I'm doing some sample problems to prepare for midterm and am stuck on this:(adsbygoogle = window.adsbygoogle || []).push({});

The question talked about many materials at low temperatures obeying Debye's Law C=A(t/θ)^3

it said that for a diamond θ is 1860K and asked to evaluate the specific heats at 20K and 100K.

For this I just used that formula given. The part I'm having trouble with is how much heat is required to heat one mole of diamond between 20K and 100K.

I know that

To heat the diamond from 20 to 21 K, you need:

0.0024 J/molK

from 21 to 22 K, you probably need a little more

0.0026 J/molK ( more or less)

and so on until you heat it from 99 to 100 K where you need:

0.301 J/molK

so you need to add up

0.0024 + 0.0026 + ... +.................. + 0.301 to get to the final answer - it should probably look like:

(0.0024 + 0.301) / 2 x (100 - 20 K) = 12.136 J/mol

But this is not the correct answer. How can I apply calculus in order to obtain a more correct answer?

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# Calculating heat

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