Re: Melting ice and insulation

Jim-

There are several things that affect how fast ice melts, but the biggest 
ones are how much heat is in the environment around the ice, the amount of 
ice, and the ratio of surface area  to volume for the pieces of ice.

The amount of heat in the environment around the ice is pretty well 
indicated by temperature: a hot day melts ice faster than a cold one. You 
can slow down melting by isolating the ice from outside heat. That's what a 
cooler does: heat doesn't pass easily through its walls, so the ice doesn't 
melt.

The amount of ice is important, too. A single ice cube on a sidewalk will 
disappear faster than a large pile of ice cubes will. This is because a 
certain amount of energy is required to melt each ice cube. More ice cubes 
mean more energy is required.

The third factor, the surface area to volume ratio, is a comparison of how 
much ice there is with how much surface the ice has to absorb heat.  This 
has a very big effect on how fast ice melts and how efficiently it cools 
something it's packed around. In fact, the higher the surface area to 
volume ratio is, the faster the ice will melt and the more it will chill 
the stuff you're trying to cool with it.

Imagine three ten-pound piles of ice in your cooler (it's a BIG cooler!). 
The first pile is just a single block of ice about a foot square, so it has 
about one cubic foot (1700 cubic inches) volume. The second is a pile of 
1700 one-inch ice cubes, each one cubic inch, making a cubic foot of 
volume. The third is a pile of shaved ice, making one cubic foot volume, 
and the pieces are very, very tiny, say a thousandth of a cubic inch volume 
each, making roughly two million little chips of ice in the pile.

The big block of ice has a surface area of  12 x 12 x 6 = 864 square 
inches. The surface area to volume ratio is 864/1700 = .508. This is a 
pretty small number, so we would expect the ice to melt pretty slowly. We 
would also expect the ice not to chill the stuff in the cooler that well, 
either.

The ice cubes have a total surface area of 1 x 1 x 6 x 1700 (six faces one 
inch square per cube times 1700 cubes) = 10,200 square inches. The surface 
area to volume ratio is 10,200/1700 = 6. This isn't a really big number, 
but it's still around twelve times for the big block of ice.  We would 
expect the ice cubes to melt much faster than the block, but also to be 
almost twelve times more efficient at chilling the stuff in the cooler.

The shaved ice, assuming the pieces average a tenth of an inch square each, 
has a total surface area of around .1 x .1 x 6 x 2,000,000 (six sides a 
tenth of an inch across times two million pieces) = 120,000 square inches. 
The surface area to volume ratio is 120,000/1700 = 70.6. This is again 
almost twelve times more than the cubes, and almost 144 times more than the 
solid block. We could expect the shaved ice to melt a whole lot faster than 
the block, and we would also be justified to expect the stuff we're 
chilling in the cooler would get colder faster.

In your question you also mention adding salt to the ice. Salt acts on ice 
by lowering its melting temperature so that it melts faster than it 
ordinarily would. The faster melting ice absorbs heat from its surroundings 
faster and so chills things much better. I wouldn't want to guess what salt 
would do to the fish.

So, if you want your ice to last a long time, make sure it's in big blocks. 
If you need to chill things better, break the ice up into smaller pieces 
but expect the ice to melt faster as the pieces are made smaller. And if 
you need it to get really cold, salt the ice but expect it to disappear 
very, very fast.

Kevin