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## Heavier?

Posted by Karl Sharman on December 18, 2010 – 12:09 pm

Is frozen milk heavier than non-frozen milk. This is a trick question, it is posted on ToM. Think carefully before you answer. Please substantiate your Yes or No answer. Could also be a double or triple bluff, but it is the weekend…

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This post is under “Tom” and has 46 respond so far.

### 46 Responds so far- Add one»

1. 1. randy Said：

yes

2. 2. rachel Said：

yes

3. 3. Wizard of Oz Said：

Should be the same because the act of freezing shouldn’t add or subtract any weight.

4. 4. Chris Said：

Less. It expands so has some buoyancy due to density of the the atmosphere.

5. 5. beast Said：

milk can’t freeze

6. 6. Karl Sharman Said：

Randy, Rachel – your proof is…?
beast – I have some frozen milk in my freezer. This may blow your answer out of the water
Chris – Density… Mass….
Wizard of Oz… are you sure?

7. 7. Chris Said：

Heaviness is weight, not mass. However, it’s obviously not the answer you’re looking for.

But just in case: the milk expands when frozen, it’s mass stays the same (neglecting E = mc^2). So it displaces more air and so is more buoyant, so it has less weight.

But I think you’re probably going to have a broken bottle in your freezer.

8. 8. Doug Said：

Weight is pull of gravity on an object relative to the mass of the object, in direct proportion to its distance from the planet.

milk is mostly water and expands when frozen this expansion is due to the aligning of it s molecules in a crystal lattice, an open hexagonal (six-sided) shape. Since this is on the molecular level the expansion does not allow for other matter (air) to be introduced.

9. 9. Karl Sharman Said：

Chris, this being ToM the answer is lighter, taking into account E=mc^2. For those following in disbelief there is less movement of the atoms, therefore less energy = less mass according to Mr Einstein.
However, this is immeasurable with your average quantities of milk, by your average human.
So, relativistically – lighter.
Really – no.
All clear?

10. 10. James Said：

I would say that frozen milk is not possible. Wouldn’t the milk separate when frozen and turn into water and whatever else is in milk?

Although if milk does freeze it is obviously a straightforward answer, yes the milk will weight the same frozen or melted. Tt would be like asking, “which weights more, a pound of lead or a pound of feathers?”

11. 11. Chris Said：

Hi Karl, the buoyancy effect is measurable, the E = mc^2 is only calculable.

Laboratories, who know their stuff, take buoyancy into account when determining masses. There have been real howlers made by failing to do that.

12. 12. Al Gelman Said：

This is a nonsensical question. It’s like asking how high is up? If the question is: does a given volume of milk weight the same if it is frozen? The answer is yes. If the question is; does a particular volume of milk weigh more or less than the same volume of frozen milk? The answer is that the frozen volume weighs less (because milk (which is mostly water) expands when it freezes).

13. 13. Len Said：

Both weigh the same – nothing changed except the state from liquid to solid…

14. 14. Al Gelman Said：

By the way Cris, in the international system of units (SI), the term “weight” has been defined as being synonimous with mass. So we now (since about 1959 I believe) say that an object weighs 5 kilograms.

15. 15. Karl Sharman Said：

Chris – hence the “relativistically”
Al Gelman – The question, as mathematic/physics theory, is not non-sensical as Chris highlights in post 9 – the difference is calculable. Bouyancy is a factor in the real world, but wouldn’t figure in the Relative equations.

16. 16. Al Gelman Said：

I don’t understand response 12. I never posted that remark!
Also Chris, I apologise for misspelling your name in response 11 Sorry.

17. 17. Chris Said：

Hi AL Gelman. The question is perfectly sensible. The given amount of milk weighs less for the reason I gave. The density reduces.

The SI unit of weight is the newton – a unit of force.

5kg weight is not an SI concept. An astronaut with a mass of 80 kg, has 0 weight when in orbit.

The weight of the frozen milk is less for the reason I gave.
The mass is a trivial amount less due to relativistic considerations.

18. 18. Chris Said：

Hi Al. Don’t worry about the mispelling – it’s very easy to make typos. I make them frequently.

