Compare the rate of loss of heat from a metal sphere at 627 with the rate of loss of heat from the same sphere at 327, if the temperature of the surrounding is 27. (nearly) (a) 6.2 (b) 5.3 (c) 4.8 (d) 7.4

Answer: (b). Net rate of heat loss ∝ T⁴ - T₀⁴, with T₀ = 300 K. T₁ = 900 K = 3T₀, T₂ = 600 K = 2T₀. (Q₁)/(Q₂) = (3⁴ - 1)/(2⁴ - 1) = 80/15 ≈ 5.3 So the answer is (b) 5.3.

Compare the rate of loss of heat from a metal sphere at 627 with the… | MHT CET 2023 (12 May, Shift 2)

Q79MHT CET 2023 · 12 MAY · SHIFT 2Medium

Thermal Radiation: Black Body, Stefan & Wien

Compare the rate of loss of heat from a metal sphere at $627^\circ\text{C}$ with the rate of loss of heat from the same sphere at $327^\circ\text{C}$ , if the temperature of the surrounding is $27^\circ\text{C}$ . (nearly)

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Answer: (b)

Net rate of heat loss $\propto T^4 - T_0^4$ , with $T_0 = 300\text{ K}$ .
$T_1 = 900\text{ K} = 3T_0$ , $T_2 = 600\text{ K} = 2T_0$ .
$\frac{Q_1}{Q_2} = \frac{3^4 - 1}{2^4 - 1} = \frac{80}{15} \approx 5.3$
So the answer is (b) 5.3.

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