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 $\times {10}^{-8}W{m}^{-2}{K}^{-4}$.

Answer 1

r = 1 cm = $1\times {10}^{-2}$m,

A = $4\pi ({10}^{-2}{)}^2$

= $4\pi \times {10}^{-4}{m}^2$

e = 0.3, $\sigma =6\times {10}^{-8}$

$\frac{E}{t}=e\sigma A(T_2^4-T_1^4)$

= $0.3\times 6\times {10}^{-8}\times 4\pi \times {10}^{-4}\times \left[\right(1000{)}^4-\left(300{)}^4\right]$

= $0.3\times 6\times 4\pi \times {10}^{-12}\times [1-0.0081]\times 1012$

= $0.3\times 64\times 3.14\times 9919\times {10}^4$

= $4\times 18\times 3.14\times 9919\times {10}^{-5}$

= 22.4 = 22 W.