Why Does the Stefan-Boltzmann Law Use Temperature to the Fourth Power?

AI Thread Summary
The discussion centers on the application of the Stefan-Boltzmann law in calculating the net energy transfer between a sphere and its environment. The sphere's temperature must be converted to Kelvin for accurate calculations, as using Celsius leads to errors. The law states that the power radiated is proportional to the fourth power of the absolute temperature, which arises from integrating Planck's law across all frequencies and angles. Participants clarify that the temperatures of the sphere and environment should not be equal, as the sphere will absorb energy from the hotter environment until thermal equilibrium is reached. Understanding the fourth power relationship is crucial for accurate thermal radiation calculations.
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Homework Statement


a sphere of radius 1/2meter, temperature 27*C, and emmisisvity 0.85 is located in an environment of 77*C. What is net flow of energy transferred in 1 second.


Homework Equations


So in my notes i have notes that say "heat transfer by radiation":
P= stefans constant * Area sphere * emisivity * T^4

stef's constant= 5.67*10^-8 W/m^2 K^4
A= area
T= absolute kelvin temp
e= emmisivity
and Area of Sphere= 4*pi*r^2

and "Heat by absorbtion"
when i suppose by Conservation energy these values would be equal..
however the equation is the same except for the T values show

T^4- Te^4

Te= temp of the environment



The Attempt at a Solution



As i have been writing this i realized where I went wrong. I used Celcius temps instead of KELVIN temps! however, can anyone explain to me/give me an example that i can think of, why the Temperatures are to the FOURTh power? that certainly seems like a alot...?
 
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when i suppose by Conservation energy these values would be equal..
however the equation is the same except for the T values show

No, the two values should definitely not be equal. The sphere's temperature is less than that of the environment, meaning the environment will transfer energy to the sphere until the two temperatures equalize.

As i have been writing this i realized where I went wrong. I used Celcius temps instead of KELVIN temps! however, can anyone explain to me/give me an example that i can think of, why the Temperatures are to the FOURTh power? that certainly seems like a alot...?

The Stefan-Boltzmann law comes from integrating Planck's law over all frequencies and all solid angles. See: http://en.wikipedia.org/wiki/Stefan–Boltzmann_law#Derivation_of_the_Stefan.E2.80.93Boltzmann_law
 
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