf- TASrubrt+ PvapAVsubaJ - P,,AV.,b,t = AGrub-rt-PvapAVsubst= -PuapAVsubat
