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

by CarbonWater
Tags: curve, exercise, linear, logarithmic
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CarbonWater
#1
Jan28-11, 05:16 PM
P: 20
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.
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Delphi51
#2
Jan28-11, 06:16 PM
HW Helper
P: 3,394
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.
CarbonWater
#3
Feb1-11, 04:27 PM
P: 20
Thank you. That was what my professor was looking for.


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