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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