Contents of Today S.J.T.U. Phase Transformation and Applications Review previous Condition of equilibrium Phase equilibrium First order transitions:variation of equilibrium pressure with temperature Clapeyron equation in vapor equilibria Variation of vapor pressure of a condensed phase with total applied pressure Variation of vapor pressure with particle size Second-order transition SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 7 equilibrium I Contents of Today Review previous Condition of equilibrium Phase equilibrium First order transitions: variation of equilibrium pressure with temperature Clapeyron equation in vapor equilibria Variation of vapor pressure of a condensed phase with total applied pressure Variation of vapor pressure with particle size Second-order transition
Review S.J.T.U. Phase Transformation and Applications Properties relations Entropy of Mixing,Partial Molar Quantities 热力学关系式的应用 p65.213 OAG =△V p ap Os aH aH S,o SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 7 equilibrium I Review Properties relations Entropy of Mixing，Partial Molar Quantities 热力学关系式的应用 T T P V P S ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ − = 0 ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ T VU p.65, 2.13 V p G T Δ= ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂Δ∂ T p pC ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ S pT ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ S T ⎟⎠⎞ ⎜⎝⎛ ∂∂σ T p V V ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ − 1 H S T ⎟⎠⎞ ⎜⎝⎛ ∂∂ σ εH S , ⎟⎠⎞ ⎜⎝⎛ ∂∂
Index of nomenclature S.J.T.U. Phase Transformation and Applications Equilibrium:平衡 Phase equilibrium:相平衡 First order transitions:一级相变 Second-order transition:二级相变 SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 7 equilibrium I Index of nomenclature Equilibrium: 平衡 Phase equilibrium: 相平衡 First order transitions: 一级相变 Second-order transition: 二级相变
Introduction to equilibrium S.J.T.U. Phase Transformation and Applications The concept of equilibrium is fundamental Stable,unchanging with time and certain properties of the system are uniform throughout The system may not be homogeneous in form -Co-existence of ice and water ·Phase A portion of matter that is uniform throughout,not only in chemical composition,but also in physical state The usefulness of many metallic,polymeric,and ceramic systems depends on the presence,at equilibrium,of various different phases in the material SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 7 equilibrium I Introduction to equilibrium • The concept of equilibrium is fundamental • Stable, unchanging with time and certain properties of the system are uniform throughout • The system may not be homogeneous in form – Co-existence of ice and water • Phase – A portion of matter that is uniform throughout, not only in chemical composition, but also in physical state – The usefulness of many metallic, polymeric, and ceramic systems depends on the presence, at equilibrium, of various different phases in the material
Condition of equilibrium S.J.T.U. Phase Transformation and Applications Two states are in equilibrium when no reversible work can be done by having the system change between those two states 2 OWrer.12 =0 MA Figure 4.1 Machine MA to trans- form mass m from state I to state 2. The temperatures in the two states must be equal .A consequence of the second law of thermodynamics Otherwise... SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 7 equilibrium I Condition of equilibrium • Two states are in equilibrium when no reversible work can be done by having the system change between those two states δWrev →21. = 0 • The temperatures in the two states must be equal •A consequence of the second law of thermodynamics •Otherwise…
Condition of equilibrium(2) S.J.T.U. Phase Transformation and Applications Deal with partial molar quantities First law +PE+KE)dn.-(H+PE+KE)dn2++W=du Second law 5n,1-S,2dn2+ hw =ds -7m+西aM-xm酸-1s The properties of the machine do not change at steady state dU and dS-0 G+PE+KE)dn2-G+PE+KE)dn =OWo SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 7 equilibrium I Condition of equilibrium (2) dS T lw T Q dnSdnS iiii =−+− δ δ 2,2,1,1, ( ) ++ i 1, i 1, ( ++− )i 2, i 2, δδ =++ dUWQdnKEPEHdnKEPEH Deal with partial molar quantities iiii 2,2,1,1, δδ −=+−+− TdSlwQdnSTdnST The properties of the machine do not change at steady state dU=0 and dS=0 First law Second law ( ) ( ) ++ ii 2,2, ++− ii 1,1, = δWdnKEPEGdnKEPEG rev
Condition of equilibrium(3) S.J.T.U. Phase Transformation and Applications (G+PE+KE)2dn-(G+PE+KE)dn,oWc Condition of equilibrium 8W,em1→2=0 G+PE+KE)dn,=G+PE+KE)dn At the same potential energy level and kinetic level G,2-Gn,=AG,=0G,2=G1 4,2=4,1 In term of the chemical potential of i States 1 and 2 are in equilibrium with respect to material i if the partial molar Gibbs free energy (or chemical potential)of i is the same in both states. SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 7 equilibrium I Condition of equilibrium (３) ( ) ( ) ++ 2, ii ++− 1, ii = δWdnKEPEGdnKEPEG rev Condition of equilibrium δWrev →21. = 0 ( ) ( ) ii ii ++ 2, ++= 1, dnKEPEGdnKEPEG ( ) 0 1,2, GdnGG iiii =Δ=− = GG ii 1,2, ii 1,2, At the same potential energy level and kinetic level μ = μ In term of the chemical potential of i States 1 and 2 are in equilibrium with respect to material i if the partial molar Gibbs free energy (or chemical potential) of i is the same in both states
Condition of equilibrium(4) S.J.T.U. Phase Transformation and Applications 4,2=4,1 For single-component (G2-G )dn =AGdn=8Wro If the difference in Gibbs free energy between the two states 1 and 2 is negative,then the reversible work term is negative. That means that the material may change spontaneously from state 1 to state 2 because no work needs to be done to force the change;in fact,work can be generated by the change.The potential to do so might be dissipated as lost work,but the potential to do reversible work exists. SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 7 equilibrium I Condition of equilibrium (4) μ = μii 1,2, ( ) − 12 = Δ = δWdnGdnGG rev For single-component If the difference in Gibbs free energy between the two states 1 and 2 is negative, then the reversible work term is negative. That means that the material may change spontaneously from state 1 to state 2 because no work needs to be done to force the change; in fact, work can be generated by the change. The potential to do so might be dissipated as lost work, but the potential to do reversible work exists
Barometric equation S.J.T.U. Phase Transformation and Applications The points 1 and 2 are at different altitudes.If the two are at equilibrium. G2-G1+Mg(22-21)=0 Figure 4.2 Equilibrium between top and bottom of a column of gas at constant temperature. At constant temperature,assuring ideal gas behavior dG-Vdp-RTdp-RTd(n p) G2-G RTIn P2 p RTIn P2+Mg(2-1)=0 P Represent the variation of pressure with height for an ideal gas. SJTU Thermodynamics of Materials Spring20o6©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 7 equilibrium I Barometric equation • The points 1 and 2 are at different altitudes. If the two are at equilibrium. 0)( − 12 + − zzMgGG 12 = At constant temperature, assuring ideal gas behavior ( ) pRTddp p RT dpVGd === ln 1 2 12 ln p p =− RTGG 12 0)(ln 1 2 zzMg =−+ p p RT ⎥⎦⎤ ⎢⎣⎡ 12 −−= zz 12 )(exp RTMg pp Represent the variation of pressure with height for an ideal gas
Phase equilibrium S.J.T.U. Phase Transformation and Applications When a material composed of a single component exists in different physical states,the two states will be at equilibrium when the molar Gibbs free energies of the two states are equal. SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 7 equilibrium I Phase equilibrium When a material composed of a single component exists in different physical states, the two states will be at equilibrium when the molar Gibbs free energies of the two states are equal