Project ForgeA flat plate made of cast iron is exposed to a solar flux of 600 W/m² at an ambient temperature of 25°C. Assume that the entire solar flux is absorbed by the plate. Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669×10⁻⁸ W/m²-K⁴. Neglect all other modes of heat transfer except radiation. Under the aforementioned conditions, the radiation equilibrium temperature of the plate is _________ °C (round off to the nearest integer).
Explanation
By Kirchhoff's law, the plate's low-temperature emissivity equals its low-temperature absorptivity: ε=0.21. At equilibrium, absorbed solar flux equals the NET radiative exchange with the 25°C (298K) surroundings: 600 = 0.21×σ×(T⁴−298⁴). Solving: T⁴=600/(0.21×5.669×10⁻⁸)+298⁴≈5.040×10¹⁰+0.789×10¹⁰≈5.828×10¹⁰, T≈491.3K≈218°C.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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