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Calculating heat

  1. Oct 17, 2011 #1

    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?
     
  2. jcsd
  3. Oct 17, 2011 #2
    Well, I have not met that Debye dude, but I think that you need to simply integrate and evaluate the expression at the two limits

    your integral would result in something like this: [A/(θ)^3] T^4/4

    evaluate that expression at 100 and 20 and subtract such numbers.

    does this help? maybe?
     
  4. Oct 30, 2011 #3

    s7b

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    This makes more sense then my attempt. Thanks :)
     
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