3.1 The property relation S.J.T.0. Phase Transformation and Applications A closed system consisting of a homogeneous material with uniform properties throughout First law:dU=0+oW Second law: 82 ds= w T T Tds 80-Slw dU TdS+oW Slw =TdS &Wrex All the work terms: dU Tas-Pav Surface,electrical,stress effects,etc dH Tas +Vap 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 3.1 The property relation A closed system consisting of a homogeneous material with uniform properties throughout. First law: dU = δQ +δW Second law: T lw T Q dS δ δ = − TdS = δQ −δlw TdS Wrev dU = TdS +δW +δlw = +δ All the work terms: Surface, electrical, stress effects, etc dU = TdS − PdV dH = TdS +VdP
3.2 The Functions F and G(1) S.J.T.0. Phase Transformation and Applications F:the Helmholtz free energy G:the Gibbs free energy Measures of the work required to change a system from one state to another. dU TdS+oWrer Integrating at constant temperature W=△U-TAS=AU-△(TS)=△(U-TS) U-TS is defined as the Helmholtz free energy F Wrer =AF 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 3.2 The Functions F and G (1) F: the Helmholtz free energy G: the Gibbs free energy Measures of the work required to change a system from one state to another. dU = TdS +δWrev Integrating at constant temperature W U T S U (TS) (U TS) rev = Δ − Δ = Δ − Δ = Δ − U-TS is defined as the Helmholtz free energy F Wrev = ΔF
3.2 The Functions F and G(2) S.J.T.0. Phase Transformation and Applications G:the Gibbs free energy The useful work that can be done by the system must be calculated exclusive of the P-V term. oWre =oWre,-Pdv =du-Tds Integrating at constant temperature and pressure W=△U+PAV-T△S=△(U+PV-TS) =△(H-TS)=△G G=H-TS dF =-SdT-Pdv dG =-SdT +Vdp 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 3.2 The Functions F and G (2) G: the Gibbs free energy Wrev = Wrev − PdV = dU −TdS * δ δ The useful work that can be done by the system must be calculated exclusive of the P-V term. Integrating at constant temperature and pressure H TS G Wrev U P V T S U PV TS = Δ − = Δ = Δ + Δ − Δ = Δ + − ( ) ( ) * G = H −TS dG SdT VdP dF SdT PdV = − + = − −
3.2 The Functions F and G(3) S.J.T.0. Phase Transformation and Applications PV TS H=U+PV G=H-TS F=U-TS 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 3.2 The Functions F and G (3) F ≡U −TS G ≡ H −TS H ≡U + PV
3.2 The Functions F and G(4) S.J.T.0. Phase Transformation and Applications dU =TdS-Pdv dF=-SdT-Pdv Pt G H dG =-SdT +Vdp T S F U dH TdS +VdP 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 3.2 The Functions F and G (4) dU = TdS − PdV dF = −SdT − PdV dG = −SdT +VdP dH = TdS +VdP