Which bit of post 12 don’t you understand. You’re post 10 said the problem is non-sensical; Karl’s post 12 said that the problem is not non-sensical. I accept that Karl’s post structure seemed to imply that you had commented on buoyancy; which you hadn’t done.

19. 19. Chris Said：

…ooops, bad edit, my post 10. I said “the density reduces” and forgot to add “so the buoyancy increases”. Unless we are considering the milk to be in a vacuum – but then we have a whole new ball-game.

20. 20. Chris Said：

Now to shoot my own foot. According to Wikipedia, the ISO (not SI) definition of weight specifically excludes atmospheric buoyancy effects, but it doesn’t say how that is achieved.

But the article also uses the term “apparent weight” when dealing with immersed bodies.

21. 21. Al Gelman Said：

I’m sorry Chris, but the question as stated is nonsensical. Suppose I asked you: which is heavier rocks or feathers? You would tell me that my question made no sense! Obviously a rock measuring 1 cubic centimeter will weigh less than a boxcar full of feathers (eliminating the weight of the box car of course). Now substitute milk for rocks, and frozen milk for feathers and that is essentially your original question. As for the question of buoyancy, once again my original statement applies. First of all, the buoyant force has nothing to do with the weight of milk, frozen or otherwise. The buoyant force is a function of the method of measurement. (In fact the buoyant force could be used as the method of measurement!) The buoyant force is equal to the weight of the fluid displaced. So if we are talking about a given volume of milk the buoyant force is the same for the same volume of frozen milk. If we are talking about a volume of milk (say one litre) that has expanded because it is frozen to say 1.1 liters we would find that the buoyant force is greater than before, because it is displacing more fluid. (Also, you didn’t specify what the fluid was – air- water – olive oil …?, at what temperature and pressure?)

22. 22. Karl Sharman Said：

Al, it was my question, not Chris’s. The question as stated is asking the question which is heavier, of the same material, but in a different physical state. It did state that it was a trick question. Yes, there is no difference in “heaviness” (neatly avoiding weight and mass there) that current instumentation could detect. However, it can be calculated that there is a theoretical difference in the same quantity of a material dependent on it’s state (fluid/solid) and the energy contained therein, thanks to Mr Einstein.

23. 23. Chris Said：

Hi Al. 1 kg of feathers has the same weight as 1 kg of rocks – that’s completely understandable. It isn’t nonsensical.

As you didn’t mention the amounts of the rocks and feathers, the question is still sensical, it simply can’t be answered without more information.

In the case of the milk, we are dealing with the same amount of substance throughout. So a yes or no answer is available, the only issue seems to be due to the definition of weight. ISO say buoyancy does not affect the weight – by definition. So Karl is right, only E = m c^2 is relevant. I’m completely satisfied with that.

I see that you agree that the buoyant force is higher for the frozen milk. I had said that the buoyancy was due to atmospheric displacement – so air is the buoying fluid. As for the temperature etc., obviously I mean at the same pressure and temperature with liquid and frozen milk. But asking for the fluid and it’s state is nitpicking and will lead to far more difficult to deal with issues – proverbially, we’ll start looking at the trees and fail to see the forest. If the buoying fluid isn’t specified, it’s sensible to assume it’s the same in both cases.

I’m not quite sure what you mean by the buoyant force is a function of the method of measurement. If you mean that you immerse the milk in different fluids, then of course that will affect the buoyancy. Personally I was considering atmospheric air throughout.

The fundamental fact is that W = m g, where W is weight, m is mass and g is the acceleration due to gravity. g is the only item that hasn’t been discussed (on this page, so far). Some authorities say g is the local value and also includes a contribution due to the Earth’s spin. Some use an international standard value of g – that required determing the mass of the object. But I don’t want to get deeply into those issues – they are based on differing definitions of weight.

24. 24. Chris Said：

…aargh. I see that Karl hadn’t specified that it was the same sample of milk in each case. I had simply assumed it to be so. Clearly (in view of his follow ups) so had Karl.

