111505

# 111505 - BE.342/442 Tuesday, November 15, 2005 Topics...

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In a homogeneous multicomponent system, all extensive properties can be related by U = U(S,V,N i ,…N r ,Q) U S V , N i , ..., N r , Q T U V S , N i , ..., N r , Q ≡− P U N i V , S , Q µ U Q S , N i ,..., N r , V F j Where U is the internal energy, V is the volume, N i is the number of moles of species i, S is entropy, and Q is charge. We can focus in on the internal energy of a surface by assuming zero volume and zero moles on the interface. The intensive variables are defined as the partial derivatives of the internal energy with respect to their conjugate extensive variables, with all other variables held constant. This is how we define the interfacial surface tension γ LV , interfacial chemical potential µ i LV , interfacial surface temperature T LV , and interfacial electrical potential φ LV . The differential form of the interface internal energy can then be written for a liquid-vapor interface as the Gibbs dividing surface equation: dU LV = T LV dS LV + γ LV dA LV + Σµ i LV dN i LV + φ LV dQ LV Rearranging, we obtain the Gibbs Absorption Equation: γ LV = -SdT LV - ΣΓ i d µ i LV - q LV d φ LV Here, Γ is the surface fraction due to non-adsorbed chains. The total entropy of the system is the sum of the entropies of the liquid phase, the vapor phase,
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## This note was uploaded on 11/11/2011 for the course BIO 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.

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111505 - BE.342/442 Tuesday, November 15, 2005 Topics...

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