lec18 - MIT OpenCourseWare http/ocw.mit.edu 8.044...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 8.044 Statistical Physics I Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Maxwell Relations ∂E ∂E dE ( S, V ) = ∂S V dS + ∂V S dV expansion = T dS − P dV 1 st and 2 nd laws ∂T ∂P ⇒ ∂V S = − ∂S V 8.044 L18B1 ∂T dE ( S, L ) = T dS + F dL = ∂ F ⇒ ∂L S ∂S L ∂T ∂H dE ( S, M ) = T dS + HdM = ⇒ ∂M S ∂S M Observe: d ( T S ) = T dS + SdT d ( P V ) = P dV + V dP 8.044 L18B2 Helmholtz Free Energy F ≡ E − T S ∂S ∂P dF = − SdT − P dV ⇒ ∂V T = ∂T V Enthalpy H ≡ E + P V ∂T ∂V dH = T dS + V dP ⇒ ∂P S = ∂S P 8.044 L18B3 Gibbs Free Energy G ≡ E + P V − T S ∂S ∂V dG = − SdT + V dP = ⇒ − ∂P T ∂T P E , F , H and G are called ”thermodynamic potentials”. 8.044 L18B4 The Magic Square Mnemonic-V S x E F dE = T dS + Xdx -T ∂S ∂V ( − 1) = ( − 1)( − 1) H P G ∂P T (+1) ∂T P X 8.044 L18B5 Homework problem 6-2, A Strange Chain l F F L = N l tanh( l F /kT ) For small extensions 1 α = − T 8.044 L18B5b Example Elastic Rod...
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lec18 - MIT OpenCourseWare http/ocw.mit.edu 8.044...

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