Chapter 8: Thermodynamics378.9Thermodynamic potentialWhen the number of particles within a system changes this number becomes a third quantity of state. Becauseaddition of matter usually takes place at constantpandT,Gis the relevant quantity. If a system exists of morecomponents this becomes:dG=-SdT+Vdp+±iμidniwhereμ=²∂G∂ni³p,T,njis called the thermodynamic potential. This is apartial quantity. ForVholds:V=c±i=1ni²∂V∂ni³nj,p,T:=c±i=1niViwhereViis the partial volume of componenti. The following holds:Vm=±ixiVi0=±ixidViwherexi=ni/nis the molar fraction of componenti. The molar volume of a mixture of two componentscan be a concave line in aV-x2diagram: the mixing contracts the volume.The thermodynamic potentials are not independent in a multiple-phase system. It can be derived that∑inidμi=-+, this gives at constantpandT:∑ixidμi=0(Gibbs-Duhmen).
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