Power required to keep a sphere at 3300K

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To maintain a tungsten sphere at 3300K, the power input required is determined by the Stefan-Boltzmann law, factoring in the sphere's emissivity and the surrounding temperature. Initial calculations yielded a power output of 579657.66W, but this was later corrected to 579617.6619W due to miscalculations. The discussion emphasizes the need to account for the energy radiated away by the sphere, which must be matched by the power input to maintain its temperature. Participants highlighted the importance of significant figures in reporting calculations, suggesting a more accurate result around 1.14 e 4W. Overall, the key takeaway is the necessity of precise calculations and understanding the energy balance for thermal systems.
CurtisB
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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?
 
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I forgot to mention that you have to take the Stefan-Boltzmann constant to be 5.67×10−8
 
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?
 
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 into maintain the sphere at that temperature?

EDIT- sorry I completely missed the homework section of the forum.
 
Last edited:
CurtisB said:
If the sphere radiates that much energy won't that amount ov energy be required to be put back into maintain the sphere at that temperature?
Yes. You are right.
 
CurtisB said:
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 into maintain the sphere at that temperature?

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

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

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