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One thing you cannot describe a Carnot cycle engine as is a constant volume process. None of the four legs on an indicator diagram occur at constant volume. I do not know of a mechanism (if that is the right word) that is capable of extracting work with the working fluid at constant volume in a carnot engine.
There is a type of heat engine known as constant volume ( or Rochas) cycle engine that has two of the legs vertical (const vol)and two with the adiabatic gamma law expansion.
Another type with a (single) constant volume leg and a single adiabatic leg is the Lenoir gas engine.
However work is only only during the non constant volume parts of each cycle.