12-平衡條件與理&ae

12-平衡條件與理&ae

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Unformatted text preview: Molecular BioEngineering Laboratory ioE 理想混合與濃度決定性質 ¡ 平衡條件 ¡ 理想混合與非理想混合 ¡ Chemical potential equation ¡ Colligative Properties BioE Fundamental Equations for a Multi- Component System components m i phases dn Vdp SdT dG dn pdV SdT dA dn Vdp TdS dH dn pdV TdS dU i i i i i i i i i i i i , , 3 , 2 , 1 , , , , 1 1 1 1 L L = = + + − = + − − = + + = + − = ∑∑ ∑∑ ∑∑ ∑∑ = = = = = = = = φ γ β α χ μ μ μ μ α χ χ χ α χ χ χ α χ χ χ α χ χ χ BioE Equilibrium Conditions At equilibrium, ( ) ( ) ( ) ( ) ( ) φ φ φ φ φ φ β β β β β β α α α α α α φ α χ χ χ μ μ μ μ μ μ μ μ μ μ m m m m m m m i i i p T V T p S V S V U dn dn dn dn dn dn dn dn dn dn dG dA dH dU dS + + + + + + + + + + + + + + + = = = = = = = ∑∑ = = L L L L 2 2 1 1 2 2 1 1 2 2 1 1 1 , , , , , , , BioE Spontaneous Reponses ( ) , > V U dS According to the 2nd law of thermodynamics when a spontaneous action happens in an isolated system. ) ( , < > − ⇒ > − + = + − = ∑∑ ∑∑ ∑∑ ∑∑ χ χ χ χ χ χ χ χ χ χ χ χ μ μ μ μ i i i i i i V U i i i i i i dn dn dS dn pdV dU TdS dn pdV TdS dU BioE Spontaneous Reactions ( ) ( ) ( ) ( ) ( ) , , , , , , , < < < < < > ∑ i i i p T V T p S V S V U dn dG dA dH dU dS μ BioE Phase Equilibrium φ β α φ β α φ β α φ α χ χ φ α χ χ φ α χ χ χ χ χ μ μ μ μ μ μ μ μ μ μ m m m m i i i dn dn dn dn = = = = = = = = = = = = = = ∑ ∑ ∑ ∑∑ = = = L L L L L 2 2 2 1 1 1 2 1 BioE Chemical equilibrium d ) ( d d d , d d , d d , d d , = + + − − = + + − − = − = + = − = + = − = − = − = − = + ⎯→ ⎯ + ∑ D C B A D C B A i i D D D C C C B B B A A A d c b a d c b a n d n d n n c n c n n b n b n n a n a n n dD cC bB aA μ μ μ μ ξ μ μ μ μ μ ξ ξ ξ ξ ξ ξ ξ ξ BioE ) ( , , , , , , = = = + + + + − − − − = = = = − = − = − = + + + → + + + ∑ ∑ ∑ i i i i i i r q P C B A i i i C B P C B A d d r q p c b a dn rd dn qd dn pd dn cd dn bd dn ad dn rR qQ pP cC bB aA μ ν ξ μ ν ξ μ μ μ μ μ μ μ ξ ξ ξ ξ ξ ξ L L L L L L BioE P , T , x i dependence of μ i ? ) , , , , ( , , , , , , , , = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ ∂ ∂ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ − = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ − = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ ∂ ∂ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ = = p T A id A A T A T x T id A x T id A A p A p x p id A x p id A A p T A id A x T id A x p id A id A B A id A x n V p G n p n S T G n T dx x dp p dT T d x x T p A A A A A A μ μ μ μ μ μ μ μ μ V S L BioE Chemical Potential, μ ¡ 理想混合與非理想混合...
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This note was uploaded on 11/11/2010 for the course CHE CH2005 taught by Professor 曹恒光 during the Spring '10 term at National Central University.

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12-平衡條件與理&ae

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