Second-order transition(2) S.J.T.U. Phase Transformation and Applications as-dr-o) p ds=dSB dS-dS-0-CCd-Wus-L.cdp" VA=VREV dp △Cp The thermal expansion dTeg VTe9△a coefficient does change! △O dTeg △B SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 9 Chemical equilibrium ll
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 9 Chemical equilibrium II Second-order transition (2) dp TV dT TC Sd p p ⎟⎠⎞ ⎜⎝⎛ ∂∂ −= A B = SdSd ( ) eq AABB eq eq ApBp A B dpVVdT T CC SdSd −− αα − ==− ,, 0 = BA =VVV Δα Δ = eq p eq eq TV C dT dp The thermal expansion coefficient does change! β α Δ Δ = eq eq dT dp
Superconductivity:an example S.J.T.U. Phase Transformation and Applications 2 C。-C,=-T.4 ≠0 atT-To Normal state Super conducting state Tc→ Figure 4.8 Critical temperature as a function of magnetic field for a superconducting material. SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 9 Chemical equilibrium Il
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 9 Chemical equilibrium II Superconductivity: an example 0 2 0 ⎟ ≠ ⎠⎞ ⎜⎝⎛ Η∂ −=− dT =TatT c sn VTCC cμ
Index of nomenclature S.J.T.U. Phase Transformation and Applications Activity:活度 Fugacity:逸度 Reference state/standard state:参考态/标准态 Equilibrium constant:平衡常数 Ellingham diagrams:Ellingham 化学反应的方向和限度 SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 9 Chemical equilibrium Il
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 9 Chemical equilibrium II Index of nomenclature Activity：活度 Fugacity：逸度 Reference state / standard state：参考态 / 标准态 Equilibrium constant：平衡常数 Ellingham diagrams： Ellingham图 化学反应的方向和限度
Introduction S.J.T.U. Phase Transformation and Applications Physical equilibrium. Chemical equilibrium. Activity Fugacity dG Vdp(dG =-SdT+VdP,withdT=0) dG=RT P -RTdInP P SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 9 Chemical equilibrium Il
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 9 Chemical equilibrium II Introduction Physical equilibrium. Chemical equilibrium. Activity Fugacity = ( = − + withdTVdPSdTdGVdPdG = )0, PRTd P dP RTGd == ln
5.1 THERMODYNAMIC ACTIVITY (1) S.J.T.U. Phase Transformation and Applications dG=VdP(dG=-SdT+Vdp,with dT=0) If the gas is ideal (RT/P) then dG=RT=RTd In P P For a real gas,we can define a function,fugacity (f),by analogy to pressure: dG=RTdInf Limf/P=1 P→0 AG=G2-G=RT"dinf=RTI f M-t RT'In SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 9 Chemical equilibrium Il
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 9 Chemical equilibrium II 5.1 THERMODYNAMIC ACTIVITY (1) = ( = − + , dTwithVdPSdTdGVdPdG = )0 If the gas is ideal then : = PRTV )/( PRTd P dP RTGd == ln For a real gas , we can define a function , fugacity (f) ,by analogy to pressure : = ln fRTdGd PLimf = 1/ P → 0 1 2 12 ln ln 2 1 f f RTfdRTGGG ff =−=Δ = ∫ 1 2 12 ln ff μμ =− RT