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प्रश्न
A small blackened solid copper sphere of radius 2.5 cm is placed in an evacuated chamber. The temperature of the chamber is maintained at 100 °C. At what rate must energy be supplied to the copper sphere to maintain its temperature at 110 °C? (Take Stefan’s constant σ to be 5.67 × 10-8 J s-1 m-2 K-4) and treat the sphere as a blackbody.)
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उत्तर
Data: r = 2.5 cm = 2.5 × 10-2m, T0 = 273 + 100 = 373 K, T = 273 + 110 = 383 K,
σ = 5.67 × 10-8 J s-1 m-2k-4
The rate at which energy must be supplied =
`sigma"A" ("T"^4 - "T"_0^4) = sigma4pi"r"^2("T"^4 - "T"_0^4)`
= (5.67 × 10-8) (4) (3.142) (2.5 × 10-2)2 (3834 - 3734)
= (5.67) (4) (3.142) (6.25) (3.834 - 3.734) × 10-4
= 0.9624 W
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