A solid sphere (density = 8900 kg / m 3 and specific heat capacity S = 390 J − kg − 1 − K − 1 ) of radius 10 cm is at an initial temperature T 1 = 200 K . It is then suspended inside a chamber whose

Question

A solid sphere (density = 8900 kg / m 3 and specific heat capacity S = 390 J − kg − 1 − K − 1 ) of radius 10 cm is at an initial temperature T 1 ​ = 200 K . It is then suspended inside a chamber whose walls are at almost 0 K. Calculate the time required for the temperature of the sphere to drop to T 2 ​ = 100 K . Given σ = 5.67 × 1 0 − 8 W / m 2 − K 4

TestHub · Accepted Answer

Radiative cooling: − MS d t d T ​ = σ ( 4 π r 2 ) T 4 , with M = 3 4 ​ π r 3 ρ t = 3 σ ρ r S ​ ∫ T 2 ​ T 1 ​ ​ T 4 d T ​ Substituting values gives t = 595165 s = 165 h rs 19 min (option D).

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