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s7b
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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?
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?