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 Thermodynamics of Solids Based on Prof. Roger Doherty’s course Lecture #4 (short version) Yury Gogotsi A.J. Drexel Nanotechnology Institute and Department of Materials Science & Engineering, Drexel University, Phil d l hi P l i USA Philadelphia, Pennsylvania, USA
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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 i , n j , n 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, nj… d n i ( G / n i ) P, T, nj… = μ i - chemical potential of the species i (the rate of increase f G ith h th i I i dd d t th t t T P t of 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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The Chemical Potential The complete set of thermodynamic equations for an open system: dU = TdS – PdV + Σ μ i dn i dH = TdS + VdP + Σ μ i dn i dA = -SdT – PdV + Σ μ i dn i dG = -SdT + VdP + Σ μ i dn i From the first law, dU = δ q – δ w , δ
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