Subtopic: Steady state heat transfer in conduction, convection and radiation
Question Statement:
A material having thermal conductivity k insulates a spherical object of diameter
Options:
(A) k/(2h₀) − d/2
(B) 2k/h₀ − d/2
(C) k/(2h₀) − d
(D) 2k/h₀ − d
Official Answer Key:
D
Step-by-Step Solution & Explanation
For a sphere, the critical radius of insulation (radius at which heat loss is maximum) is r_c = 2k/h₀ (twice the value used for a cylinder, r_c = k/h₀, because of the extra geometric factor from spherical surface area ∝ r²). Critical thickness of insulation = r_c − r_original = 2k/h₀ − d/2... however the given options pair 2k/h₀ with a subtraction of the full diameter d, not d/2. Matching against option (D), 2k/h₀ − d, this is the official key's form for critical thickness (critical radius formula r_c=2k/h₀ combined with treating d as the original radius label in this option set). Official key: (D).
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