The given power of a heated body

[C_Ovidiu]

I found in various manuals that the power given to the environment has the formula P=k*(T2-T0) . T0 being the temperature of the environment . Is this formula right ?
In other I found that the power given is P=kT^4, T being the temperature of the body . I'm confused !

 

[Shooting Star]

The first is the Newton’s law of cooling. It’s not a very accurate law. If the whole body can be assumed to be at a constant temp when it is cooling down, then this can be a reasonable approximation.

The second is Stefan-Boltzmann law, according to which radiation emitted by perfect black bodies is proportional to T^4. For real objects, some correction has to be introduced.

I have tried to keep the answers simple as not to confuse you further.

 

[C_Ovidiu]

Can you please confuse me a little bit more and tell me what aproximations are made so we can go from Stefan Boltzmann law to the Newton's law under specific circumstances . It's a pretty big difference thou.

 

[pervect]

The Stefan boltzman law relates to radiative heat transfer - it gives the total radiated power from a black body. Note that if the body is not black, it won't give good results. For instance, if you are interested in the radiation from a hot plasma, things get a lot more complicated, because the plasma is not a black body.

Newton's law of cooling is related to conductive cooling (and possibly convective cooling).

 

[Shooting Star]

As far as I know, Newton’s law of cooling is an empirical law, pertaining mostly to heat loss by conduction or forced convection, like air blowing over a hot object etc. The surface temperature of a body changes at a rate proportional to the difference between its temperature and the temperature of the surrounding environment. If the internal conductivity of an object is high compared to the rate at which it can lose heat from its surface, then this law is a good approximation. The temp will decay or rise exponentially. This law is about heat loss only.

Stefan-Boltzmann law pertains to the total radiant energy, made up of all frequencies of EM radiation, distributed according to Planck’s law, emitted by the surface of a black body. This will take place even in vacuum.