If the heat capacity of a substance is correctly represented by an equation of the form, 
show that the error resulting when 
is assumed equal to 
evaluated at the arithmetic mean of the, initial and final temperatures is 
What will be an ideal response?
For consistency with the problem statement, as
where
DefineCPam as the value of CP evaluated at the arithmetic mean temperature 
Then:
Where
Whence,
Define ? as the difference between the two heat capacities:
This readily reduces to: 
yields the required answer.
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