Power required to keep a sphere at 3300K

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Homework Help Overview

The problem involves calculating the power required to maintain a tungsten sphere at a high temperature of 3300K, given its emissivity and the temperature of the surrounding environment. The context is rooted in thermal radiation principles, specifically using the Stefan-Boltzmann law.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the Stefan-Boltzmann law to determine the power radiated by the sphere and the implications of that power for maintaining the sphere's temperature. Questions arise regarding the accuracy of numerical values and significant figures in calculations.

Discussion Status

The discussion is ongoing, with participants attempting to clarify their calculations and reasoning. Some have pointed out potential errors in numerical computations and the importance of significant figures, while others are exploring the relationship between the power radiated and the power required to maintain the sphere's temperature.

Contextual Notes

Participants note the need to consider significant figures in their calculations, as well as the assumption that heat conduction along the supports is negligible. There is also a mention of the specific value of the Stefan-Boltzmann constant to be used in the calculations.

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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