John McCarthy
Computer Science Department
Stanford University
Stanford, CA 94305
jmc@cs.stanford.edu
http://www-formal.stanford.edu/jmc/
August 21, 1997
It follows from the second law of thermodynamics that separating the constituents of a mixture requires a certain minimum expenditure of energy. If a rare constituent of a mixture is to be separated the second law implies that the rarer the constituent, the more energy is required to separate a unit amount of it.
Our object is to apply these considerations to the extraction of minerals from low grade ores, with special attention to the limiting case in which the substance is being extracted from ``country rock'', i.e. from rock in which the substance is present in the same concentration as it is present in the earth's crust. Our conclusion is that the energy required by the second law of thermodynamics can make only a tiny addition to the costs involved in extracting ores even when country rock is the source of the mineral.
These calculations are motivated by the claim by various writers (I'll get the references) that civilization is dependent on high grade ores which will be soon exhausted, and the extraction of minerals from low grade ores is limited by energy costs of separating the ore from rock required by the second law of thermodynamics.
The claim is mistaken.