例子续1 S.J.T.U. Phase Transformation and Applications 系统达到平衡时，即 dG 0 因为dnB≠0 所以 哈=哈 上式表明，对于多组分多相系统的平衡条件是：“除系统中各 相的温度和压力必须相等外，任一组分在各相中的化学势也 必须相等。”即 4哈=4哈=…=哈 0相 B相 SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin Lecture 12 Solution I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 12 Solution I 例子续1 系统达到平衡时，即 dG = 0 因为 dnB ≠ 0 所以 αβ = μμ BB 上式表明，对于多组分多相系统的平衡条件是：“除系统中各 相的温度和压力必须相等外，任一组分在各相中的化学势也 必须相等。”即 βα γ BB "=== μμμ B α相 β相
例子续2 S.J.T.U. Phase Transformation and Applications 若上述转移过程可以实现，则 0相 β相 dG=(uu)(dng)< 因为dng>0 所以 哈<g 组分B有dn由o相 进入B相 上式表明物质总是由化学势较高的相自发转移到化学势较 低的相，直到该物质在两相中的化学势相等。 对比水与水位、电流与电势的关系，也有某种势的意思， 所以称为化学势 SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 12 Solution I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 12 Solution I 例子续2 上式表明物质总是由化学势较高的相自发转移到化学势较 低的相，直到该物质在两相中的化学势相等。 对比水与水位、电流与电势的关系，也有某种“势”的意思， 所以称为化学势 若上述转移过程可以实现，则 −= < 0))(( dG dnBBB αβ μμ 因为 所以 dnB > 0 αβ < μμ BB 组分B有dnB由α相 进入β相 α相 β相
化学势判据 S.J.T.U. Phase Transformation and Applications ∑4sdnB≤0 ∑4，d,≤0 这一判据式讨论具体的平衡规律、过程的方向与限度 SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 12 Solution I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 12 Solution I 这一判据式讨论具体的平衡规律、过程的方向与限度 ∑ ≤ 0 B μ dnBB 化学势判据 ∑ ≤ 0 i ii μ dn
P,V,Xi影响化学势 S.J.T.U. Phase Transformation and Applications 1,温度的影响 ∂G 29R =-S aT) ,xi 2,压力的影响 气相 aG RT =V L= dG=RTdln P aP P T,xi 3,组成的影响：偏摩尔Gibbs自由能 SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin Lecture 12 Solution I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 12 Solution I P, V, Xi影响化学势 S T G i xP ⎟ −= ⎠⎞ ⎜⎝⎛ ∂∂ , dT TC S P ∫ = 2980 0298 1，温度的影响 2，压力的影响 V P G i xT ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ , PRT V = 气相 = ln PRTdGd 3，组成的影响：偏摩尔Gibbs自由能
Thermodynamic activity(1) S.J.T.U. Phase Transformation and Applications Fugacity is defined for gases: dGi RTd(Infi) Thermodynamic activity of a component,i,is defined as: n0 The fugacity of the componentiin its standard state. The fugacity of a condensed phase is equal to the fugacity of the vapor phase in equilibrium with it. The fugacity of the vapor is equal to the pressure of the vapor,if the vapor in equilibrium with the condensed phase is ideal. SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 12 Solution I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 12 Solution I )(ln i i = fRTdGd D i i i f f α ≡ Thermodynamic activity (1) Fugacity is defined for gases: Thermodynamic activity of a component, i, is defined as: D i f The fugacity of the component i in its standard state. The fugacity of a condensed phase is equal to the fugacity of the vapor phase in equilibrium with it. The fugacity of the vapor is equal to the pressure of the vapor, if the vapor in equilibrium with the condensed phase is ideal