Final answer:
The maximum thermal efficiency of a heat engine operating between -20°C and 15°C is approximately 12.15%, according to the Carnot Efficiency formula. The inventor's claimed efficiency of 10% is below this theoretical maximum, suggesting their design is within the realm of possibility considering real-world engineering constraints.
Step-by-step explanation:
The question posed concerns the maximum thermal efficiency of a heat engine operating between temperatures of -20°C (253 K) and 15°C (288 K). According to the Carnot Efficiency formula, which is the theoretical maximum efficiency for a heat engine, the efficiency (η) is determined by the temperatures of the hot source (Th) and cold sink (Tc) in kelvins according to η = 1 - (Tc/Th). In this case, that would be η = 1 - (253 K/288 K), which is approximately 12.15%. Therefore, the maximum thermal efficiency for a power cycle working between these temperatures is approximately 12.15%, which means the inventor's claim of a 10% thermal efficiency is below the theoretical maximum but still within the realm of possibility, especially when considering engineering challenges and real-world conditions that typically prevent achieving the theoretical maximum.
As an additional example, the Carnot Efficiency for a heat engine operating between boiling water (373 K) and freezing water (273 K) would be η = 1 - (273 K/373 K), which results in a maximum possible efficiency of 26.8%. These examples illustrate how temperature differences between the heat source and the heat sink directly influence the theoretical efficiency of heat engines.