I haven't seen thermal diffusivity mentioned in the discussions about pans. It's the conductivity divided by density and heat capacity. It in effect determines how uniformly the object heats up. The Wiki article mentions a flash method for measuring it - apply a pulse of heat at one end of the sample, and measure the temperature change along its length. Think of that as a refined version of putting a pan on the burner for a bit, and measuring the temperature away from the burner.
For copper, it is 111 mm2/s
pure aluminum lower at 84, with alloys in the 60s and 70s
carbon steel 12
stainless steels around 4
iron is 23 (on the Wiki table), but this is probably pure iron. My guess is that cast iron is more like carbon steel, or maybe even lower
Air is around 20, as is steam. But water is 0.14
Since diffusivity of water is so much lower than the metals, it's the property of the water that determines bulking heating time, much more so than the pan's. Convection, and eventually boiling bubbles speed up the heating of the water. And the pattern of bubbles reflects diffusivity in the pan bottom.
This property came to my attention in a food science article discussing thermal properties of foods, ending with an example of a baked Alaska, where the low diffusivity of meringue and cake keep most of the ice cream frozen while the meringue is browned.
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