Quote:
Originally Posted by pigglet
I believe I understand your analogy, and thus I have this question: if you have a rectangular rainbow that is x units long, and another rectangular rainbow which is x/4 units long, with the same "non-dimensionalized" spectrum across them, I do not understand how this would not affect the color gradient, as I would think it would have to be "compressed" on the shorter rectangular rainbow. Would that compression not essentially represent a more severe temperature gradient, in the longitudinal direction? I wholeheartedly agree with your radial statements.
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It would be compressed, but think of the shape of the water bottle. The height is significantly greater than the diameter, even at 75% full. Therefore the radial temperature profile is much more significant than the vertical one because most of the heat transfer is going to occur through the sides. That's what I meant... Not that it doesn't change the profile, just that the change is relatively insignificant.
Oh, and sorry for the confusion between the bottle being open and opened. So much for convection.
Wait a minute... I believe we're all forgetting something here... Water is a LIQUID!!! Therefore it flows within itself (because of simple molecular motion) which to a great degree evens out whatever temperature gradient may have occured if the mass was solid. This being the case the rate of the temperature (energy) change is based only on the conductivity, thermal mass and surface area / volume ratio. Since the conductivity is constant and the surface area / volume change is not large (small increase?) then the only factor reamining to play a role is the thermal mass. The SA/volume ratio remaining relatively constant idea depends a lot on the shape of the top of the bottle. If it was semicircular (low SA/volume), then I may have to toss this idea out the window since this area of the bottle was the area vacated in the 3/4 full bottle (and yes, a smaller cylander would have a greater SA/V becasue the surface area of the ends does not change). Either way, I would expect the reduction in thermal mass to play a greater role than the increase in SA/vol.