Physics Asked by Fritz Kuhn on June 21, 2021
Two scenarios:
Solid metal cylinder of $43^circ$ C is placed in room of $23^circ$ C
Identical solid metal cylinder of $3^circ$ C is placed in another (identical) room of $23^circ$ C at the same time.
Assume heat transfer by conduction (cylinder on the ground) is negligible. Which cylinder reaches equilibrium with the room faster? Do they reach it at approximately the same point in time?
Thanks! Just an interesting thought. I don’t need sleep. I need answers.
At the first order, they will reach at the same approximate time. The heat transfer due to convection is based on the difference between the surface temperature and the free air temperature, and is independent of their absolute values.
However, when one gets into the nitty gritty, an "it depends" starts to surface. We can't treat the cylinder as a bulk solid with uniform temperature. It will develop a gradient as it cools, hottest at the center and coolest at the edges. The steepness of this gradient will be defined by the thermal conductivity of the material, and that is a temperature dependent quantity. In metals, that quantity increases with temperature, but in non-metals it can be relatively constant. One also has to consider the radiative losses, which are proportional to $T^4$, so they do scale with temperature.
The effect of those details is left as an exercise to the reader. But to the first order, they will cool at the same rate.
Answered by Cort Ammon on June 21, 2021
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