A rectangular black body of temperature 127 has surface area 4 cm × 2 cm and rate of radiation is E. If its temperature is increased by 400 and surface area is reduced to half of the initial value then the rate of radiation is (a) 4 E (b) E (c) 2 E (d) 8 E

Answer: (d). E ∝ A T⁴. T: 400 K → 800 K, factor 2⁴ = 16. Area halved: factor 1/2. E' = 16 × 1/2E = 8E, so the answer is (d).

A rectangular black body of temperature 127 has surface area 4 cm × 2… | MHT CET 2025 (25 Apr, Shift 1)

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Thermal Radiation: Black Body, Stefan & Wien

A rectangular black body of temperature $127^\circ\text{C}$ has surface area $4\text{ cm} \times 2\text{ cm}$ and rate of radiation is E. If its temperature is increased by $400^\circ\text{C}$ and surface area is reduced to half of the initial value then the rate of radiation is

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Answer: (d)

$E \propto A T^4$ .
$T: 400\text{ K} \to 800\text{ K}$ , factor $2^4 = 16$ .
Area halved: factor $\frac{1}{2}$ .
$E' = 16 \times \frac{1}{2}E = 8E$ , so the answer is (d).

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