190> 5.2.2 Chemical potentials In a phase transformation,the variation of free energy is taken into account. Chemical potentials is a measure of the ability of a given component from one phase to another. It can be expressed by HA=(om)T,P,nB A small amount of the component A(dnA)moves from a to B phase with T and P=constant.This implies a variation of the total free energy named dG' Assuming dna small enough not to vary the composition phase,it is valid the following equation(T,P,ng =constant) dG'=μadna Considering also B,the total variation of free energy is dG=μAdna+μBdng SINO-ITALIAN CAMPUS
SINO-ITALIAN CAMPUS 5.2.2 Chemical potentials In a phase transformation, the variation of free energy is taken into account. Chemical potentials is a measure of the ability of a given component from one phase to another. A small amount of the component A (dnA ) moves from α to β phase with T and P=constant. This implies a variation of the total free energy named dG’ Assuming dnA small enough not to vary the composition phase, it is valid the following equation (T, P ,nB =constant) dG’=μAdnA Considering also B, the total variation of free energy is dG=μAdnA+μBdnB It can be expressed by 𝜇𝐴 = ( 𝜕𝐺 ′ 𝜕𝑛𝐴 )𝑇,𝑃,𝑛𝐵
190> The molar fraction X= na+nB Therefore the variation of free energy will be: G=μaXa+μBXg Knowing the trend of G as function of Xg(and therefore also of XA=1-Xg the chemical potentials may be derived SINO-ITALIAN CAMPUS
SINO-ITALIAN CAMPUS The molar fraction : 𝑋𝐴 = 𝑛𝐴 𝑛𝐴+𝑛𝐵 Therefore the variation of free energy will be: G=μAXA+μBXB Knowing the trend of G as function of XB (and therefore also of XA=1-XB ) the chemical potentials may be derived
190 A了可7E Given the curve of Gibbs free energy-component, The chemical potentials of two components are derived from the tangent to the curve G vs Xg dG WA=G-XB dxB dG UB=G-XA A dxA Xa SINO-ITALIAN CAMPUS
SINO-ITALIAN CAMPUS Given the curve of Gibbs free energy-component, The chemical potentials of two components are derived from the tangent to the curve G vs XB 𝜇𝐴=G-𝑥𝐵 𝑑𝐺 𝑑𝑥𝐵 𝜇𝐵=G-𝑥𝐴 𝑑𝐺 𝑑𝑥𝐴
190 TONGJI UNIVERSTT AG#0 implies the presence of chemical potentials △Gmx Q (a) Two phases are under equilibrium when the single components have the same chemical potentials in the different phases SINO-ITALIAN CAMPUS
SINO-ITALIAN CAMPUS ΔG≠0 implies the presence of chemical potentials 𝜇𝐴 𝛼 = 𝜇𝐴 𝛽 𝜇𝐵 𝛼 = 𝜇𝐵 𝛽 Two phases are under equilibrium when the single components have the same chemical potentials in the different phases
190 ONGJT UN1vERS、 Multiphases are under equilibrium when the single components have the same chemical potentials in the different phases 4(1)=h(2)=4(3)==u:k) SINO-ITALIAN CAMPUS
SINO-ITALIAN CAMPUS Multiphases are under equilibrium when the single components have the same chemical potentials in the different phases 𝜇𝑖 (1) = 𝜇𝑖 (2)= 𝜇𝑖 (3)=…= 𝜇𝑖 (𝑘)