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Regression (I think) of Newton's Law of Cooling

  1. Mar 13, 2012 #1
    1. The problem statement, all variables and given/known data
    Using a data logger, I have collected data for two cooling cups: the temperature (c) at 1 second intervals. My task was to model this data using two methods.

    "METHOD 1: Use EXCEL or the regression analysis capability of your graphic calculator"
    "METHOD 2: Find the constants in the model (A0 and k) by constructing a linear function relating lny and t."

    I chose to use Excel for method 1. I have attached the spreadsheet.

    2. Relevant equations
    Newton's Law of Cooling: y=A0*e^kt


    3. The attempt at a solution
    I have attached the graphs that I have been able to produce (method 1) in a word document. I am unable to do method 2, as I'm really stuck for ideas.

    Thank-you! Any help is much appreciated :)
     

    Attached Files:

    • u1.doc
      u1.doc
      File size:
      118 KB
      Views:
      56
    • u1.xls
      u1.xls
      File size:
      43 KB
      Views:
      75
    Last edited: Mar 13, 2012
  2. jcsd
  3. Mar 13, 2012 #2

    Mark44

    Staff: Mentor

    For method 2, the idea is to find constants A0 and k for which lny = kt + A0. If you plot lny versus t, this equation represents a straight line.
     
  4. Mar 14, 2012 #3
    Thanks for your response!

    Would it be safe for me to assume that (from y= mx + c), k is equal to m and A0 is equal to c?
     
  5. Mar 14, 2012 #4

    Mark44

    Staff: Mentor

    Yes.
     
  6. Mar 14, 2012 #5
    Be careful! - Its really "c = ln(A0)"
     
  7. Mar 14, 2012 #6

    Mark44

    Staff: Mentor

    No, not if the OP is working with the equation lny = kt + A0.
     
  8. Mar 15, 2012 #7
    Yes, that is is correct, and I stand corrected. I was assumming the OP's original equation was, as he stated in "Relevant equations", of the form [itex]y = A_0 \cdot e^{kt}[/itex].
     
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