Cecil responds here to the question whether frozen milk is heavier than liquid milk.
Of course it doesn’t actually weigh more.
But in the example given, the lady didn’t actually say it weighed more, she said it felt heavier. Now my point is simply this. Frozen liquid does actually feel heavier when you carry it. Due to the sloshing of the liquid in the container a rhythm or wave will cause the weight vary. At times it (briefly) it will feel lighter, of course when the weight is dispersed back on you it “gets heavier” and you compensate for that change. But if you get in time with the “wave” you can use it to your advantage when carrying a heavy fluid object. As opposed to a block of ice…it just sits there, heavy either way.
I think Unca forgot to think about the condensation of water or moisture from the air on the containers because of freezing. The plastic bags in my refrigerator (1.1 liters) are 20 cm high and 10 cm wide. The surface of one of this (essentially) flat bags is about 400 square cm. If the frozen layer is 1 mm thick, we are talking of 40 grams of water. If you are carrying a 10 or 12 pack box, this means about an extra pound, for those of you in non-metric countries. You could probably feel a 5 % increase in weight.
If the box is deeply frozen, then the water inside in the form of ice could, as a limit, fill all the voids. Probably this is the reasoning behind your common sense telling you that the box is going to be heavier. My common sense also tells me that a stone does not increase its weight so much, probably because the relation between surface and weight is much smaller.
Sorry: I forgot. To go into the subject a little mor deeply, could be added that when you study highway construction, you learn that there is a moisture content in sand or gravel that maximizes volume and another that maximizes weight.
I´ve had many arguments wiht truck owners about rejecting or accepting a truck of sand (sold by volume) because of its humidity, when what I wanted was weight.
This is an example of a complex change in weight because of films of water on surface of solids. The relationship is far from lineal and, I think, really interesting. Is the base for the theory of compacting granular layers.
While we’re at it, the weight of the bag of milk would change a little bit due to the volume change when the milk freezes. I don’t know whether milk gets denser or less dense when it freezes, and it’s probably a smaller effect than water condensing on the bag, but I’d bet the change in buoyancy due to the change in density swamps the change in mass due to E = mc[sup]2[/sup].
Milk gets less dense when it freezes, as anyone knows living outside of the tropics and old enough to remember milk bottles. Nevertheless, the mass doesn’t change at all as a result of freezing (apart from the usual possibility of air-bubble effects), and the weight would change only by the pretty-darned-immeasurable effects of buoyancy in air and of the center of gravity of the milk being an inch further from the center of the Earth.
I responded to the Heavy Milk thread on 11/03/04:
Actually the milk is imperceptibly LIGHTER. As the Milk turns to Ice, it is actually less dense and therefore slightly more BOUYENT to the surrounding air. Instead of flexing inward when she grips it, the carton bulges slightly outward. This makes it feel heavier because the grip is slightly weaker as the fingers are more open.
Cecil knows this, he was just testing us.
rwj