3.3 Chemical Potentials (1) S.J.T.0. Phase Transformation and Applications Closed systems consisting of a homogeneous material with uniform properties throughout. U=U(S,V) -S =-P av dU aU dv &G as =-S =V aP dU Tds-Pdv OH =T as aU aU =T =-P as av H U SJTU Thermodynamics of Materials Fall 2012 ©X.J.Jin Lecture 5 property relation
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2012 © X. J. Jin Lecture 5 property relation 3.3 Chemical Potentials (1) Closed systems consisting of a homogeneous material with uniform properties throughout. dU = TdS − PdV dV V U dS S U dU U U S V V S ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ = = ( , ) P V U T S U V S ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ P V F S T F V T ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ V P G S T G P T ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = − ⎠⎞ ⎜⎝⎛ ∂∂ V P H T S H P S ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂
3.3 Chemical Potentials(2) S.J.T.0. Phase Transformation and Applications The thermodynamic equations will be extended to deal with changes in composition through additions of mass The equations are used especially for the treatment of solutions and chemical equilibria, where molar compositions are important.We will denote mass by the letter,n,number of moles. U=U(S,V,n;) dU aU as s+ + dn; S,V,n;≠n H dU=TdS-PaW+∑ aU dn; S,V,ni≠ni U SJTU Thermodynamics of Materials Fall 2012 ©X.J.Jin Lecture 5 property relation
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Fall 2012 © X. J. Jin Lecture 5 property relation 3.3 Chemical Potentials (2) The thermodynamic equations will be extended to deal with changes in composition through additions of mass. ( , , )i U =U S V n The equations are used especially for the treatment of solutions and chemical equilibria, where molar compositions are important. We will denote mass by the letter, n, number of moles. i S V n n V n S n i i dn n U dV V U dS S U dU j i i i ≠ ∑ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ = , , , , i S V n n i i dn n U dU TdS PdV j ≠ i ∑ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = − + ,