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
as the value of 
evaluated at the arithmetic mean temperature 
As in the precedingproblem,
Whence,
Define ? as the difference between the two heat capacities:
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