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

1. Jan 10, 2010

### gary350

I take a gallon of milk out of the refrigerator the temperature of the milk is 45 deg F. I set the milk on the back porch at 6 pm. It is 20 deg F outside next morning at 6 am the milk is frozen solid.

I put the gallon of milk back into the 45 deg F refrigerator and it takes 3 days for it to thaw out.

Why???

2. Jan 11, 2010

### Staff: Mentor

If the temp stayed at 20 F, the answer is probably just wind.....though 45F seems a little high for a fridge.

3. Jan 11, 2010

### uart

Hi Gary. It may just be due to temperature differential asymmetry between freezing and thawing. I know you said 20F outside and 45F inside (and freezing point of milk is about 31F) but you know that the outside temperature will vary throughout the night and I suspect that it's actually getting somewhat colder than 20F in the early hours of the morning.

Also 45F sounds a little high for the inside fridge temperature, 36F to 40F would be more typical. Finally you may find the fridge internal temperature actually drops even further in response to having relatively large frozen object placed in it (especially if the fridge is infrequently opened and closed).

4. Jan 11, 2010

### cronxeh

I tried finding a solution, but I'm too tired to care, someone else can give it a shot

------------------------------------------------------------------------------
density of milk = 1035 kg/m^3
mass of milk= 3924 grams

Cp= 1.97 kJ/kg deg C below 0
Cp= 3.77 kJ/kg deg C above 0
delta T = 13.88 degrees
Latent heat of Fusion = 84 kJ/kg
thermal conductivity 0.17 J m^(-1) s^(-1) K^(-1) at 20° C

Starting conditions: -6.66 deg C
End conditions: 7.22 deg C
Enthalpies:
Q1= -6.66 C -> 0
Q2= Heat of fusion
Q3= 0-> 7.22 C

Q1= m*Cp*DeltaT = 3.924 kg * 6.66 C * 1.97 Kj / kg * C = 51.48 kJoules
Q2= 84 kJ/kg * 3.924 kg = 329.61 kJoules
Q3 = 3.924 kg * 7.22 C * 3.77 kJ/kg * C = 106.80 kJoules

Qtotal = Q1 + Q2 + Q3 = 487.89 Kjoules = 116608.51 calories

Estimating surface area of a carton of 1 gallon of milk..
Surface area of cylinder = 2*pi*r^2 + 2*pi*r*h
Since 1 gallon is 231 cubic inches, suppose the diameter is 4.4 inches, and height is 12 inches

(4.4*4.4*12=232). So the radius is 2.2 inches, and height is 12 inches.. Surface area = 497.62 sq. in.

Heat applied to carton of milk by convection (in 45 deg F heat): Q=hA(Ts-Ta)

Using Newton's law of cooling, time required to heat an object: t=mCp(Ts-Tf)/Q
------------------------------------------------------------------------------

Long story short I got 5 days on one attempt, you need to get the right h for the solution (h=Heat transfer coefficient ). The h will depend on milk jug/carton material (plastic or glass or metal), plus as others have mentioned introducing a frozen block into the fridge will drop the ambient temperature.

Last edited: Jan 11, 2010
5. Jan 11, 2010

### D H

Staff Emeritus
Was there a breeze blowing the night you placed the milk bottle outside? There is little, if any, wind inside a refrigerator. A breeze or a wind will significantly change the heat transfer rate.

6. Jan 11, 2010

### dacruick

He said the milk started in the 45F fridge. then he put it into the freezer, it froze, then he put it back into the fridge and it took 3 days.

My question is, did you leave it in the freezer for longer than the 12 hours, or did you measure 12 hours, leave it there, and put it in the fridge later. If you did that, it is possible for the frozen milk to be even colder.

If you measured the 12 hours, then put it back in the fridge then I have two hypotheses.

The first being something to do with the molecular structure of milk being different for frozen milk, and liquid milk.

and second, I remember from high school chemistry something about there being a certain amount of energy that during a phase change that is used up to change from phase to phase. So what im trying to say is that, maybe more energy is required to change phases back to liquid than there is for a phase change to solid. This also might have something to do with molecular structure.

These are just guesses though. And if you want to search up that phase change thing, my memory is pushing me to say that its called latent heat of fusion or something like that. Give it a shot, and let me know if you get an answer.

7. Jan 11, 2010

### MotoH

wrong.

