Much of the northeast U.S. is currently digging its way out from all the snow. Snow is a big pain in many northern states. Upstate New York can get over 2.8 m (~100 in) of snow a year. Why don’t we just run a giant heater to melt it all? How much would it cost to melt all the snow in Buffalo?
The total area of Buffalo, NY is about 2.6×109 m2 (~1000 miles2). From the numbers above, we can compute the total volume of snow,
volume = height · area
= (2.8 m) · (2.6×109 m2)
= 7.3×109 m3.
Snow has a density of about 80 kg/m3. From this, we can compute the total mass of snow,
mass = density · volume
= (7.3×109 m3) · (80 kg/m3)
= 5.9×1011 kg.
The amount of energy it takes to melt a solid is called the heat of fusion. The heat of fusion of ice is 334 kJ/kg, meaning it takes 334 kJ of energy to melt 1 kg of ice. From the previous problem, the cost of energy is about 12.56 cents per kW·hrs. From this data, we can compute the total cost to melt one year worth of snow in Buffalo,
cost = (total mass of snow) · (heat of fusion of ice) · (cost of energy)
= (5.9×1011 kg) · (334 kJ/kg) · (12.56 cents per kW·hrs)
= $6.9×109.At almost $7 billion a year, it would cost about 40% of NASA’s entire budget.