Lab Exercise: How do I make a logarithmic curve linear?

  1. 1. The problem statement, all variables and given/known data
    In a certain experiment, the power (P) radiated by a light bulb filament was measured as a function of the filament's absolute temperature (T).

    Data:
    P(W)
    0.45
    0.95
    1.8
    3.5
    5.6

    T(K)
    1000
    1200
    1500
    1800
    2000

    (a) Plot the data (Done)

    (b) Assume a power function and re-plot the data.

    2. Relevant equations

    Unsure.

    3. The attempt at a solution

    I plotted the data and it looks like a natural logarithm. I'm not sure what to do next. Raising each T value to the power of 2 straightens out the curve a bit but not completely. Is that what it means to assume a power function? If a power function is y=kx^a, how do I know which exact a to take and where do I get k from? Thanks.
     
  2. jcsd
  3. Delphi51

    Delphi51 3,410
    Homework Helper

    Suppose P = T^n.
    Then ln(P) = ln(T^n) = n*ln(T).
    If you graph your data as ln(P) vs ln(T), (and the data is perfect) you will get a straight line with slope n. Imperfect data (isn't it always?), the slope of a trend line is the best value for n.
     
  4. Thank you. That was what my professor was looking for.
     
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