Can an object be heated no hotter than the temperature of the flame beneath it? …

Can an object be heated no hotter than the temperature of the flame beneath it? For example, if the temperature of a candle flame is 1770° C and the melting point of the solid being heated above it is 1800° C, would the solid ever melt if the flame were held under it long enough? — MR, Ohio

The answer is a qualified no. Heat always flows from hotter objects to colder objects, so the solid can’t get any hotter than the flame that’s heating it. But this observation is stems from the laws of thermodynamics, particularly the second law of thermodynamics. Unlike Newton’s laws of motion, which are rigid, inviolable laws that are never, even violated in our universe, the second law of thermodynamics is a statistical laws—it says that certain events are extremely unlikely but doesn’t say that they are truly impossible. The flow of heat from hotter to colder is a statistical law, not a rigid mechanical law. So it is possible, although extraordinarily unlikely, that heat can flow from the 1770° C flame to the 1799° C solid and warm that solid all the way to 1800° C. However, for any reasonable sized solid (say, more than 10 atoms), the possibility of this occurring is going to be so unbelievably small as to be ridiculous. It’s as unlikely as taken a crystal wineglass that has been crushed into dust and then dropping it on the floor and having the impact reassemble the wineglass into its original pristine form. The laws of motion don’t forbid such as fantastic result, but it sure would be unlikely. I’ve tried it several times myself, without success. But then, you’re not going to be able to melt your solid with a not-hot-enough flame, either. You’d have to wait a few ages of the universe just to have that solid climb a tiny fraction of a degree above the temperature of the flame. For 20 degrees… forget it.

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