  The extended phase space thermodynamics and heat engines for static
spherically symmetric black hole solutions of four dimensional conformal
gravity are studied in detail. It is argued that the equation of states (EOS)
for such black holes is always branched, any continuous thermodynamical process
cannot drive the system from one branch of the EOS into another branch.
Meanwhile, the thermodynamical volume is bounded from above, making the black
holes always super-entropic in one branch and may also be super-entropic in
another branch in certain range of the temperature. The Carnot and Stirling
heat engines associated to such black holes are shown to be distinct from each
other. For rectangular heat engines, the efficiency always approaches zero when
the rectangle becomes extremely narrow, and given the highest and lowest
working temperatures fixed, there is always a maximum for the efficiency of
such engines.
