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

1. Nov 14, 2013

### manal950

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

2. Nov 14, 2013

### SteamKing

Staff Emeritus
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

3. Nov 14, 2013

### manal950

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

4. Nov 14, 2013

### nasu

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.

5. Nov 14, 2013

### manal950

It must to make temperature with power 4 ?

6. Nov 14, 2013

### nasu

Yes.

7. Nov 14, 2013

### manal950

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

8. Nov 14, 2013