Quote:
|
Originally Posted by pigglet
This is an important assumption as well...I believe that for significant flow to occur via natural convection, rather large density changes are required. I agree that this affect occurs, no doubt. The fluid is also tightly confined by the bottle, if it's a 20 oz., which also has affects on the flow. Natural convection, as I understand it, is much more pronounced in homogeneous gases than in homogeneous liquids.
|
It is, but it's still significant in liquids except at very low temperatures. Let's do some math, shall we? Say the water was at 10*C, (283K or 50*F) since the car was probably warmer than that when he stopped driving, but the water temperature had probably not equilibriated. One Kelvin is the energy equivalent to 1 cal/mol for water (it takes 1 cal to increase the temp of 1 mol of water 1 K). So assuming all the 273 K worth of energy goes into rotation since that's the point at which the molecule stops rotating and starts vibrating and the other 10 K worth of energy is in the form of movement. In all likelihood, it's probably more than that, but it's AT LEAST that much. So that makes 10 cal/mol which is equivalent to 41.84 Joules/mol. Now the kinetic energy formula tells us KE = 1/2*m*v^2. The mass of a mol of water is 18 grams, or 0.018 kg to keep standard units. So v = sqrt(2*KE / m) which equals a little over 68 meters per second. Granted, they are not actually moving across the bottle a few hundred times because they are colliding with each other and probably stay in relatively the same place, 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.
Quote:
|
Originally Posted by pigglet
This is the statment that I am not so sure about, at least in the way you mean it. I still believe that the temperature difference between, say 25 deg. C, and 0 deg. C is going to be a larger factor, at least at first. However, I will agree with you that the center of the liquid will be cooling due to conduction affects, and some convection affects, and this will tend to decrease the temperature gradient. However, any type of diffusive/conductive transport will be a function of the conductivity, the thermal mass (which is essentially the specific heat, correct?) and SA/V. I just don't think that the water is isothermal.
|
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.
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
Quote:
|
Originally Posted by pigglet
I'm not so concerned about the reduction in SA/V ratio, as the increase in heat flux on the smaller volume. I will wholeheartedly agree that there will be affects related simply to the smaller volume of the cylinder that is 1/4 full...as I said before, I just don't think that the cylinder is isothermal, and that the rate of cooling / phase change is strongly affected, although not completely dominated, by the rate of the heat flux within the liquid. Note that if the water is considered to be isothermal, then the heat flux within the cylinder is more or less zero, and this would imply that the entire bottle would freeze more or less instantly. As I said before, I've never actually performed the experiment in a controlled fashion, but I believe that the water tends to freeze first at the edges, and the phase boundary moves into the center of the volume. Is this not correct?
|
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.
The heat flux within the cylander being zero is not the case. 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.