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.

Answer 1

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 = 4$\pi$r²
A = 4$\pi$ (10⁻²)²
A = 4$\pi$ × 10⁻⁴ m²

Rate at which energy must be supplied is given by

$e\sigma A\left(T_2^4-T_1^4\right)$
= (0.3) × 6 × 10⁻⁸ × 4$\pi$ × 10⁻⁴ × ((1000)⁴ − (300)⁴)
= 22.42 $\approx$ watt = 22 watt