GATE 2024 CH – Question 37
The temperatures of two large parallel plates of equal emissivity are 900 K and 300 K. A reflection radiation shield of low emissivity and negligible conductive resistance is placed parallelly between them. The steady-state temperature of the shield, in K, is
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Correct answer: (A) 759
Explanation
At steady state the net radiation flux from the hot plate to the shield equals the flux from the shield to the cold plate. With the same emissivity on both sides of the shield, $T_1^4 - T_s^4 = T_s^4 - T_2^4$, so $T_s = \left(\frac{T_1^4 + T_2^4}{2}\right)^{1/4} = \left(\frac{900^4 + 300^4}{2}\right)^{1/4} = (3.321 \times 10^{11})^{1/4} = 759$ K.