Contents of Today S.J.T.U. Phase Transformation and Applications Review previous Equlibrium Thermodynamic activity Chemical equilibrium Gaseous equilibrium Solid-vapor equilibrium Sources of information on Chemical equilibrium and adiabatic flame temperature etc. 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 Contents of Today Review previous Equlibrium Thermodynamic activity Chemical equilibrium Gaseous equilibrium Solid-vapor equilibrium Sources of information on Chemical equilibrium and adiabatic flame temperature etc
Review previous lecture (1) S.J.T.U. Phase Transformation and Applications Condition of equilibrium Phase equilibrium相平衡/化学反应的平衡 W,e.1→2=0 42=41G2=G 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 Review previous lecture (1) Condition of equilibrium Phase equilibrium相平衡/化学反应的平衡 δWrev →21. = 0 1,2, = GG ii 1,2, μ = μii
Variation of vapor pressure with particle size S.J.T.U. Phase Transformation and Applications The pressure on a small droplet is the sum of the imposed gas pressure and the internal pressure generated by the surface tension of the material 2mrY=2△p 2Y A= ViPr RTIn Figure 4.7 The force holding two hemispheres together is 2mry:the force pushing them apart is mAP. where△P=2ylr. r) The vapor pressure above the small particles is greater than the vapor pressure In- 2Y above the large particles.Material would RT then move through the gas phase from small particles to larger ones.Coarsening SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin ecture 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 Variation of vapor pressure with particle size The pressure on a small droplet is the sum of the imposed gas pressure and the internal pressure generated by the surface tension of the material Δ= prr 2 2 πγπ r p 2γ =Δ e Tl RTpV π π = ln e l RT r V π γ π ln 2 ⎟ =⎠⎞ ⎜⎝⎛ ⎟⎠⎞ ⎜⎝⎛ = rRTV l e γ ππ 2 ln The vapor pressure above the small particles is greater than the vapor pressure above the large particles. Material would then move through the gas phase from small particles to larger ones. Coarsening
饱和蒸气压 S.J.T.U. Phase Transformation and Applications 饱和蒸气压概念 将一杯纯溶液置于密闭的钟 罩内，一定时间后液面将有 液相 气相 所下降，直到罩内气体压力 达到一定数值为止。此时的 A G(A) P1 气体压力称为该液体的饱和 蒸气压，简称蒸气压。分子 B G(B) P2 运动学，蒸发与凝聚的速度 相等时，气液两相达到动态 平衡条件 平衡。 G(A,liquid)=G(gas,P1) 。 饱和蒸气压的应用 G(B,liquid)=G(gas,P2) 一凝聚态某组元的化学势 4G(A-→B,liquid)=4G(gas,P1→P2) 一化学反应气相的化学势 4G(gas,P1→P2)=P7dG ·例子 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 饱和蒸气压 • 饱和蒸气压概念 – 将一杯纯溶液置于密闭的钟 罩内，一定时间后液面将有 所下降，直到罩内气体压力 达到一定数值为止。此时的 气体压力称为该液体的饱和 蒸气压，简称蒸气压。分子 运动学，蒸发与凝聚的速度 相等时，气液两相达到动态 平衡。 • 饱和蒸气压的应用 – 凝聚态某组元的化学势 – 化学反应气相的化学势 • 例子 液相 气相 A G(A) P1 B G(B) P2 G( A,liquid ) G( = gas,P1 ) G( B,liquid ) G( = gas,P2 ) 平衡条件 ΔG( A B,liquid ) G( →= → Δ gas,P1 P2 ) P2 P1 ΔG( gas,P1 P2 ) dG → = ∫
Second-order transition S.J.T.U. Phase Transformation and Applications First derivatives of G with respect to T and p are continuous and the second derivatives of G with respect to T and P are discontinuous S=SB S=S(T,p) dS dT dp T dS = dp 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 First derivatives of G with respect to T and p are continuous and the second derivatives of G with respect to T and P are discontinuous BA = SS = ( , pTSS ) dp p S dT T S Sd p T ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ = dp TV dT TC Sd p p ⎟⎠⎞ ⎜⎝⎛ ∂∂ −= p p TS TC ⎟⎠⎞ ⎜⎝⎛ ∂∂ =
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