A Long Haul

 

We've already had inches of snow building up in Ann Arbor, making it a little more difficult to get around, and it got me wondering about snow removal in a city.  For large snowfalls, there isn't really room for big piles, so the snow would need to be hauled elsewhere.  How much cheaper is that than melting the snow with, say, blowtorches?

Melting snow involves overcoming the latent heat of the ice crystals.  This is the energy contained in the crystalline structure – I've mentioned this property before in the case of candle wax.  If we assume the snow is already at the melting point of 0°C, then we still need 334 kJ of energy per kilogram of snow.

Figuring out the energy needed to move the snow is a little more complicated, since it involves converting the gas mileage.  Current semi trucks get about 6.5 mpg with diesel fuel.  Diesel engines are relatively efficient (though they produce nastier byproducts), converting about 45% of the chemical energy into mechanical work.  The final piece we need is the amount of energy in a given volume of fuel, 35.8 MJ/L.  Putting these together, we can find the energy needed to move a truckload of snow a given distance: 2.16 x 10^-5 miles/kJ.

The maximum weight this truck can carry is 80,000 pounds, so we can calculate the energy to melt that much, 1.21 x 10^10 Joules (not jigawatts, sadly).  So how far would we need to haul the snow to make it more efficient to melt?  26 million miles, or several trips to the moon and back, but only 1/5th of the way to Mars.

I wasn't expecting to have a breakthrough snow removal technique, but this does seem a little high.  It's possible I'll find a mistake later, so take these results with a grain of salt (yet another snow-removal method).

Correction: I left out a factor of 10^-5 in my calculation above.  The actual distance is 262 miles.  Thanks, Kevin!