Condition of equilibrium S.J.T.0. 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 oW,e1→2=0 MA 回 Figure 4.1 Machine MA to trans- form mass m from state 1 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 Spring2008©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © 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 Wrev.12 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.0. Phase Transformation and Applications Deal with partial molar quantities First law (▣+PE+KE)dmu-(匠+PE+KE)2dn,2+2+oW=dU Second law S女5血9的 -TS dn +TS,.dn.2-80+lw=-TdS The operties of the machine do not change at steady state dU-0and dS-0 G+PE+KE)2dn2-G+PE+KE)dn =5Wrc SJTU Thermodynamics of Materials Spring2o08©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 7 equilibrium I Condition of equilibrium (2) dS T lw T Q Si dni Si dni ,1 ,1 ,2 ,2 H PE KE i,1 dni,1 H PE KEi,2 dni,2 Q W dU Deal with partial molar quantities TS dn TS dn Q lw TdS i,1 i,1 i,2 i,2 First law Second law The properties of the machine do not change at steady state dU=0 and dS=0 i i i i Wrev G PE KE ,2 dn ,2 G PE KE ,1 dn ,1
Condition of equilibrium (3 S.J.T.0. Phase Transformation and Applications G+PE+KE)2dn,-(G+PE+KE)dn,=oWc Condition of equilibrium 6Wem12=0 G+PE+KE)2dn,=(G+PE+KE)dn, At the same potential energy level and kinetic level (G,2-G.)din,=AG,=0 G,2=G 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 Spring2008©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 7 equilibrium I Condition of equilibrium (３) G PE KE i,2 dni G PE KE i,1 dni Wrev Condition of equilibrium Wrev.12 0 i i i i G PE KE dn G PE KE dn ,2 ,1 Gi,2 Gi,1 dni Gi 0 Gi,2 Gi,1 At the same potential energy level and kinetic level i,2 i,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
Condition of equilibrium(4) S.J.T.0. Phase Transformation and Applications 4,2=4,1 For single-component (G2-G)dn=AGdn=8W,e 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 Spring2008©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 7 equilibrium I Condition of equilibrium (4) i,2 i,1 G2 G1 dn Gdn Wrev 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
S.J.T.U. Phase Transformation and Applications Height level----Chemical potential 1 2 1 2 Non-equilibrium Equilibrium Wre Wre =0 SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 7 equilibrium I
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 7 equilibrium I Non-equilibrium Equilibrium 1 2 Height level ----Chemical potential Wrev 0 0 Wrev 1 2