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According to the Stefan-Boltzmann Law: $P=e\sigma AT^{4}$ For any body However, the power it releases when its surroundings has a temperature $T_s$ is $P=e\sigma A(T^{4}-T_{s}^{4})$ (assuming that the body is hotter than its surroundings). Why is the power emitted also dependent on the temperature of the surroundings, and Why isn't it $P=e\sigma A(T-T_{s})^{4}$?

(Also, I'm a high school physics student, so I'll have trouble understanding more complex concepts)

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$P=(\epsilon\sigma T^4)A$ is the power radiated by the object at a temperature $T$ irrespective of its surroundings. But the surroundings also emit radiation which is absorbed by the object which is proportional to the 4th power of the temperature of surroundings. So the net radiation emitted is the difference between the both.

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  • $\begingroup$ Why does is absorb energy from its surroundings? Doesn't heat always go from the hotter to the colder body? $\endgroup$ – AntPalmer Apr 11 at 7:13
  • $\begingroup$ @AntPalmer Not really. There is a NET transfer of heat from a hotter to a colder body. Any body would radiate and absorb energy, but whether it absorbs(or radiates) more is determined by whether its colder(or hotter) than its surroundings. $\endgroup$ – Boingboingboing Apr 11 at 7:19
  • $\begingroup$ @AmbicaGovind Got it now, thanks! $\endgroup$ – AntPalmer Apr 11 at 7:33
  • $\begingroup$ @AntPalmer: If the answer is to your satisfaction, please accept it. RNR will receive extra credit for positing an accepted answer. $\endgroup$ – Semoi Apr 11 at 8:30
  • $\begingroup$ Thanks man I appreciate that. $\endgroup$ – RNR Apr 11 at 9:18

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