a small blackened solid copper sphere of radius 2.5cm and absorption coefficient 0.9 is placed in an evacuated chamber. The temperature of the chamber is maintained at 27°C. At what rate must energy be supplied to the copper sphere of maintain its temperature at 127°C ?
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Answer:
r=2.5cm=2.5×10
−2
m,
T
0
=273+100=373K, T=273+110=383K,
σ=5.67×10
−8
Js
−1
m
−2
K
−4
The rate at which energy must be supplied
σA(T
4
−T
0
4
)=σπr
2
(T
4
−T
0
4
)
=(5.67×10
−8
)(4)(3.140)(2.5×10
−2
)
2
(383
4
−373
4
)
=(5.67)(4)(3.142)(6.25)(3.834−3.734)×10
−4
=0.9624W
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