In an external environment of temperature ( T) kelvin, a sphere at temperature ( 3T) kelvin has cooling rate R₁. When the temperature of that sphere falls to ( 2T) kelvin, the cooling rate R₂ of the sphere will become (a) 15/16R₁ (b) 11/16R₁ (c) 7/16R₁ (d) 3/16R₁

Answer: (d). Net rate of cooling ∝ Ts⁴ - T⁴. At 3T: (81 - 1)T⁴ = 80T⁴; at 2T: (16 - 1)T⁴ = 15T⁴ R₂ = 15/80R₁ = 3/16R₁ So the answer is (d).

In an external environment of temperature ( T) kelvin, a sphere at… | MHT CET 2026 (17 Apr, Shift 1)

Q23MHT CET 2026 · 17 APR · SHIFT 1Medium

Thermal Radiation: Black Body, Stefan & Wien

In an external environment of temperature ( $T$ ) kelvin, a sphere at temperature ( $3T$ ) kelvin has cooling rate $R_1$ . When the temperature of that sphere falls to ( $2T$ ) kelvin, the cooling rate $R_2$ of the sphere will become

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Answer: (d)

Net rate of cooling $\propto T_s^4 - T^4$ .
At $3T$ : $(81 - 1)T^4 = 80T^4$ ; at $2T$ : $(16 - 1)T^4 = 15T^4$
$R_2 = \dfrac{15}{80}R_1 = \dfrac{3}{16}R_1$
So the answer is (d).

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