Anyways, it would have just gotten colder and colder outside, so it was probably a ways below 20 F, and putting it into the fridge slowed down the warming process by about 40 degrees or so. It does make sense that it took longer to thaw than freeze because it wasn't extremely warm in the fridge, and we all know thawing something on the counter is faster than in the fridge.

EDIT:
Why did you put the milk on the back porch???

8. Jan 11, 2010

### D H

Staff Emeritus
Re-read the original post. He put the milk on the back porch, not in the freezer, for 12 hours.

9. Jan 11, 2010

### ChmDudeCB

Changing temperature outside, humidity differences, wind differences

10. Jan 11, 2010

### dacruick

oh, well in the case, you should do what i said haha

11. Jan 11, 2010

### Staff: Mentor

Note, any cooling below freezing or heating above isn't going to have much of an impact here because the latent heat of fusion is going to be an order of magnitude larger than even the heat required to change the temp by 20F

12. Jan 11, 2010

### cronxeh

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

I'm lacking thermodynamics background to come up with the solution, but from the looks of it, the Newton's law of (heating) is applicable to the convection heating in the fridge, but in addition you have surface conduction on the bottom of the milk carton at the contact with the fridge. If you take h to be between 1 and 5 (for there is no wind current in the fridge) you should get your answer.

13. Jan 11, 2010

### DaveC426913

OK wait. You can't solve it but you're OK knocking other people for not solving it because you think it must be easy. And you figure it probably involves conduction through the carton's bottom...

Got it.

14. Jan 11, 2010

### Staff: Mentor

I'm just a BS in ME...
Surface conduction is essentially nonexistent because the contact area of a milk carton is a tiny fraction of the surface area of the carton.

15. Jan 11, 2010

### cronxeh

No, I'm knocking lack of interest in this problem. I think its a fascinating problem and I'm having a hard time solving it. I think someone with a PhD will be able to do this in 10 minutes if he just tried.

Although it is a small area, the difference can still be hours when is taken in context of days. As milks thaws the ice will stay on the bottom in direct contact with the surface of the milk carton.

And HEY.. there are 270 views on this thread.. Who are you people?? Make yourselves known, contribute to the discussion!

Last edited: Jan 11, 2010
16. Jan 11, 2010

### DaveC426913

17. Jan 11, 2010

### cronxeh

Why won't I be sure about this? I said it, I must be somewhat sure of it, right?

18. Jan 11, 2010

### DaveC426913

Do you have reason to believe that milk-ice, being mostly water, would behave differently than water-ice?

19. Jan 11, 2010

### cronxeh

Yes. Oh, I'm sorry, you want my reason?

20. Jan 11, 2010

### DaveC426913

Sure.

21. Jan 11, 2010

### cronxeh

OK.. I think as milk freezes the fat and proteins and all heavy molecules float to the bottom, and as it thaws the water which is of lesser density than the milk, will float up, separating the milk and watery-milk. The iced milk with fats and proteins will be on the bottom.

Last edited: Jan 11, 2010
22. Jan 11, 2010

### DaveC426913

But fat floats in water...

Yes, model it. You're ten feet from the kitchen, a glass of milk and a freezer. But by all means, model it on your computer. :tongue2:

23. Jan 11, 2010

### cronxeh

When milk freezes it forms cryoglobulin with IgM and precipitates to the bottom.

I'm telling you, this is a fascinating problem! Not only you have difference in density with temperature, you have differences in temperature with temperature.

24. Jan 12, 2010

### dacruick

How about you try it again only with better conditions this time. Instead of putting it on your porch. then come back if you cant figure it out. Use the fridge and the freezer only, so the temperatures are always constant. I don't see it being possible that it takes 6 times the amount of time to melt in the reverse conditions that it took 12 hours to freeze in.

25. Jan 12, 2010

### Redbelly98

Staff Emeritus
I have a PhD, but lacking your fascination with this problem I am unable to devote sufficient time to it.

As I see it, there is too much unknown or questionable information:

• We have doubts about the 45F fridge temperature.
• How does the OP know the milk was frozen solid, as in completely? Perhaps the central part of the milk did not completely freeze, but with the outer part frozen one cannot squeeze it.
• As has been pointed out, wind chill will increase the freezing rate outside. Just how fast was the wind that night? We don't know.