[amelius]

That model doesn't explain the relatively sharp drop in the beginning.

[spiralcoaster]

It absolutely does. The model that came closest simply used that model twice in the same equation. One for the cup and one for the air.

[coder68]

It does? There is a fast drop followed by a long decay, exponential in fact. The cooling rate is proportional to the temperature difference, so the drop is sharpest at the very beginning when the object is hottest.

[amelius]

I mean that initial drop doesn't look like it is part of the same exponential decay.

[kbelder]

https://teatrade.co.uk/learning/physics-of-teh-tarik-foam.ht...

Apparently the act of pouring has a huge effect on temperature because of the surface area :: volume ratio of the fluid as it streams (and turbulence after striking the bottom). The site above claims a single pour can drop it 20-30 degrees. There may be a similar effect here.

[bryan0]

Are you sure? I believe Newtown's law of cooling says the temperature will drop sharply at the beginning:

dT/dt = -k(T_0 - T_room)

so T(t) = T_room + (T_0 - T_room) exp(-kt)

exp(-x) has a fast drop off then levels off.

[cyberax]

Ha. My university professor used this in a lab to catch people who slack off.

There is another factor here: convection. Its speed depends on the viscosity of the fluid and the temperature difference both. And viscosity itself depends on the temperature, so you get this very sharp dropoff.

[amelius]

https://www.electronics-tutorials.ws/rc/time-constant.html

scroll down, these graphs just don't look similar.

[lacunary]

probably dominated by the cup as the ambient temperature initially and then as air/the counter top as the ambient temperature on the longer time scale, once the cup and the liquid near equilibrium