An inventor designs a heat engine that operates in a closed cycle between a high-temperature reservoir at \(600\text{ K}\) and a low-temperature reservoir at \(300\text{ K}\). In each cycle, the engine absorbs \(1000\text{ J}\) of thermal energy from the high-temperature reservoir, delivers \(600\text{ J}\) of useful mechanical work, and exhausts \(400\text{ J}\) of thermal energy to the low-temperature reservoir. An engineer analyzes the patent proposal and determines that this engine is physically impossible to construct. Which of the following statements provides the correct physical explanation for why the proposed engine cannot operate as claimed?