A solid copper sphere of diameter 10 mm, is cooled to a temperature of 150 K and is then placed in an enclosure at 290 K. Assuming that all interchange of heat is by radiation, calculate the initial r

Question

A solid copper sphere of diameter 10 mm, is cooled to a temperature of 150 K and is then placed in an enclosure at 290 K. Assuming that all interchange of heat is by radiation, calculate the initial rate of rise of temperature of the sphere. The sphere may be treated as a black body. ρ co pp er ​ = 8.93 × 1 0 3 kg/m 3 , s = 3.7 × 1 0 2 J kg − 1 K − 1 ; σ = 5.7 × 1 0 − 8 W m − 2 K − 4

TestHub · Accepted Answer

m s d t d T ​ = σ A ( T s 4 ​ − T 4 ) with m = 3 4 ​ π r 3 ρ , A = 4 π r 2 . d t d T ​ = r ρ s 3 σ ( T s 4 ​ − T 4 ) ​ with r = 5 × 1 0 − 3 m. T s 4 ​ − T 4 = 29 0 4 − 15 0 4 = 7.073 × 1 0 9 − 5.06 × 1 0 8 = 6.57 × 1 0 9 K 4 d t d T ​ = ( 5 × 1 0 − 3 ) ( 8930 ) ( 370 ) 3 ( 5.7 × 1 0 − 8 ) ( 6.57 × 1 0 9 ) ​ = 16520 1123 ​ ≈ 0.068 K/s Option (B).

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