15:48:33 Graphical Representation(5) S.J.T.U. Phase Transformation and Applications Page 11/46 G-GA-G=RTIngA GA° G° GArel GA=μB 个 Ggrel A B GB=μB xB> Figure 7.5 Plot of G versus xs to show geometrical relationships between molar Gibbs free energy and mole fraction of B.(Note free choice of level for Ge and Ge.) SJTU Thermodynamics of Materials Spring2007©X.J.Jin Lecture 12 Solution Il
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 12 Solution II Page 11/46 15:48:33 Graphical Representation (5) A A A rel A =−= RTGGG lnα o
15:48:33 Relative Partial Molar Quantities (2) S.J.T.U. Phase Transformation and Applications Page 12/46 M=n4F+nBF公 For one mole of solution, 业M=xF+xBF8 rel U,F,G,H,S,V The equations for variations of thermodynamic properties with temperature, pressure,and so on apply to solutions as well as to pure components. dGrl =-SredT G=GA-GA=RTInaA SJTU Thermodynamics of Materials Spring2007©X.J.Jin Lecture 12 Solution Il
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 12 Solution II Page 12/46 15:48:33 Relative Partial Molar Quantities (2) rel B B rel AM A += VnVnV rel B B rel M A A += VxVxV dTSGd rel rel −= A A A rel A =−= RTGGG lnα o For one mole of solution, U, F, G, H, S, V The equations for variations of thermodynamic properties with temperature, pressure, and so on apply to solutions as well as to pure components
15:48:33 Enthalpy of Mixing:Ideal Solution S.J.T.U. Phase Transformation and Applications Page 13/46 To summarize,for an ideal solution: Gw=RT∑xhx HM=0 SM=-R∑xlnx Ey =0 SJTU Thermodynamics of Materials Spring2007©X.J.Jin Lecture 12 Solution Il
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 12 Solution II Page 13/46 15:48:33 Enthalpy of Mixing: Ideal Solution To summarize, for an ideal solution: = ∑ i M ii ln xxRTG −= ∑ i M ii ln xxRS H M = 0 = 0 V M
15:48:33 Graphical Representation S.J.T.U. Phase Transformation and Applications Page 14/46 Line? Slope =o 个 8→ 8 (a) (c) Slope=-∞ T T2 8→ A B B (d) b Figure 7.4 Molar properties for an ideal solu- tion A-B:(a)volume of mixing,(b)enthalpy of mixing,(c)entropy of mixing,and (d) Gibbs free energy of mixing. SJTU Thermodynamics of Materials Spring 2007 ©X.J.Jin Lecture 12 Solution Il
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 12 Solution II Page 14/46 15:48:33 Graphical Representation Line?
15:48:33 S.J.T.U. Phase Transformation and Applications Page 15/46 V+xa =7B OxB)T.P XA V-XB7 xB)T.P xB XA Pur Pu A B XB> Figure 7.3 Plot of V versus xB to show geometrical relationships in an A-B solution. SJTU Thermodynamics of Materials Spring2007©X.J.Jin Lecture 12 Solution Il
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 12 Solution II Page 15/46 15:48:33 A B PT B V x V xV = ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ − , B B PT A V x V xV = ⎟⎟⎠⎞ ⎜⎜⎝⎛∂∂ +