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Question

A spherical tungsten piece of radius 1.0 cm is suspended in an evacuated chamber maintained at 300 K. The piece is maintained at 1000 K by heating it electrically. Find the rate at which the electrical energy must be supplied. The emissivity of tungsten is 0.30 and the Stefan constant \sigma is 6.0 ×108Wm2K4.

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Solution

r = 1 cm = 1×102m,

A = 4π(102)2

= 4π×104m2

e = 0.3, σ=6×108

Et=eσA(T42T41)

= 0.3×6×108×4π×104×[(1000)4(300)4]

= 0.3×6×4π×1012×[10.0081]×1012

= 0.3×64×3.14×9919×104

= 4×18×3.14×9919×105

= 22.4 = 22 W.


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