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Unformatted text preview: Lecture 17 20 .110/5.60/2.772 Fall 2005 1 Phase Equilibria: One component systems Phase diagrams Clapeyron Equation Phase Rule Phase Equilibria in a One Component System Goal : Understand the general phenomenology of phase transitions and phase coexistence conditions for a single component system. The Chemical Potential controls phase transitions and phase equilibria, as well as equilibrium in chemical reactions. Know that at equilibrium, of each component is the same everywhere in the system If have multiple phases i , must have same value in every phase. Here well deal with one component systems only. Remember our definition of : n G = Fundamental equation: Vdp SdT dG + = divide by n dp V dT S d + = (T,P) dp p dT T d T P + = This allows us to say that S T P = and V p T = Why are we interested in ? Phase with the lowest value of is the most stable phase 20.110J / 2.772J / 5.601J Thermodynamics of Biomolecular Systems Instructors: Linda G. Griffith, Kimberly Hamad-Schifferli, Moungi G. Bawendi, Robert W. Field Lecture 17 20 .110/5.60/2.772 Fall 2005 2 For example, consider two phases (liquid and solid) of water at a fixed (T, p). If s (T, p) = l (T, p) then liquid water and ice coexist If s (T, p) > l (T, p) then the water is in the liquid phase If s (T, p) < l (T, p) then the water is in the solid phase How does (T)? Slope of line is entropy s P s S T = l P l S T = g P g S T = steepest negative shallowest negative S gas >> S liq >S solid at a given T, pick the lowest value Note also: @ T=T m , solid and liquid phases coexist s (T, p) = l (T, p) Now, want to describe phase properties as a function of state variables, (p,T)....
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- Spring '06