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Originally Posted by pigglet
C4 : Just for my clarification, you are stating that molecular velocities would be minimum 30 m/s, not that natural convection flowrates would approach this velocity? I believe the question would be how many collisions occur, how fast does this translate into the transfer of energy, and does this transfer occur via conduction or convection? Perhaps I am incorrect?
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Molecular velocities. I got lazy and didn't want to actually bother calculating the actual conductive heat transfer in the water itself. You can do this with the density and some other junk to get the mean free path, which then with the velocity can give you the collision frequency. Assume a collision efficiency and you'll get a relative energy transfer per collision. Take this and the mean free path and the collision frequency and you can figure out how fast the energy is moving relative to the energy difference in the container. Again, I'm lazy and don't feel like doing this math nor do I feel like remembering the formulas (or looking them all up).
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Originally Posted by pigglet
Precisely. I disbelieve that the water in the bottles is instantaneoulsy isothermal at the beginning of the experiment, you do.
I agree that there is a small increase in SA/V ratio as the volume decreases, as far as the liquid phase is concerned. The statement you make above concerning the heat flux is also based on the concept of isothermal conditions in the liquid, so that becomes the crux of the discussion, as far as I can see.
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Well... We can do the above math and figure out which one of our assumptions is more correct, although I don't really feel like it (nor do I have the time now) so we'll leave it up in the air for now.
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Originally Posted by pigglet
I agree - and I understand what you are saying. At the same time, if
q=-k*del(T), and del(T) = 0, then this has certain implications. There will be no flux of heat within the phase, as there is no driving force for transport, as far as I understand it. How the phase responds to change is another issue, as far as I understand it, and nothing in reality approaches the idealized case of the responsive isothermal phase.
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Sure it does. Put a gas in a bottle, for example. That'll stay very isothermal, even with no convection. It's all dependent on molecular motion.
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Originally Posted by pigglet
I agree with these statement wholeheartedly, but question their validity outside the theoretical world. Heat, in the form of kinetic energy, must be transported out of the bottle somehow, and I claim that the primary mechanism is via conduction, although natural convection will undoubtedly occur. You seem to be stating that natural convection affects will dominate in some fashion, such that the contents in the bottle tend to stay at nearly isothermal conditions and warmer contents from the interior will tend to go to the cooler areas, due to density differences, and exchange heat at the boundaries. Is this a correct summation of your position? Otherwise, what mechanism due you propose is responsible for the heat transfer? I understand your molecular calculations, and although I didn't check the numbers I'll trust your accuracy. As I understand it, conduction is an averaged engineering approximation for molecular collisions due to their kinetics energy, convection tends to be dominated by density differences or pressure forces. Perhaps I am incorrect.
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Well, when I initially said that water inherently "flows" I meant moreso that it moves freely on a molecular level than it actaully flows as a whole. So yes, this molecular motion is still conduction and not convection. While water is a good insulator in the sense of it having a high specific heat, it is a poor "insulator of itself" if you will, because a large degree of molecular motion quickly evens out the heat within the system.
The heat removal through the plastic is obviously conduction as no mass is flowing through the plastic, but I'm sure you understand that.
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Originally Posted by pigglet
I am simply happy that we can dork out on heat transfer.  |
We most definitely are dorking out. Haha...