The given power of a heated body

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Discussion Overview

The discussion revolves around the formulas for the power emitted by a heated body, specifically comparing Newton's law of cooling and the Stefan-Boltzmann law. Participants explore the contexts in which each formula applies, including assumptions and limitations related to heat transfer mechanisms.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant presents two formulas for power: P = k*(T2 - T0) and P = kT^4, expressing confusion about their validity.
  • Another participant identifies the first formula as Newton’s law of cooling, noting it is an approximation valid under certain conditions, while the second is the Stefan-Boltzmann law, which applies to black bodies and requires corrections for real objects.
  • A request is made for clarification on the approximations that allow the transition from the Stefan-Boltzmann law to Newton's law under specific circumstances, highlighting the perceived significant difference between the two laws.
  • Further clarification is provided that the Stefan-Boltzmann law pertains to radiative heat transfer from black bodies, while Newton's law relates to conductive and convective cooling, emphasizing the empirical nature of the latter.
  • It is noted that Newton’s law is applicable when the internal conductivity of an object is high compared to its heat loss rate, and that it describes heat loss rather than total energy emission.

Areas of Agreement / Disagreement

Participants express differing views on the applicability and accuracy of Newton's law of cooling versus the Stefan-Boltzmann law, with no consensus reached on the conditions under which each law is valid.

Contextual Notes

Participants mention that the accuracy of Newton's law depends on assumptions about temperature constancy and the nature of the heat transfer (conductive vs. radiative), as well as the characteristics of the body in question (e.g., black body vs. real object).

C_Ovidiu
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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 !
 
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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.
 
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.
 
The Stefan Boltzmann 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).
 
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.
 

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