# lec11 - MIT OpenCourseWare http:/ocw.mit.edu 8.044...

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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 .

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Thermodynamics focuses on state functions: P, V, M, S ,... Nature often gives us response functions (derivatives): 1 ± ∂V ² 1 ± ∂V ² 1 ± ∂V ² α V ∂T P κ T ≡− V ∂P T κ S ≡− V ∂P adiabatic ± ² ∂M χ T ∂H T 8.044 L11B1
± ² ± ² Example Non-ideal gas Given Gas ideal gas for large T & V ∂P Nk = ∂T V V Nb ∂P NkT 2 aN 2 = + ∂V T ( V Nb ) 2 V 3 Find P 8.044 L11B2

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∂P ± ² ∂P ± dP = ² dV + dT ∂V T ∂T V ² ± ² ± ³ ∂P ³ Nk P = ∂T V dT + f ( V )= V Nb dT + f ( V ) NkT = ( V Nb ) + f ( V ) 8.044 L11B3
± ² ∂P NkT NkT 2 aN 2 = ( V Nb ) 2 + ³ f ± ( ´µ V ) = ( V Nb ) 2 + ∂V T V 3 ³ ´µ · 2 aN 2 aN 2 f ( V )= dV = + c V 3 V 2 NkT aN 2 P = ( V Nb ) V + c 2 but c =0 since P NkT /V as V →∞ 8.044 L11B4

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U Observational fact final W initial
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## This note was uploaded on 11/08/2011 for the course PHYSICS 8.004 taught by Professor Staff during the Spring '08 term at MIT.

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lec11 - MIT OpenCourseWare http:/ocw.mit.edu 8.044...

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