Lecture18A - Maxwell Relations and Non-ideality(22.3-5...

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Lecture 18 1 Maxwell Relations and Non-ideality (22.3-5) There are lots of mathematical tricks and games we can play V S V S U U dU TdS PdV dS dV S V U U T and P S V = - = + = = - but since then this is a Maxwell relation V S S V S V U U V S S V T P V S = = - Similarly for V T P S dA PdV SdT T V = - - =
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Lecture 18 2 Now for equations of state (which involve relationships between Pressure, Temperature, and Volume), it is very useful to express entropy and other functions using these new equations. at constant Temp T V V S P P dS dV V T T = = 2 1 1 so If V is very large, our gas is ideal. V V V P S dV T = ( 29 , ' (will write id for ideal) ideal V ideal V V P S T V S dV T - = 2 for vdW gas: V RT a P R P V b V T V b = - = - - ( 29 ' , ln id V id V id dV V b S T V S R R V b V b - - = = - -
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Lecture 18 3 For an ideal gas: V P RT R T T V V = = 2 1 2 1 ' ln for an isothermal process V V V dV S R R V V = = Earlier (from “fun” with math) we showed using: then solving for dS: V T U U dU TdS PdV dT dV T V = - = + 1 1 V T U U dS dT P dV T T T V = + + ( 29 1 from dA Maxwell relation T T V S U P
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