I transcribed the data and fitted dual exponentials to it. When time t is in minutes, the data seem to follow T(t) = 20 + 25e^(-2.3*t) + 54e^(-0.034*t) T

I transcribed the data and fitted dual exponentials to it. When time t is in minutes, the data seem to follow T(t) = 20 + 25e^(-2.3*t) + 54e^(-0.034*t) This is very close to what the LLMs suggested. If I wanted to make an initial guess at this as accurate as the LLMs, what would I need to know? My interpretation of the coefficients is: (a) 20 ℃ represents the room temperature this will eventually reach. (b) 25 ℃ is how much of the temperature the mug will absorb as it is heating up. (c) The decay -2.3 represents how fast heat is transferred to the mug. (It will be halfway after 20 seconds.) (d) 54 ℃ is the differential between room temperature and starting temperature once we've accounted for the loss of 25 ℃ to heat the mug. (e) The decay -0.034 is how fast heat is transferred out of the mug to the room. (It will be halfway to room temperature after 20 minutes.) I'm okay with (a), and I could probably have guessed (d) once I know the other parameters. I can also sort of see myself figuring out (b): I would guess the heat capacity of the mug would be maybe 500 × 0.6 = 300 J/K, do the same for the water (4000×0.2 = 800 J/K). Some work later this comes out to a temperature loss of 20 degrees. Close enough. But even if I tried to use my intuition for how hot the mug feels as these processes go on, I would have ended up nowhere near -2.3 and -0.034 for the decay coefficients. What would I need to know about convection, mug materials, and air properties to guess that more accurately? Is it a neat coincidence or a good, very approximate rule of thumb that heat transfer to air is about 60× slower than that to ceramic-like solids?