Sum

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}.

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#### 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* = 4π*r*^{2}

*A* = 4 π (10^{−2})^{2}

A = 4 π × 10^{−4} m^{2}

Rate at which energy must be supplied is given by

eσA (T_{2}^{4} - T_{1}^{4})

= (0.3)× 6 × 10^{-8} × 4π × 10^{-4}×((1000)^{4} - (300)^{4})

= 22.42 ≈ watt = 22 watt

Concept: Stefan's Law

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