How to Calculate Temperature Using Stefan's Law?

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SUMMARY

The discussion focuses on calculating temperature using Stefan's Law, specifically addressing the relationship between power, surface area, emissivity, and temperature. The user seeks clarification on whether to take the result of the equation to the 1/4th power after calculating power divided by the product of Stefan's constant, surface area, and emissivity. The confusion arises from a significant error in the power calculation, which is noted to be 94%. The correct application of the formula is confirmed, emphasizing the importance of accurate power measurements when determining temperature.

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  • Understanding of Stefan-Boltzmann Law
  • Knowledge of emissivity and its impact on thermal radiation
  • Familiarity with power calculations in watts
  • Basic algebra for manipulating equations
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Laconic
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Well I have a problem where I have calculated the power in watts, and I know the surface area and emissivity, so I am trying to calculate the temperature using Stefan's Law. So here is my question, and this is basically reassurance. The temperature from the equation is to the 4th power so when I take the Power over Stefan's constant * Surface Area * Emissivity do I then go and take it to the 1/4th power. I think I have just confused myself, and the reason I am questioning it is that I get a huge difference in what my answer should be. This may be in part to a 94% error on my power calculation, but I am measuring the temperature of the sun. Any guidance is appreciated.

Thanks.
 
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Yes. In general,

A = X^{n} \rightarrow X = A^{\frac{1}{n}}
 

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