PS5_08-Solution(2)

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

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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 VT V nRT qC T d T d V V qq qd T d V TV n R T CT V δ δδ =+ ⎛⎞ ⎜⎟ ⎝⎠ == satisfy the requirement: V T XX ⎡⎤ ∂∂ = ⎢⎥ ⎣⎦ () rev 0 The expressions are not equal, so q is an inexact differential V V T T V V nRT nR V = = b) (McQ&S, 20-4) rev 0 q 0 The two expressions are equal, so is an exact differential V V T T V nR T = =
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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 EkT E B B B BB B B QN V E e V E e E V E kT Q Tk Q T EE Sk TT =Ω ⎛⎞ + ⎜⎟ ⎝⎠ +Ω =+ 3) (McQ&S, 20-25) 2 1 21 12 surr 0 ln ln 10 1 8.314 ln 13.4 2 0 since this process was carried out reversibly S0 1 3 rev rev V rev sys V sys tot tot sys nRT U q w Pdv dV V q VP nR Sd V n R n R TV V P J bar J Sm o l mol K bar K S SS δδ δ ∆= → = = = ∆= = = = = = ∫∫ .4 13.4 JJ KK =− 4) Calculate the increase in entropy (J/K) when 2.00 mol of a monatomic ideal gas (C v = 3/2 nR) are heated from 300 K to 600 K and simultaneously expanded from 30.0 L to 50.0 L 22 11 From Eq. 20.1 ( ) 33 ln ln 36 0 0 5 0 2 8.314 ln 2 8.314 ln 2 300 30 17.3 8.5 25. rev V rev V nRT qC T d T d V V T nR T d V V dT dV Sn R n R n R n R JK J L S mol mol mol K K mol K L S = + + = + + ⋅⋅ + = 8 J K
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Problem Set #5 -3- Note: Since entropy is a state function, you could also treat this as an isothermal
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PS5_08-Solution(2) - Chem 444B Homework Set #5 - Solutions...

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