Final answer:
The thermal efficiency of the Stirling cycle is calculated using the formula Eff = 1 - Qc/Qh. The Stirling engine's efficiency in the given example is 48%, while the Carnot efficiency is 50%.
Step-by-step explanation:
The question asks to derive the thermal efficiency of the Stirling cycle and then compare it to the Carnot cycle when both are operating between the same two heat reservoirs.
To calculate the efficiency of a Stirling engine, we use the formula efficiency (Eff) = 1 - Qc/Qh.
In the provided example, the engine transfers 25 kJ to the hot reservoir (Qh) and 13 kJ to the cold reservoir (Qc). Hence, the efficiency is Eff = 1 - 13 kJ / 25 kJ = 0.48 or 48%.
Comparatively, the Carnot efficiency (Effc) is given by Effc = 1 - Tc/Th, which in this case is 1 - 300 K / 600 K = 0.50 or 50%.
In the example, the Stirling engine's efficiency is 96% of the Carnot efficiency, significantly higher than commonly achieved efficiencies.