What is the name of the statement of the second law that prohibits a perfect heat engine?

The Kelvin–Planck statement says that no cyclic device can take heat from a single reservoir and convert it entirely into net work. It is the second-law statement that rules out a perfect heat engine.

A real heat engine absorbs heat from a high-temperature source, converts part of that energy into work, and rejects the remainder to a colder sink. The Kelvin–Planck statement says that the rejected heat cannot be eliminated if the engine operates in a cycle. Consequently, no engine can have 100 percent thermal efficiency.

The statement is associated with William Thomson, later Lord Kelvin, and Max Planck, although related ideas developed from earlier work by Sadi Carnot and Rudolf Clausius. The Clausius statement gives an apparently different formulation: heat cannot spontaneously flow from a colder body to a hotter one.

These two formulations are equivalent. Violating either would permit a violation of the other. Carnot’s theorem further shows that the maximum possible efficiency between two fixed temperatures is achieved only by a reversible Carnot engine.