# A radiator in a domestic heating system operates at a surface temperat

A radiator in a domestic heating system operates at a surface temperature of 55 C.
Determine the rate at which it emits radiant heat per unit area if it behaves as a black body ? why we did not square the temperature
I mean ( 273 + 55)^4

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SteamKing
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A radiator in a domestic heating system operates at a surface temperature of 55 C.
Determine the rate at which it emits radiant heat per unit area if it behaves as a black body ? why we did not square the temperature
I mean ( 273 + 55)^4

Because radiation is proportional to the fourth power of the absolute temperature, not the square.

See the Stefan-Boltzmann Law:

http://en.wikipedia.org/wiki/Stefan–Boltzmann_law

my question why in the answer we did not say ( ( 273 + 55)^4 ) not ( 273 + 55) without power 4

Maybe same reason they did not put the right order of magnitude for the Stefan-Boltzmann constant (10^(-8) in SI units).
It may be simply some typo(s). The result seem to be OK. So they did take the fourth power to get that number.

It must to make temperature with power 4 ?

Yes.

ok and this value 5.6697 X 10^-8 for what ?