There was a bunch of snow in Boston this year—and some of it's still there. Yes, in July some of the snow has not yet melted. Why? There are a couple of reasons, some of them have to do with physics.

Piles of Snow

According to weather.com, Boston had 110 inches of snow this winter. Sure, some of this snow melted at different times—but much of it didn't. What do you do with all this snow? Suppose that there was just 50 inches (1.27 m) of snow that covered an area that was 1 square mile. If you take all of this snow and move it to a football field, it would stack 600 meters high (almost 2,000 feet). So you can see the problem with the massive amounts of Boston snow. If you want to clear the roads, you have to put the snow somewhere. This makes giant piles of snow.

Snow Mixed With Trash

When trucks plow snow covered roads, they don't just get the snow. They also gather up stuff that was on the ground before the snow (and after the snow). Typically this stuff is call "trash." With regards to melting, there's a big difference between snow and trash.

How Does Snow Melt?

So you have your big pile of snow (with trash in it). Snow is essentially ice with lots of air spaces. How does this ice turn into water? It needs energy. This energy to melt snow gets to the snow through two processes: radiation and conduction. As the sun shines on the snow, the light transfers energy that can cause melting. Everyone knows that when you stand in the sunlight, you feel warmer—exactly the same thing for the snow. Conduction is a transfer of energy through contact. So, what is touching the snow? Just two things: the ground and the air. If these things are warmer than the snow (which is very likely in July) then they will transfer energy into the snow to melt it.

Simple right? Yes, it's simple except for one thing. Both heat conduction and radiation transfer energy through the surface of the snow pile. Big snow piles cause a problem.

Size Matters

The amount of energy you need to melt snow depends on the amount of snow—this is proportional to the volume. The transfer of energy goes through the surface area of the pile. With those two ideas we find that bigger piles take longer to melt. Let's look at an example.

Here I have two cubical piles of snow. Pile A is a 1 meter cube (1 x 1 x 1) and pile B is a 2 meter cube (2 x 2 x 2). I can easily calculate the volumes of these cubes (length times width times height).

Doubling the length of the snow cube increases the volume by a factor of 8. Pile B would need 8 times the energy in order to melt. Now, what about surface area? A cube has 6 sides where each side has an area of length times width. That means the two surface areas would be:

Doubling the length of the snow cube increases the surface area by a factor of 4. Perhaps you can see the problem. As you make a bigger pile of snow you need much more energy to melt it. However, a bigger pile doesn't increase in surface area enough. The ratio of volume to surface area still depends on size. Big things are not the same as small things and big piles of snow are more difficult to melt. Of course the Boston snow pile isn't a cube, but it still is difficult to double the volume as well as double the surface area.

Oh, and don't forget about the trash. Once a giant pile of snow with a little bit of trash starts to melt, the snow leaves but the trash doesn't. This trash can sort of insulate the snow as well as provide shade. Of course trash could also help it melt faster if it's the right kind of trash. Black pieces of metal would help, but shiny potato chip bags would not.

Actually, this snow-trash mixture is very similar to the way scientists find meteorites in Antarctica. Meteorites hit glaciers and then the glaciers move and melt at certain places. When they melt, they drop trash (or meteorites in this case) at that place. Boom—instant meteorite loot.

But will the Boston snow pile melt? Sure, it will just take time. Hopefully it will melt before the next snow storm.