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

[teggenspiller]

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 absorption"
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 absorption 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 a lot...?

 

[ideasrule]

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 celsius 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 a lot...?

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