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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 σ is 6.0 × 10−8 W m−2 K−4.
Solution
Given:
Radius of the spherical tungsten, r = 10−2 m
Emissivity of the tungsten, e = 0.3
Stefan's constant, σ = 6.0 × 10−8 W m−2 K−4
Surface area of the spherical tungsten, A = 4πr2
A = 4 π (10−2)2
A = 4 π × 10−4 m2
Rate at which energy must be supplied is given by
eσA (T24 - T14)
= (0.3)× 6 × 10-8 × 4π × 10-4×((1000)4 - (300)4)
= 22.42 ≈ watt = 22 watt
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