Two spherical black bodies have radii r 1 and r 2 . Their surface temperatures are T 1 and T 2 . If they radiate same power then r 2 r 1 is

Question

Two spherical black bodies have radii r 1 and r 2 . Their surface temperatures are T 1 and T 2 . If they radiate same power then r 2 r 1 is, T 1 T 2, T 2 T 1, T 1 T 2 2, T 2 T 1 2

MARKS App · Accepted Answer

Q t = σ A T 4 i . e . p o w e r = σ A T 4 ∴ f o r s a m e p o w e r ∴ A ∝ 1 T 4 ∴ A 2 A 1 = T 1 4 T 2 4 ∴ 4 π r 2 2 4 π r 1 2 = T 1 4 T 2 4 ∴ r 2 r 1 = T 1 T 2 2

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