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now, think about diffusion, more specifically entorpy: movement of heat from a higher "concentration" source to a lower concentration source. this movement can be facilitated/sped up by larger differences in concentration.
since water at 90 degrees has a larger energy difference with a 0 degree environment than water at 70 degrees with a 0 degree environment, the water at 90 degrees will actually freeze faster, because the heat in the 90 degree water will diffuse/escape from the water much more quickly as a result of entropy.
Are you claiming that once the 90 degree water reaches 70, that it will then cool faster than water that simply started at 70?
Thought experiment:
Put 90 degree water in one freezer. Wait until it reaches 70. At that instant, you put some 70 degree water in another freezer.
Now you have two freezers, each with an identical container of 70 degree water.
What happens now? Why/how would the water in one freezer cool faster?
In my response to zmarsh below I attempted to encapsulate the above argument in a rigorous fashion. If there's an error in the math or logic, please point it out to me.
(And BTW, I was a double major math-chem until midway in my junior year at which time I realized that math was the place for me.)
If you're willing to believe in something like that, maybe we should talk about a bridge that I have for sale.
What it actually does is it cools down in really really tiny steps (infinitesimally small for the methematically minded). So it cools one really small step (it's not an actual step even, but it's easier to imagine if you view it as tiny tiny steps) and then cools another tiny step and so on, and the speed changes in equally extremely small steps. Now if you imagine these steps to become as small as they could possibly be you will see that the speed changes CONSTANTLY.
To sum up, once the water that was initially 90F reaches 70F it will at that point cool exactly as slowly as water that was 70F to begin with. Same with water that started at 95F or 110F or 75F, because the speed changes constantly and in tiny steps, not in big leaps and will always reach the same value at 70F.
You can imagine it a bit like the shape of a skateboard halfpipe (slow,gradual change in incline) vs stairs (flat, then a drop, then flat again and so on).
The compressor cycles according to the internal temperature of the freezing chamber. When you put more heat into one freezer than you do into the other, you trigger the thermostat to turn on the compressor in that freezer faster. There is hysteresis. *(did I spell that right?) in this process. The freezer puts more effort into removing heat than is needed to achieve freezing. That freezer will temporarily get colder than the other one. So the hotter water has more effort applied to removing its heat than the cooler water does. It can, therefore, indeed be frozen sooner.
If you were simply using a heat sink (such as a quantity of existing ice) to remove the heat from the water, this would not be so, but since you are using an active system, it is.
so if TH is the length of time for the hot water to reach 0 C, and TC is the length of time for the cold water to reach 0 C, and DT is the difference between those times, then
TC > TH ________because the cold water takes longer to reach 0 C, and
DT = TC - TH ____DT is how much more time it takes for the cold water to reach 0 C than it took for the hot water.
But since the hot water starts out at a higher temperature than the cold water did, the hot water will at some point in its cooling reach the temperature that the cold water started at. Let's call this time D. From there, the amount of time for the hot water to reach 0 C should be equal to TC, the amount of time for the cold water to reach 0 C. At this point in time the hot water has cooled to exactly the temperature that the cold water started at so from here it should take that same amount of time to reach 0 C.
Now we can represent the amount of time for the hot water to reach 0 C as:
TH = D + TC ______Because the hot water MUST at some time go through the temperature that the cold water started at.
Now substitute the right hand side of the second equation for TH in the first equation.
DT = TC - TH
DT = TC -(D + TC)
DT = TC -D -TC
DT = -D
But DT and D CANNOT be the negative of each other because they are both positive numbers representing durations.
So TC cannot be larger than TH.
Furthermore, TC must be larger than TH, because if they were ever equal that would mean that D were 0, i.e., at some pair of hot and cold temperatures, the hot water would have to cool INSTANTANEOUSLY to the lower temperature.
The next time you see a picture taken by the Hubble Space Telescope, THAT was the kind of thing I did for a living until I retired. (And NO, I was not involved with the flawed optics. I worked on the spacecraft itself, not the payload.)
This step contains the logical leap. Yes, the hot water temp MUST at some point be equal to the initial cold water temp, but those are temperatures. It's an assumption to say that the rates of temperature change will also be equal at that point.
If you think that my assumption is unwarranted, the onus is on you to provide some reason why you think that is the case.
I also assume that the force of gravity will remain relatively constant throughout the course of my day (subject to the known variations due to irregularities in the distribution of the Earth's mass).
Would you also question that assumption? If so, why? If not, why do you question my assumption that two identical pans of water in identical freezers will freeze at the same time?
just felt like contradicting someone on this glacial movement towards a eureka moment. dont take it personally.
spent three years plumbing before i decided an obligation to clear drains is not a recurrent theme i wanted in my life.
Or do you mean that the energy (in the form of heat) must leave the warm water?
"You'll get FAR more evaporation per minute in a freezer than you will in the average house."
It should evaporate at relatively the same rate(the only difference is that the water in the freezer would cool more rapidly thus reducing evaporation)
"Have you ever put a pot of hot water outside in the winter? it steams like CRAZY."
Its not evaporating more/faster.
(the "steam" isn't actually steam but rather a mist caused by the evaporating water vapor condensing back into water once it hits the cold air)