化學(xué)勢(shì)外文翻譯-化學(xué)工程(參考版)
2025-01-23 07:50本頁(yè)面
【正文】 except jn are held constant. Another way of seeing the relationship between U and j? is integrate Equation ().This can be done by using Euler’s theorem for homogenous functions. Euler’s theorem states that if ),(),( zyxfzyxf ???? ? , () Then zfzyfyxfxf ????????? () The theorem can be easily proved by differentiating equation () with respect to ? and then setting ? equal to unity. Now ).. ..,( 1 mnnVSUU ? . Suppose the amounts of all the types of substance, called constituents, in the system were doubled or halved or, more generally, changed by the factor ? without changing any of the fundamental state variables. then the extensive variable U would be changed by ? and all the independent, extensive state variables would also be changed by the factor ? .thus U is a homogeneous function and Euler’s theorem can be applied to it: () From the differential of we know that TSUknV??????? ??, PVU knS ?????????? , jnVSj knU ???????????? , () Substituting the relations of Equation () in the Equation(),we have kkk nVSjmj jnSnV nUnVUVSUSU,1, ???????? ????????? ????????? ??? ?? jmj j nPVSTU ????? 1 ? () Recall that the Gibbs function is defined as PVSTUG ??? . It is therefore immediately clear that jmj jnG ??? 1? () If only one constituent is present, then nG ?? or nG?? 。 隨后，（ ）式得到重要結(jié)論 ? ? jj jPT dndG ?? ?, （ ） The chemical potential Until now we have confined our discussion to closed physical systems， which cannot exchange matter with their surroundings. We turn our attention in this chapter to open systems, in which the quantity of matter is not fixed. Supposed that dn kilomoles of matter
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