Lab Exercise: How do I make a logarithmic curve linear?by CarbonWater Tags: curve, exercise, linear, logarithmic 

#1
Jan2811, 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 replot 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
Jan2811, 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. 



#3
Feb111, 04:27 PM

P: 20

Thank you. That was what my professor was looking for.



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