1 gal Milk freezes in 12 hrs thaws out in 3 days. WHY?

[cronxeh]

What is this 45 degrees nonsense? No refrigerator is kept at 45 degrees.

I said a box. Maybe his fridge is broken or one of those redneck fridges, or perhaps its in Arizona and the freon is missing

 

[Yeti08]

Even ignoring the wind chill factor, a normal refrigerator temperature of 36 F and an outside temperature of 20 F will make it take about three times as long to melt the milk as it takes to freeze it. The reason is the heat of fusion of water; see post #11.

Milk is a complex substance, a mix of water, proteins, and fats. Using water rather than milk, the difference in energy between 4.5 pounds of water (1 gallon) at 36 F and 4.5 pounds of ice at 20 F is about 690 BTU. Water has a high heat of fusion. The energy difference between 4.5 pounds of ice at 32 F and 4.5 pounds of water at 32 F is 645 BTU. Almost all (93.5%) of the heat transfer is freezing the water or melting the ice. Since 32 F - 20 F = 12 F and 36 F - 32 F = 4 F, the freezing will be three times faster than the melting process.

Add in a wind during the cooling and this factor of three can easily multiply to a factor of six.

I'm not sure I follow that either. The process may not be reversible, but the two points at 20F and 45F (to be consistent with other posts) have defined internal energies of 30345 and -347308 J/kg, respectively assuming atmospheric pressure. So the change in energy to go from one point to the other should be 1.426 MJ (1352 BTU) for 3.78 kg, and this should be the same regardless of the direction (hot to cold or cold to hot).

If what I said above is correct, then the reason would have to be difference in heat transfer such as the convection coefficient due to wind as others have mentioned. An additional possibility is that the process of freezing creates stratified layers based on temperature. Below 4.2C, the coldest water (by the way I'm assuming water for all my calculations) will be at the top and the warmest will be at the bottom to the water freezes from the top - this effect might speed up the heat transfer, at least by increasing the natural convection inside the container. As the ice then thaws, there will be a frozen core that won't be stratified by temperature (the bulk temperature remains 0C while two phases exist) and the solid will remain fairly centered in the container due to its structure (this is what I've observerd with thawing bottles at least...). The solid core will have a liquid surrounding that could act as an insulating barrier.

All this being said, it's alright to speculate, but I don't think there is enough information to say definitively. It would be more useful if this were a controlled experiment with known parameters.

 

[cronxeh]

So the change in energy to go from one point to the other should be 1.426 MJ (1352 BTU) for 3.78 kg, and this should be the same regardless of the direction (hot to cold or cold to hot)..

How did you get this?

 

[D H]

I'm confused about this. If we set up an ideal experiment where we froze a volume of water, storing the dumped energy, and then later, put that stored energy back into the water to melt it, we'd have completely reversed the process, right? In this ideal setup, would the melting process still take longer than the freezing process?

You haven't specified the problem fully. Is the water/ice staying at 32 F, or changing temperature as well as changing phase? What are the temperatures of the surrounding environment?

Almost all of the heat transfer in this process is melting ice at 32 F / freezing water at 32 F. That is the key to the problem. Reversibility is a red herring in this case.

The process may not be reversible, but the two points at 20F and 45F (to be consistent with other posts) have defined internal energies of 30345 and -347308 J/kg, respectively assuming atmospheric pressure. So the change in energy to go from one point to the other should be 1.426 MJ (1352 BTU) for 3.78 kg, and this should be the same regardless of the direction (hot to cold or cold to hot).

First point: Those numbers are (20F and 45F) are inconsistent with the observation.

Second point: Yes, the energy change is the same (absolute) in both directions. So what? That does not mean the warming and cooling times will be the same.

 

[Yeti08]

How did you get this?

Internal energy of water at 1 atm and 20F = -1428 kJ/kg. Internal energy of water at 1 atm and 45F = 30.34 kJ/kg. Given 1 gallon to be 3.78 kg that total change in energy comes out to about 1.43 MJ. (Data taken from EES)

First point: Those numbers are (20F and 45F) are inconsistent with the observation.

Those are the numbers from the original post, so that's what I used.

Second point: Yes, the energy change is the same (absolute) in both directions. So what? That does not mean the warming and cooling times will be the same.

My point is that just saying the heat of fusion is the answer doesn't explain anything since it is the same amount of energy both ways. Also, I never said it would freeze and warm in the same time period and went on to speculate on why.

