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Originally Posted by C4 Diesel
It is, but it's still significant in liquids except at very low temperatures.... but I would argue this is enough molecular motion to keep the bottle fairly isothermal. Even at 2*C you would get about 30 m/s.
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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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To answer your question... Thermal mass is the specific heat multiplied out by the mass of the object in question and its temperature. It's basically a measurement of how much energy (heat) it has, but in this case they are fairly interchangable since they relate directly to each other.
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Thank you - that is more or less what I was assuming, based on energy balances, etc.
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The way I see it, the actual temperature difference across the plastic will only matter if the water or the air is not considered to be isothermal isothermal (which I believe them both to be). Aside from that, I don't know how the temperature difference would effect the bottles differently.
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Precisely. I disbelieve that the water in the bottles is instantaneoulsy isothermal at the beginning of the experiment, you do.
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If the SA/V ratio did not change, then the heat flux would be proportionally less in the smaller volume than in the larger one due to the smaller surface, and not greater as you stated it. This actually supports the bottles reducing in temperature at the same rate. I take it this isn't actually what you meant, however, so I'll leave that one for you to think about again.
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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 (notwithstanding the post above concerning the affect of saliva / contamination on the freezing point of the liquid - let's assume the bottle was opened and the contents poured into a cup?)
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The heat flux within the cylander being zero is not the case.
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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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This would lead to the ouside freezing immediately and then insulating the rest of the mass. What an isothermal situation implies (under an ideal isothermal assumption) would be that the flux within the mass is INFINITE, that is as soon as there is a heat change in the system, the entire system instantly equilibriates itself. Whatever caused the change in heat still has to deal with the heat capacity of the mass, so the temperature of the mass and the environment would not instantly equilibriate, however.
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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.
Thank you for your responses. I am enjoying this conversation, and as coolhands stated above, regardless of whether I am correct or you are correct, or it is a melange of viewpoints that is correct, I am simply happy that we can dork out on heat transfer.
