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了-xm酸-1s The properties of the machine do not change at steady state dU and dS-0 G+PE+KE)2dn,2-G+PE+KE)dm =oWeo SJTU Thermodynamics of Materials Spring2007©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © 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 Spring2007©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © 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 Spring2o07©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © 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-RTdln 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 Spring2007©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © 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