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