# lec17 - 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 . ENTROPY AND THE 2 nd LAW 2 1 2 1 T bath dS ≥ 0 dS 1 ≥ dQ 1 / T bath 8.044 L17B1 S as a State Function Note: adiabatic ( ≡ d /Q = 0) constant S if the ⇒ change is quasistatic. This is the origin of the sub- script S on the adiabatic compressibility. 1 ∂V 1 ∂V κ T ≡ − V ∂P T κ S ≡ − V ∂P S 8.044 L17B2 Example A Hydrostatic System ∂S ∂S dS = ∂T V dT + ∂V T dV by expansion 1 P = T dU + T dV from dU = T dS − P dV 1 ∂U 1 ∂U = dT + + P dV T ∂T V T ∂V T by expansion of U But the cross derivatives of S must be equal. 8.044 L17B3 ∂ 1 ∂U 1 ∂ 2 U = V T ∂T V T T ∂V ∂T ∂ 1 ∂U 1 ∂U 1 ∂ 2 U 1 ∂P + P = − T 2 ∂V T + P + + T T ∂V T V T ∂V ∂T T ∂T V Equating these two expressions gives ∂U ∂P + P = T ∂V T ∂T V ∂U ∂P = T V − P ∂V T ∂T New Information! Does not contain S !...
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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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lec17 - MIT OpenCourseWare http/ocw.mit.edu 8.044...

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