# Energy math question

1. Sep 18, 2013

### courtneywetts

1. The problem statement, all variables and given/known data

The filament of typical light bulb is at a temperature of about 3,000 K. For a 100 W bulb, what is the surface area of the filament. You can assume that the entire 100 W goes into heating the filament and the filament has an emissivity of 1.

2. Relevant equations
The equation is P= e(sigma)(A)(T^4)
P is power
e is the emissivity
sigma is the constant 5.67 x 10 ^-5

3. The attempt at a solution

I have gotten to the point where i got 2.2 x 10^-5 m.
The answer in the back of the book is 22 mm^2.
I can't figure out how this was gotten.

2. Sep 18, 2013

### vela

Staff Emeritus
Your answer is a length; the book's answer is an area. Does that give you any ideas?

You need to convert the units.

3. Sep 18, 2013

### courtneywetts

Can someone help me convert these units?

4. Sep 19, 2013

### collinsmark

Where did you get this sigma number, and what are the units of the number? Are you sure the exponent on the 10 is correct?

I think your thinking of the Stefan–Boltzmann law.

$$P = \varepsilon \sigma A T^4$$
In SI units, $\sigma = 5.670400 \times 10^{-8} \ [\mathrm{\ J \ s^{-1} \ m^{-2} \ K^{-4}} \ ]$.

Or if you'd rather uses Watts instead of Joules/sec, you could say, $\sigma = 5.670400 \times 10^{-8} \ [\mathrm{\ W \ m^{-2} \ K^{-4}} \ ]$

Well, it seems that you used the correct "-8" in your $\sigma$ to get that value, instead of the "-5" that you had listed in the relevant equations section. :thumbs:

But you need to look at the units you ended up with. Is area measured in meters or square meters?

How many square millimeters are in one square meter?

Last edited: Sep 19, 2013