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 T V P T 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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lec17 - MIT OpenCourseWare http://ocw.mit.edu 8.044...

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