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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 in 0.30 and the Stefan constant σ is 6.0 × 10-8 W/m2-K4.

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 in 0.30 and the Stefan constant σ is 6.0 × 10-8 W/m2-K4.

Grade:10

2 Answers

Jitender Pal
askIITians Faculty 365 Points
9 years ago
Sol. r = 1 cm = 1 × 10^–3 m A = 4π(10^–2)^2 = 4π × 10^–4 m^2 E = 0.3, σ = 6 * 10^-8 E/t = Aσe(T base 1^4 – T base 2^4) = 0.3 × 6 × 10^–8 × 4π × 10^–4 × [(100)^4 – (300)^4] = 0.3 × 6 × 4π × 10^–12 × [1 – 0.0081] × 10^12 = 0.3 × 6 × 4 × 3.14 × 9919 × 10^–4 = 4 × 18 × 3.14 × 9919 × 10^–5 = 22.4 ≈ 22 W
Pmt
15 Points
5 years ago
Net rate of loss of heat=A×sigma×e[(1000)^4 (300)^4]. Solve this to get the answer.

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