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# phys documents (dragged) 43 - Chapter 8 Thermodynamics 37...

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Chapter 8: Thermodynamics 37 8.9 Thermodynamic potential When the number of particles within a system changes this number becomes a third quantity of state. Because addition of matter usually takes place at constant p and T , G is the relevant quantity. If a system exists of more components this becomes: dG = - SdT + Vdp + ± i μ i dn i where μ = ² G n i ³ p,T,n j is called the thermodynamic potential. This is a partial quantity . For V holds: V = c ± i =1 n i ² V n i ³ n j ,p,T := c ± i =1 n i V i where V i is the partial volume of component i . The following holds: V m = ± i x i V i 0= ± i x i dV i where x i = n i /n is the molar fraction of component i . The molar volume of a mixture of two components can be a concave line in a V - x 2 diagram: the mixing contracts the volume. The thermodynamic potentials are not independent in a multiple-phase system. It can be derived that i n i i = - + , this gives at constant p and T : i x i i =0 (Gibbs-Duhmen).
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