kyarazen wrote:whether it conducts through the base still depends on the material you sit your pot on. a flatter pot will still have a larger surface area than a round one for the same volume and not equal. there is no contradiction is there? i had always observed that flatter pots cool faster than tall pots.
would it be possible to have a 100ml pot of fixed surface area on the same volume in 2 shapes of sphere vs flat ellipsoid? you can mathematically derive it, just to give you some parameters you can consider the following semi axis of a = 10, b = 10, c= 10, that would give you a perfect round volume at approx 418x, surface area is 1200+, versus a flat spheroid of a = 14.1, b = 5, c = 14.1, volume approx 416x, surface area 1500+.
even in F1, clays were changing all the years. maybe the clay expert can share with us how it evolved from the early 50s to the 90s and which era did which clay appear and disappear
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I think everybody agrees (and the data in your blog shows it) that flatter pots cool faster.
To make a fair comparison we must compare pots of different shapes but equal volume. The reason being that, when hot water is poured in, the heat that is provided is (roughly) proportional to the mass of water held by the pot, that is, the pot's volume in ml = cm^3 = grams.
A spherical or ellipsoidal shape have rather ill defined contact area with the surfaces they sit on (mathematically it is just a point = zero area). I think a better model for a pot is a cylinder of height H and basal radius R.
The volume of the cylinder (pot) is V = pi R^2 H
The surface area of the cylinder is S = 2 pi R (R + H)
If we use the first equation to solve for H, and substitutes in the second
equation, we get the following law for the surface area as a function of the
basal radius:
S(R) = 2 pi R^2 + 2V/R
This a non-monotonic function of the basal radius, R. In particular, it has
a minimum for H = 2R, at which point the surface area equals 6 pi R^2, that is, one and a half times the surface area of a sphere of radius equal to R.
Below is a plot of S(R) normalized to the minimum of the surface area as a function of R divided by the basal radius at the minimum. It shows the non-monotonic behavior mentioned earlier.
The above considerations illustrate the rather simple fact that we can have two different cylindrical-shape pots of the same volume, one flat and one tall.
It then naturally follows that, if the heat loss is radiative and therefore proportional to the total surface area of the pot, then one can have two pots of the same volume but different shape (tall and flat) that will cool at (roughly) the same rate.
IMO, the only way out of this contradiction with the experience is to notice that a large fraction of the initial cooling happens conductively through the base of the pot by releasing heat to the surface it sits on. Since a flat pot has larger contact area with the latter than a tall pot, it should cool faster.
It is also natural to expect that heat conduction occurs dominantly through the bottom of the pot because it is in contact with a solid surface which can conduct heat much more efficiently than the air surrounding the pot. For the surface in contact with the air, the dominant mechanism is radiative, as pointed out above, but this should dissipate less heat for the relatively small temperature differences between the pot and the surrounding air.