# l18 - 20.110J / 2.772J / 5.601J Thermodynamics of...

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Lecture 18 20 .110/5.60/2.772 1 Clausius Clapeyron equation Condensed phase equilibria CLAUSIUS-CLAPERYON EQUATION We derived the Clapeyron Equation last lecture: This is exact! Let’s examine this for equilibrium between solid-liquid and solid-solid phases. For example, fusion: fus fus V S dT dp coexist = ¸ ¹ · ¨ © § use fus fus S T H = We can make some assumptions about these types of phase equilibria. ³ ³ = ' 2 1 fus fus m m T T p p T dT V H dp assume H fus , V fus are independent of p,T ¸ ¸ ¹ · ¨ ¨ © § = m m fus fus T T V H p p ' 1 2 ln T m =melting temp @p 2 , T m =melting temp @ p 1 T m -T m ~0 (expect small change in T m ) ¸ ¸ ¹ · ¨ ¨ © § + = ¸ ¸ ¹ · ¨ ¨ © § + = ¸ ¸ ¹ · ¨ ¨ © § m m m m m m m m m T T T T T T T T T ' ' ' 1 ln ln ln Since fraction is small, then T T T T T T T m m m m m = ¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § ' ' ln Then β α ¸

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## This note was uploaded on 11/11/2011 for the course BIO 20.010j taught by Professor Lindagriffith during the Spring '06 term at MIT.

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l18 - 20.110J / 2.772J / 5.601J Thermodynamics of...

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