 

[D H]

My point is that just saying the heat of fusion is the answer doesn't explain anything since it is the same amount of energy both ways.

It explains almost everything because almost all (93.5%) of the heat transfer is between the external environment and ice or water at 32F. The amount of energy being transferred, along with reversibility, is a red herring here.

Also, I never said it would freeze and warm in the same time period and went on to speculate on why.

The easiest explanation, however, is that the refrigerator temperature in the OP is wrong. Stick a thermometer in your fridge. What does it read?

 

[cronxeh]

Internal energy of water at 1 atm and 20F = -1428 kJ/kg. Internal energy of water at 1 atm and 45F = 30.34 kJ/kg. Given 1 gallon to be 3.78 kg that total change in energy comes out to about 1.43 MJ. (Data taken from EES).

So my post #4 in this thread is wrong is what you saying?

 

[benhou]

Cmon you guys are PhDs.. you seriously can't solve this?

How do you know they are PhDs? Just wondering... I want to know who goes to the physics forum since I am here and I never knew...

 

[D H]

So my post #4 in this thread is wrong is what you saying?

A minor problem with that post is the heat capacity of liquid milk (3.77 kJ/kg; cf 3.93 kJ/kg (see http://www.engineeringtoolbox.com/specific-heat-fluids-d_151.html).

That is a minor problem compared to the latent heat of fusion you used in that post, 84 kJ/kg. The value for water is 334 kJ/kg. While milk is not water, it is pretty close to water. I can't imagine that the dissolved salts and suspended proteins and fats reduce the heat of fusion by a factor of four.

 

[Yeti08]

It explains almost everything because almost all (93.5%) of the heat transfer is between the external environment and ice or water at 32F. The amount of energy being transferred, along with reversibility, is a red herring here.

That explains that most of the energy in the process is going towards the heat of fusion. That doesn't say why the rates would be different for heating and cooling. So the majority of heat transfer occurs while the milk is at 32F, why does this effect heat transfer? I see this as a problem of rates, whereas you're quoting quantities. Things like differing Grashof numbers (due to differing expansion coefficient and viscosity) and differing Prandtl numbers at the different air temperatures would change the free convection coefficients (assuming no substantial convection from wind, which is probably a poor assumption) thus possibly changing the freezing/thawing time.

The easiest explanation, however, is that the refrigerator temperature in the OP is wrong. Stick a thermometer in your fridge. What does it read?

I am well aware that most refrigerators are colder than the 45F quoted in the OP. However, that really shouldn't make a difference (as concerned with the reason for differing times) as long as the initial and final temperatures are the same. That is to say, if the initial and final temperature are the same, be it 35F, 45F or 85F, the time to reach 20F and back to the initial temperature should, at first glance, be the same. In my opinion, this was not a well controlled experiment, so all we can really do is speculate.

 

[D H]

That explains that most of the energy in the process is going towards the heat of fusion. That doesn't say why the rates would be different for heating and cooling. So the majority of heat transfer occurs while the milk is at 32F, why does this effect heat transfer? I see this as a problem of rates, whereas you're quoting quantities.

I've been talking about rates all along. Everyone else is bringing up red herrings such as the total energy transfer, reversibility, etc.

That is to say, if the initial and final temperature are the same, be it 35F, 45F or 85F, the time to reach 20F and back to the initial temperature should, at first glance, be the same.

The bulk of the heat transfer is in freezing the liquid milk / melting the frozen milk. To first order, the time it takes to accomplish this freezing/melting will be proportional to the absolute temperature difference between 0C and the outside/fridge. Freezing will occur faster than melting if the outside temperature is further below freezing than the 'fridge is above freezing. Freezing will occur slower than melting if the temperature differences are reversed (outside temp is closer to 0C than is the 'fridge temperature).

 

[Yeti08]

I've been talking about rates all along. Everyone else is bringing up red herrings such as the total energy transfer, reversibility, etc.



The bulk of the heat transfer is in freezing the liquid milk / melting the frozen milk. To first order, the time it takes to accomplish this freezing/melting will be proportional to the absolute temperature difference between 0C and the outside/fridge. Freezing will occur faster than melting if the outside temperature is further below freezing than the 'fridge is above freezing. Freezing will occur slower than melting if the temperature differences are reversed (outside temp is closer to 0C than is the 'fridge temperature).

Okay, now I see your point. I probably should have seen that myself...