Tungsten filament-finding length of coil

[laural]

Homework Statement

Tungsten wire has an emissivity of 0.35. A tungsten filament in a light bulb can be considered to emit light only from the sides of the filament (consider it a cylinder... they are usually wire "cylinders" wrapped into coils.). If the operating temperature of the filament of a small 18W light bulb is 2800 K and the diameter of the filament is 0.25 mm, then what is the length of the coil (in cm)? Assume the inside of the light bulb is under vaccuum, and that the ends of the filament do not contribute any heat radiation, since they are attached to the circuit...and assume other energy loss in the circuit is negligible.

Homework Equations

I will be using & to represent delta as I am unsure how change in is represented on keyboard.

&Q/&t = ekAT^4 where k is the Stefan-Boltzmann constant and = 5.67 x 10^-8 W/m^2K^4

The Attempt at a Solution

I plugged in 18W as the rate of change of heat per time, and the provided emissivity for e

Plugged 2800 K in for change in temperature.

So:

18W= (0.35)*(5.67 x 10^-8 W/m^2K^4
)*A*(2800^4 K)

Solved A= 1.48x10^-5

Then used A=(pi)r^2h,

And solved h= 0.30 cm

I have been struggling with this problem and am not sure if this is right. I would appreciate it if someone would review my work.

Thank-you.

Edit: I realized I was using the wrong formula. Changed.

 

[rl.bhat]

Check the calculation.
h = 1.48x10^-5/pix(0.125x10^-3)^2

 

[ogb p]

Your approach to the problem is correct, but there are a few minor errors in your calculations. First, when plugging in the values for the temperature and the Stefan-Boltzmann constant, make sure to use the absolute temperature in Kelvin, not the change in temperature. So it should be (2800 K)^4 instead of (2800^4 K).

Also, when solving for the area, you should use the diameter of the filament, not the radius. So it should be (pi)(0.25 mm)^2 instead of (pi)r^2.

Finally, when solving for the length of the coil, you should use the cross-sectional area of the filament, not the total surface area. So it should be (pi)(0.25 mm)^2 instead of 1.48x10^-5.

With these corrections, your final answer should be h = 0.60 cm. Overall, your approach and understanding of the problem is correct, but be careful to use the correct values and units in your calculations. Keep up the good work!