A perpetual engine with an efficiency equal to 1 would theoretically be 100% efficient, meaning it converts all input energy into useful work with no waste energy. However, such a machine cannot exist due to the second law of thermodynamics, which states that some energy will always be lost as waste heat in any energy transformation process. This loss of energy is unavoidable in real-world systems due to factors like friction, resistance, and heat dissipation. A perpetual engine would violate this fundamental law, making it impossible to create a machine that operates indefinitely without any energy loss or external energy input, and hence it would not work.