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If you have one body that radiates heat at a constant rate and, forgive my simple assumption, thus constant temperature, and a body that may absorb this heat, may the temperature of second body ever become higher than that of the first?

Simpler put, can temperature build up over time, as a result of say, initially "colder" second body unable to shed absorbed heat quickly enough, and so, with energy conservation and all, you'd have for example 100° heat source heating up something to twice that temperature? Factors would be environment that does not aid in heat dissipation, second body material dissipating heat slow enough, and others I may not know about -- in lay man terms where most of the energy given off by first body can only be absorbed by the second body, and not so much the environment.

The question arose from reading people debate about the famous Hudson river emergency aircraft landing incident with captain Sullenberger, where in particular some, in my opinion, rightfully claim the loss of life and collateral damage to populated areas should the aircraft attempt to land in Teterboro airport, would be much higher because, among other things, burning jet fuel would weaken building steel structures and cause their collapse etc. The counter claim was along the lines of that jet fuel burns at 800° while steel melts at just under twice that temperature, and so apparently burning jet fuel cannot melt steel. My limited understanding makes me think that it's more complex than that -- that jet fuel burning at 800° can cause temperature build up in steel in such vicinity and circumstances where steel material can't dissipate the absorbed heat quickly enough and the latter thus may reach melting point.

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    $\begingroup$ While 800$^\circ$ C is not enough to melt steel, it is hot enough to significantly weaken the strength of steel. If you weaken steel so it has only $1/3$ the strength the designers wanted it to have, things fall apart. $\endgroup$ – Peter Shor Dec 8 '18 at 15:22
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No, it can't. It was shown by Kirchhoff more than 150 years ago (it was the foundation of the theory of black-body radiation). He considered the extreme case when bodies may only exchange energy between each other and proved - using the second principle of thermodynamics - that whatever their radiation properties may be, at equilibrium they must reach the same temperature.

In the usual case the heated body will dissipate energy through other ways - conduction, radiation towards other bodies. So energy exchange will be less favourable, and it should be expected that the heated body will never reach the heater's temperature.

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  • $\begingroup$ Thank you, this was rather enlightening. I am marking this as the correct answer, even though I may not be the right person to assess the correctness here :) $\endgroup$ – amn Dec 8 '18 at 15:07

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