10-mathematics manupulation

# 10-mathematics manupulation - Mathematical manupulation in...

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Mathematical manupulation in Thermodynamics ± Exact differential and Maxwell relation ± Δ U, Δ H, Δ S calculations for van der Waals gases ± Δ U, Δ H, Δ S calculations for Berthelot gases ± Joule Thomson coefficient

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Three techniques ± Conditions for exact differential ± Divide through rule ± Cyclic rule
Conditions for exact differential y x x y x y y M x x M y dy y M dx x M dM y x M M = + = = then al. differenti exact an is only ) , ( if al. differenti exact an is then if Qdy Pdx dM x Q y P y x + = =

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VdP SdT dG PdV SdT dA VdP TdS dH PdV TdS dU TS H Q TS U A PV U H + = = + = = + Basic Equations of Thermodynamics
Maxwell s Relations P T V T P S V S T V P S T P V S S V P T S P V T = = = =

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Divide through rule y y s s s s s t x P t M x y Q P x M t y Q t x P t M Qdy Pdx dM = + = + = + = al, differenti exact an is if
P P P V V V P T T V T T T S T C T H T S T C T U T V T V V P S T P H P T P T P V S T V U = = = = = + = = = Applications of divide through rules

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V V V T T P T V T P T P T P T T V U T T U V V C = = = = 2 2 P P P T T P T P T V T T V T V T P H T T H P P C = = = = 2 2 Pressure and volume dependence of Heat Capacity
A. Calculations for van der Waals gas 2 2 V a n nb V nRT P = 2 T T R C ig vm γβ α + + = 2 2 2 2 0 V a n P T P T T P nb V nR T P V V V = = =

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Δ U, Δ
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10-mathematics manupulation - Mathematical manupulation in...

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