For a non-sealed cup of hot liquid, the significant majority of cooling happens at the exposed surface with the air, through a mixture of convection and evaporation. Modeling the cooling as being proportional to total surface area would be pretty inaccurate, although there is definitely still some conduction through the cup/mug worth considering as well.
> For a non-sealed cup of hot liquid, the significant majority of cooling happens at the exposed surface with the air, through a mixture of convection and evaporation.
I don't know enough to argue with any confidence but this is very surprising to me. Ignoring for a moment the thermal conductivity of different mug materials, it seems like a large amount of energy would go toward heating the mug up to near liquid temperature rather quickly. Then you'd have at least as much heat loss between the mug and air (compared to exposed liquid and air).
The mug I imagine we're talking about is a ceramic mug, which I believe to have high thermal conductivity just based on what processor covers are made of. It also has plenty of mass.
If you're talking about an insulated mug obviously this changes. But just the fact that insulated mugs exist proves my point that a large amount of heat is lost through the mug...
