A solid copper sphere ( e = 1 , density ρ and specific heat capacity c ) of radius r at an initial temperature 200 K is suspended inside a chamber whose walls are at almost 0 K . The time required (in

Question

A solid copper sphere ( e = 1 , density ρ and specific heat capacity c ) of radius r at an initial temperature 200 K is suspended inside a chamber whose walls are at almost 0 K . The time required (in μ s ) for the temperature of the sphere to drop to 100 K is 72 n ​ σ r ρ c ​ . Find the value of n . (All symbols have their usual meaning)

TestHub · Accepted Answer

​ − A 1 ​ dt dQ ​ = σ ( T 4 − 0 4 ) ⇒ − mc dt dT ​ = σ AT 4 ⇒ T − 4 dT = − mc σ A ​ dt ⇒ ∫ 200 K 100 K ​ T − 4 dt = − mc σ A ​ ∫ 0 t ​ dt ⇒ − 3 T − 3 ​ ​ 200 100 ​ = − mc σ A ​ t ⇒ ( 100 ) 3 1 ​ − ( 200 ) 3 1 ​ = 3 4 ​ π r 3 ρ c σ ( 4 π r 2 ) ​ ⇒ t = 72 7 ​ σ r ρ c ​ × 1 0 − 6 s ⇒ t = 72 7 ​ σ ρ pc ​ μ s ​

Physics - Heat & Thermo Question with Solution | TestHub

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