Suspended in an evacuated chamber kept at 300 K , a spherical tungsten piece of radius 1.0 cm is maintained at a temperature of 1000 K via electrical heating. Determine the rate at which electrical energy must be supplied. The emissivity of tungsten is 0.30 and the Stefan constant is 6.0 10⁻⁸ W m ⁻² K ⁻⁴ .

Step-by-step solution

The rate of electrical energy supplied must equal the net rate of heat loss by radiation to maintain a constant temperature. According to the Stefan-Boltzmann law, the net rate of heat loss is given by: P = e A (T^4 - T₀^4) Given: Emissivity, e = 0.30 Stefan's constant, = 6.0 10⁻⁸ W m ⁻² K ⁻⁴ Radius, r = 1.0 cm = 10⁻² m Surface area of the sphere, A = 4 r^2 = 4 (10⁻²)^2 = 4 10⁻⁴ m ^2 Temperature of the sphere, T = 1000 K Temperature of the surroundings, T₀ = 300 K Substituting the values into the formula: P = 0.30