  The Carnot heat engine sets an upper bound on the efficiency of a heat
engine. As an ideal, reversible engine, a single cycle must be performed in
infinite time, and so the Carnot engine has zero power. However, there is
nothing in principle forbidding the existence of a heat engine whose efficiency
approaches that of Carnot while maintaining finite power. Such an engine must
have very special properties, some of which have been discussed in the
literature, in various limits. While recent theorems rule out a large class of
engines from maintaining finite power at exactly the Carnot efficiency, the
approach to the limit still merits close study. Presented here is an exactly
solvable model of such an approach that may serve as a laboratory for
exploration of the underlying mechanisms. The equations of state have their
origins in the extended thermodynamics of electrically charged black holes.
