PS5_08-Solution(2) - Chem 444B Homework Set#5 Solutions DUE...

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Problem Set #5 -1- Chem 444B Homework Set #5 - Solutions DUE: Friday, February 29, 2008 1) a) (McQ&S, 20-3) From Eq. 20.1 ( ) This can be compared to ( ) and From the discussion in Math Chapter H, an exact differential must rev V rev V T V V T nRT q C T dT dV V q q q dT dV T V q q nRT C T T V V δ δ δ δ δ δ δ δ δ δ = + = + = = satisfy the requirement: V T V T X X V T T V = ( ) rev ( ) 0 The expressions are not equal, so q is an inexact differential V V T T V C T V nRT nR T V V δ = ∂ ⎛ = b) (McQ&S, 20-4) rev ( ) 0 q 0 The two expressions are equal, so is an exact differential V V T T V C T V T nR T V T δ ∂ ⎛ = ∂ ⎛ =
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Problem Set #5 -2- 2) (McQ&S, 20-22) ( ) ( ) ( ) / / B B 2 , , , , when there's only 1 term in the summation ln ln , , ln From Eq. 20.43, S=k ln S=k ln ln ln B B E k T E E k T B B B B B B B Q N V E e Q N V E e E Q N V E k T Q T k Q T E E T k k T k T E E S k T T S k = = Ω = + + Ω − = + Ω − = 3) (McQ&S, 20-25) ( ) 2 1 2 1 1 2 surr 0 ln ln 10 1 8.314 ln 13.4 2 0 since this process was carried out reversibly S 0 13 rev rev V rev sys V sys tot tot sys nRT U q w Pdv dV V q V P nR S dV nR nR T V V P J bar J S mol mol K bar K S S S δ δ δ = = − = = = = = = = = =
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