sandler_sm_06_03

# sandler_sm_06_03 - 6 6.3 Start with eqn. (6.2-21): dU C dT...

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Unformatted text preview: 6 6.3 Start with eqn. (6.2-21): dU C dT T P T P dV V = + F H G I K J − L N M M O Q P P V ∂ ∂ . Thus ∂ ∂ U T C V F H G I K J = V ; ∂ ∂ ∂ ∂ ∂ ∂ U T C T P T P V T P V P F H G I K J = + F H G I K J − L N M M O Q P P F H G I K J V and ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ U T U T T P T P V T P V V P F H G I K J − F H G I K J = F H G I K J − L N M M O Q P P F H G I K J . (a) Ideal gas PV RT = T P T P U T U T V P ∂ ∂ ∂ ∂ ∂ ∂ V F H G I K J − = ⇒ F H G I K J = F H G I K J (b) van der Waals gas P RT V b a V = − − 2 ; ∂ ∂ P T R V b V F H G I K J = − ; ⇒ F H G I K J − L N M M O Q P P = T P T P a V V ∂ ∂ 2 Also: dP RdT V b RT V b dV a V dV = − − − ( ) + 2 3 2 ⇒ F H G I K J = − ( ) − ( ) − = − ( ) − − ( ) L N M O Q P ⇒ F H G I K J − F H G I K J = − ( ) − − ( ) = − ( ) − − ( ) − ∂ ∂ ∂ ∂ ∂ ∂ V T R V b RT V b a V T V b a V b RV u T u T a V T V b a V b RV aRV V b RTV a V b P P V 2 3 3 1 2 3 2 2 2 2...
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