The Solar Panel Cooling System · AI Generator #GEN-6AA213AD

Physics · thermodynamics

Problem

A space-based solar panel operates in Earth's orbit where it receives direct sunlight. The panel can be modeled as a blackbody with surface area A=12  m2A = 12\;\text{m}^2 and operates at a steady-state temperature of Th=400  KT_h = 400\;\text{K}. To improve efficiency, engineers design a radiative cooling system that uses the cold space environment as a heat sink at effective temperature Tc=4  KT_c = 4\;\text{K} (cosmic microwave background). The cooling system works as a heat engine cycle between the hot solar panel and the cold space sink. Due to engineering constraints, this heat engine operates at only η=60%\eta = 60\% of the Carnot efficiency. (a) What is the Carnot efficiency for a heat engine operating between these two temperature reservoirs? (b) How much mechanical work can this actual heat engine extract per second from the thermal energy radiated by the solar panel? Use Stefan-Boltzmann constant σ=5.67×10−8  W/(m2K4)\sigma = 5.67 \times 10^{-8}\;\text{W/(m}^2\text{K}^4\text{)}.

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