A Copper sphere is suspended in an evacuated chamber maintained at 200K. The sphere is maintained at a constant Temperature of 400 K by heating electrically. A total of 150 W of electric power needed

Question

A Copper sphere is suspended in an evacuated chamber maintained at 200K. The sphere is maintained at a constant Temperature of 400 K by heating electrically. A total of 150 W of electric power needed to maintain sphere at constant temperature. When half of the copper sphere is completely blackened then 300 W electrical power is needed to maintain the same temperature of the sphere. Calculate emissivity of copper.

TestHub · Accepted Answer

150 = eA σ [ ( 400 ) 4 − ( 200 ) 4 ] ..... (i) 300 = 2 eA σ ​ [ ( 400 ) 4 − ( 200 ) 4 ] + 2 A σ ​ [ ( 400 ) 4 − ( 200 ) 4 ] ..... (ii) Dividing (ii) by (i): 150 300 ​ = e ( 2 e ​ + 2 1 ​ ) ​ ⇒ 2 e = 2 e ​ + 2 1 ​ ⇒ 2 3 e ​ = 2 1 ​ ⇒ e = 3 1 ​ hence (A).

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