I'm doing some sample problems to prepare for midterm and am stuck on this: 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?