Lecture 4 - Legendre Transforms Consider y=y(x) with a...

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Legendre Transforms Consider y=y(x) with a slope p=p(x) y x y,x φ p p, φ φ (p)= y – p x φ (p) is the Legendre transform, where y = y(x), x = x(p) and p is the independent variable φ h = - = h h for more than 1-variable, the Legendre Transform becomes ( ) j j j j j p y p x p x with
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μ = - + h = - + h h h , n , , Internal energy Na ( , , ) , What are the other state f n and are the natural variables fo tural Vari atura abl s E e r k j k j j j j j j j V S S V N j dE T dS p dV dN E S V N E E E dS dV dN S V N S V N l variables? = - - + = + + = - + + h h h ( , , ) ( , , ) ( , , ) j j j j j j j j j j j j dA S dT p dV dN A T V N dH T dS V dp dN H S p N dG S dT V dp dN G T p N Helmhotz energy Enthalpy energy Gibbs energy h = = = = h , , , , , , , , , , , , k j k k j k k j k k j k j j j j j S V N S p N V T N T p N E H A G N N N N
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w Internal constraint: couples to Ext. variables /no change on Total Value E 1 E 2 E T doesn’t change, E 1 ,E 2 changes (heat exchange) E X const. S’(E,
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Lecture 4 - Legendre Transforms Consider y=y(x) with a...

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