Special case:closed system,constant volume(2) S.J.T.U. Phase Transformation and Applications OWroy =(U:2-Unin,-T(2-Sain, aU At equilibrium S- as 月2=月 4,2=41 T,,nj≠n =4, Helmholtz free energy is used to derive the chemical potential in this constant volume case. Helmholtz and Gibbs free energy are not appreciably different in the case of solids,the work of theorists is thus made easier. SJTU Thermodynamics of Materials Spring20o7©X.J.Jin Lecture 7 equilibrium IPhase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2007 © X. J. Jin Lecture 7 equilibrium I Special case: closed system, constant volume (2) ( ) ( ) rev iiiiii 1,2, 1,2, dnSSTdnUUW ~ ~ ~ ~ δ −−−= nnVT ij ni U U ≠ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = ,, ~ nnVT ij ni S S ≠ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = ,, ~ 1,2, ~ ~ = FF ii At equilibrium μ = μii 1,2, i i nnVT ij n F F = μ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = ,, ≠ ~ Helmholtz free energy is used to derive the chemical potential in this constant volume case. Helmholtz and Gibbs free energy are not appreciably different in the case of solids, the work of theorists is thus made easier