The Phase Rule in Open Systems

Natural systems, which can exist over a range of temperatures and pressures (such as a granite), must have at least two degrees of freedom (i.e., T and P). Combining the relation / 2 with the Phase Rule, (14.47), gives 

This says that the maximum number of phases to be expected in any naturally occurring system is given by the number of components in that system. This is called the Mineralogical Phase Rule, and was pointed out by Goldschmidt in 1911. In open systems, 

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