Thermo%204%202009%20short%20version

Thermo%204%202009%20short%20version - Mat E 510...

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Mat E 510 Thermodynamics of Solids Mat E 510 hermodynamics of Solids Thermodynamics of Solids Based on Prof. Roger Doherty’s course Lecture #4 (short version) ury Gogotsi Yury Gogotsi A.J. Drexel Nanotechnology Institute and Department of Materials Science & Engineering, Drexel University, Philadelphia, Pennsylvania, USA
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ffect of System Composition on Effect of System Composition on G Since G is an extensive property, it depends on the number of moles of species present: G = G ( T,P, n , n , n , …) i j k After differentiation: dG = ( G / T ) P, ni, nj, nk dT + ( G / P ) T, ni, nj, nk dP + ( G / n i ) P, T, nj, nk d n i + … If the number of moles remains constant during the process (closed system): dG = -SdT + VdP from which: ( G / T ) P, ni, nj, nk = -S ( G / P ) T, ni, nj, nk = V Substituting we get: dG = -SdT + VdP + ( G / n i ) P, T, nj, nk d n i + … = -SdT + VdP + Σ ( G / n i ) P, T, n j … d n i ( G / n i ) P, T, n j … = μ i - chemical potential of the species i (the rate of increase of G with n i , when the species I is added to the system at T, P = const. Thus, i=k dG = -SdT + VdP + Σ μ i d n i Fundamental equation, practically very useful i=1 The above equation expresses dependence of G as a function of P, T and composition
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he Chemical Potential The Chemical Potential The complete set of thermodynamic equations for an open system:
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Thermo%204%202009%20short%20version - Mat E 510...

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