Homework Help: Power required to keep a sphere at 3300K

1. Apr 26, 2007

CurtisB

Hi guys, I have been trying to do this problem for a while and I don't have any idea what I am doing wrong. The question is

The emissivity of tungsten is 0.350 . A tungsten sphere with a radius of 1.96cm is suspended within a large evacuated enclosure whose walls are at a temperature of 300K.

What power input is required to maintain the sphere at a temperature of 3300K if heat conduction along the supports is neglected?

I used H = Aeσ(T^4 - To^4) and I get

H = 579657.66W is this right or am I completely missing the question?

2. Apr 26, 2007

CurtisB

I forgot to mention that you have to take the Stefan-Boltzmann constant to be 5.67×10−8

3. Apr 26, 2007

cesiumfrog

You've plugged numbers into a formula to calculate how much (net) energy the sphere radiates away each second (given its temperature and compared to the environment). Guess you'll need extra physical reasoning of your own to know how much power input is necessary.

What justified writing 579657.66, rather than 579657.67? :grumpy:

4. Apr 27, 2007

CurtisB

Sorry, I actually ment to write 579617.6619, I was looking at the wrong part of my working out. If the sphere radiates that much energy won't that amount ov energy be required to be put back in to maintain the sphere at that temperature?

EDIT- sorry I completely missed the homework section of the forum.

Last edited: Apr 27, 2007
5. Apr 27, 2007

lpfr

Yes. You are right.

6. Apr 27, 2007

Integral

Staff Emeritus
This is even more wrong. You are not given more then 3 significant digits. The correct answer would more like 5.8 e 5 W. Do not get into the habit of writing down every digit produced by your calculator. Pay attention to the precision of the given information.

7. Apr 27, 2007

CurtisB

Yeah, OK. The correct answer is 1.14 e 4, thats no where near any of my calculations, what am I missing here?

8. Apr 28, 2007

lpfr

I did the calculus with your numbers and I found this last value 1.14 e 4. You are making a mistake in the numerical computation.