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The theory would be that once the inner container reached 100 C with the
boiling water in the outer container at 100 C then there should be no net
conduction between the outer and inner container (delta T = 0) and thus (in
calorimetry terms--don't look Jim) no more net heat transfer occurs to the
inner container. The inner container water reaches 100 C but does not boil.
It would be interesting to know what happens in a real experiment.
rick