If a black body at 400 K surrounded by atmosphere at 300 K has rate of cooling ' R₀ ', the same body at 900 K, surrounded by same atmosphere, will have rate of cooling nearly (a) 4R₀ (b) 16R₀ (c) 36R₀ (d) (81R₀)/(16)

Answer: (c). Net rate of cooling ∝ T⁴ - T₀⁴ with T₀ = 300 K. At 400 K: (256 - 81) × 100⁴ = 175 × 100⁴ At 900 K: (6561 - 81) × 100⁴ = 6480 × 100⁴ R/R₀ = (6480)/(175) ≈ 37, nearest option 36R₀ So the answer is (c) 36R₀.

If a black body at 400 K surrounded by atmosphere at 300 K has rate… | MHT CET 2025 (21 Apr, Shift 2)

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Thermal Radiation: Black Body, Stefan & Wien

If a black body at 400 K surrounded by atmosphere at 300 K has rate of cooling ' $R_0$ ', the same body at 900 K, surrounded by same atmosphere, will have rate of cooling nearly

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Answer: (c)

Net rate of cooling $\propto T^4 - T_0^4$ with $T_0 = 300$ K.
At 400 K: $(256 - 81) \times 100^4 = 175 \times 100^4$
At 900 K: $(6561 - 81) \times 100^4 = 6480 \times 100^4$
$\dfrac{R}{R_0} = \dfrac{6480}{175} \approx 37$ , nearest option $36R_0$
So the answer is (c) $36R_0$ .

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