Two very large parallel metal plates are separated by a small vacuum gap. Plate 1 is in contact with liquid nitrogen at T₁ = 77 K; plate 2 is at room temperature, so T₂ = 300 K (see the figure). In order to reduce the heat loss by radiation, a third plate is inserted in the middle. The absorptivity of the middle plate is a=0.10 (i.e., it absorbs 10% of radiation). Both plates 1 and 2 are considered to be blackbody, and the absorptivity equals 1.0. (The Stefan-Boltzmann constant is o=5.67x10 W/(m²K)) Tm (a) Find the equilibrium temperature of middle plate Tm. (b) Find energy flux between T, and T2 plates if the middle plate is not inserted. (c) Find energy flux between T, and T2 plates at the presence of the middle plate. T₁

Elements Of Electromagnetics
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Two very large parallel metal plates are separated by a small
vacuum gap. Plate 1 is in contact with liquid nitrogen at T₁ = 77 K; plate 2 is at room
temperature, so T₂ = 300 K (see the figure). In order to reduce the heat loss by
radiation, a third plate is inserted in the middle. The absorptivity of the middle plate is
a=0.10 (i.e., it absorbs 10% of radiation). Both plates 1 and 2 are considered to be
blackbody, and the absorptivity equals 1.0. (The Stefan-Boltzmann
constant is o-5.67×10 W/(m²K))
T₁ Tm T₂
(a) Find the equilibrium temperature of middle plate Tm.
(b) Find energy flux between T₁ and T2 plates if the middle plate is
not inserted.
(c) Find energy flux between T₁ and T2 plates at the presence of
the middle plate.
Transcribed Image Text:Two very large parallel metal plates are separated by a small vacuum gap. Plate 1 is in contact with liquid nitrogen at T₁ = 77 K; plate 2 is at room temperature, so T₂ = 300 K (see the figure). In order to reduce the heat loss by radiation, a third plate is inserted in the middle. The absorptivity of the middle plate is a=0.10 (i.e., it absorbs 10% of radiation). Both plates 1 and 2 are considered to be blackbody, and the absorptivity equals 1.0. (The Stefan-Boltzmann constant is o-5.67×10 W/(m²K)) T₁ Tm T₂ (a) Find the equilibrium temperature of middle plate Tm. (b) Find energy flux between T₁ and T2 plates if the middle plate is not inserted. (c) Find energy flux between T₁ and T2 plates at the presence of the middle plate.
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