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5_60_lecture18

# 5_60_lecture18 - MIT OpenCourseWare http/ocw.mit.edu 5.60...

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MIT OpenCourseWare http://ocw.mit.edu 5.60 Thermodynamics & Kinetics Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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5.60 Spring 2008 Lecture #18 page 1 Phase Equilibria in a 1-Component System Goal: Understand the general phenomenology of phase transitions and phase coexistence conditions for a single component system. The Chemical Potential μ controls phase transitions and phase equilibria. Equilibrium condition – at equilibrium μ must be identical throughout the system When multiple phases are present in equilibrium, μ must be the same in all phases For example, consider two phases (liquid and solid) of water at a fixed (T, p). If μ s (T, p) = μ (T, p) then… liquid water and ice coexist If μ s (T, p) > μ (T, p) then… the water is in the liquid phase If μ s (T, p) < μ (T, p) then… the water is in the solid phase How does μ depend on T? Start with Fundamental Equation for Gibbs (hence for μ ) dG = − SdT + Vdp d μ = − SdT + Vdp μ = G n S and V are molar quantities μ ⎛ ∂ μ = − S = V ⎝ ∂ T p p T
5.60 Spring 2008 Lecture #18 page 2 3 rd Law tells us that S > 0 μ < 0 ⎝ ∂ T p negative slope T μ Also we know that S gas > S liquid > S solid , and μ gas μ liq μ solid = − S gas , = − S liq , = − S solid T p T p T p

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