# SM_4B - Chapter 4 - Section B - Non-Numerical Solutions 4.5...

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Chapter 4 - Section B - Non-Numerical Solutions 4.5 For consistency with the problem statement, we rewrite Eq. (4.8) as: h C P i= A + B 2 T 1 + 1 ) + C 3 T 2 1 2 + τ + 1 ) where τ T 2 / T 1 . Define C P am as the value of C P evaluated at the arithmetic mean temperature T am . Then: C P am = A + BT am + CT 2 am where T am T 2 + T 1 2 = T 1 τ + T 1 2 = T 1 + 1 ) 2 and T 2 am = T 2 1 4 2 + 2 τ + 1 ) Whence, C P am = A + B 2 T 1 + 1 ) + C 4 T 2 1 2 + 2 τ + 1 ) Define δ as the difference between the two heat capacities: δ ≡h C P i− C P am = CT 2 1 µ τ 2 + τ + 1 3 τ 2 + 2 τ + 1 4 This readily reduces to: δ = CT 2 1 12 1 ) 2 Making the substitution τ = T 2 / T 1 yields the required answer. 4.6 For consistency with the problem statement, we rewrite Eq. (4.8) as h C P i= A + B 2 T 1 + 1 ) + D τ T 2 1 where τ T 2 / T 1 . Define C P am as the value of C P evaluated at the arithmetic mean temperature T am . Then:

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## This note was uploaded on 01/29/2011 for the course CHEM 101 taught by Professor Brown during the Spring '10 term at The University of Akron.

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SM_4B - Chapter 4 - Section B - Non-Numerical Solutions 4.5...

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