What formula would I use?

Question

The United States generates some 240 million tonnes of solid waste each year, with an energy content (when dry) essentially the same as that of wood, about 20 MJ/kg. Find the equivalent in barrels of oil and compare this quantity with U.S. oil imports of about 1.7 billion barrels per year.

Answer 1

There is no formula, just a series of conversions.

First convert tonnes to kg. We can assume these are metric tonnes and each is 1 x 10³ kg. So (2.4 x 10⁸ tonnes)(1 x 10³ kg/tonne) = 2.4 x 10¹¹ kg.

Next, at 20 MJ/kg we can find how many total megajoules (MJ) there are: (2.4 x 10¹¹ kg)(20 MJ/kg) = 4.8 x 10¹² MJ.

One barrel of oil produces approximately 6.12 x 10⁹ J = 6.12 x 10³ MJ, so how many barrels of oil does this represent: (4.8 x 10¹² MJ) / (6.12 x 10³ MJ/barrel) = 0.78 x 10⁹ barrels.

1.7 billion barrels is 1.7 x 10⁹ barrels so our solid waste is a little less that half (46%) of what we import each year.

Of course these are old figures because in 2019 the US imported only 0.2 x 10⁹ barrels.