How to find emissivity of tungsten from ln graph?

[dinospamoni]

Homework Statement

I'm doing a lab where I'm trying to find the emissivity of a tungsten filament. I measured voltage and current of a bulb with a tungsten filament and found the power. Then I plotted Power vs Temperature^4 and used the slope along with surface area and Boltzmann's constant to find the emissivity. But I am expected to plot ln(P) vs ln(T) and find the emissivity and I can't quite figure out how to do that.

Homework Equations

I plotted it bas on this equation

ln(P) = ln(a) +n ln(T)

which was derived from the equation

P = aT^n

The Attempt at a Solution

I'm lost for this part. I've found everything else I'm supposed to except for this. i found n to be close enough to 4 and can find a from the intercept, but I'm not really sure what a stands for. Is that the emissivity?

 

[haruspex]

P = aT^n

Looks incomplete. At http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html it gives P = AeσT⁴, where σ is a constant, A is area and e is emissivity.

 

[RTW69]

It looks like a=Aeσ. Finding the Surface area of the tungsten element might be tricky. Perhaps you need to measure the resistance of the element, estimate length and determine surface area.

 

[dinospamoni]

Ah of course that makes tons of sense. I have the surface area so now I have everything I need. Thanks!