We have also forgotten to mention milk loss due to evaporation – but let’s not go there

25. 25. Patrick Said：

Both will have the same number of molecules. The volume & the density will inversly change (in this case the volume increses & the density decreases), but the weight remains the same

26. 26. Chris Said：

Hi Al. I see that the posting numbers have changed. Were you saying (in what is currently post 16) that someone else made a post using your name?

In view of my last post (currently 24 “…aargh”) I know understand what you’ve been driving at. I would have understood your point better if you had simply said that the question doesn’t say, whether or not, that it was the same sample of milk throughout. It is pretty clear that only you had noticed that detail (Karl hadn’t, and he posted the question).

27. 27. Noah Said：

i say no
think about it frozen is 2 kg lighter then the non’frozen milk,
2 kg is extra on the non’frozen milk

NOAH

28. 28. Noah Said：

who joins me? saying no ?

29. 29. anjo Said：

im gonna say no because when something freezes the particles in the matter squeeze or bunch together

30. 30. Tharin Said：

If you take milk and simply freeze it you will find that since the mass has not changed, the frozen milk will weigh the same as it did when it was liquid.

If however you compare liquid milk to an equal volume of frozen milk, the frozen milk having less density, therefore less mass per unit volume, will weigh less.

31. 31. felicia pagano Said：

no

32. 32. Reese Said：

no

33. 33. Tyler Said：

It depends on the amount frozen if there is the same amount of milk frozen than it will weigh the same because when something freezes its not gaining or losing any mass the only thing changing is the volume.

34. 34. atul gupta Said：

both are of same weight

35. 35. Jacob Said：

he said ‘none frozen milk’ meaning there is no milk at all so the answer is yes, frozen Milk is heavier than nothing

36. 36. ankur Said：

yes…

37. 37. nobody Said：

I agree with wizard of oz

38. 38. memeandi Said：

as liquid freazes it expaneds but that does not make it heaveier then liquid

39. 39. memeandi Said：

and dont worry Ali i got that question wrong the first time too although there would have to be a hole lot of fethers to be the same as the rock

40. 40. fab Said：

Milk does freeze. It’s even stored as frozen wheels (like a cheese, no container) during winter in some parts of Siberia.

Mass is related to an amount of matter. The amount of milk does not change, so the mass is constant.

weight is the action of gravity on a mass, so providing the milk is not changing altitude, its weight remains constant. Now milk expends upon freezing (it is mostly water), and this could affect the altitude of its centre of gravity and the weight. Not by much…

Only the measurement of weight (not weight itself) can be affected by the increase of buoyancy in air caused by the increase of volume upon freezing. This would depend on the technique of measurement.

41. 41. Fab Said：

Forgot to mention relativistic masses… Depending on definitions, an increase of thermal energy can increase a mass

42. 42. Chris Said：

Fab mentioned a very good point. The centre of mass will be higher for frozen milk by virtue of expansion.

g = GM/R², so dg/dR = -2GM/R³ = -2g/R. So dg/g = -2 dR/R

Using approximate values, g = 10, R = 6400 km = 6.4 * 10^6 m.
Guessing dR at 1 cm = 0.01 m, I get dg/g = -30 *10^(-10).

Assuming 1 kg of milk. And a reduced energy of 10^7 joules (roughly right).
Then m = E/c² => 10^7 /(3*10^8)² = 1 * 10^(-10).

So the change of centre of gravity is about one or two orders of magnitude more important than the relativistic effects.

43. 43. Ray Said：

All I know is that my son told me that the jug of milk is a bit frozen and it feels heavier. I agree with him.

Has anyone confirmed by weighing?

44. 44. Chris Said：

Hi Ray. Due to buoyancy, the jug should feel a very tiny bit lighter when it’s frozen. Anything else is psychological.

45. 45. kathy Said：

I make goat milk soap and freeze the milk in freezer bags
weighing 20 oz. when unfrozen and when I take milk out to use, it weighs 2 oz. lighter

46. 46. Chris Said：

Hi Kathy. It’s not possible for the milk to change weight so much that you could measure it, yet alone 2 ounces.

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