If the ore grade (G m kg metal per kg ore) from which a metal is extracted falls, the energy required for mining, transportation, and subsequent concentration of the ore to a level at which it can be...

If the ore grade (G_m
kg metal per kg ore) from which a metal is extracted falls, the energy required for mining, transportation, and subsequent concentration of the ore to a level at which it can be refined to metal rises at each stage, driving up its embodied energy. At its simplest we might expect the embodied energy to take the form

where A is the energy in MJ/kg metal for the refining process and B, also in MJ/kg, is the mining and transportation energy per unit ore grade. If, for copper, A = 40 MJ/kg and B = 1.2 MJ/kg, what is the embodied energy of copper mined from a deposit with a grade of 4%? How much does it increase if instead the available grade is 2%?