Suspended in an evacuated chamber kept at 300 K , a spherical...

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:

$P = e \sigma A (T^4 - T_0^4)$

Given:

Emissivity, $e = 0.30$

Stefan's constant, $\sigma = 6.0 \times 10^{-8} \text{ W m}^{-2} \text{ K}^{-4}$

Radius, $r = 1.0 \text{ cm} = 10^{-2} \text{ m}$

Surface area of the sphere, $A = 4\pi r^2 = 4\pi (10^{-2})^2 = 4\pi \times 10^{-4} \text{ m}^2$

Temperature of the sphere, $T = 1000 \text{ K}$

Temperature of the surroundings, $T_0 = 300 \text{ K}$

Substituting the values into the formula:

$P = 0.30 \times 6.0 \times 10^{-8} \times 4\pi \times 10^{-4} \times (1000^4 - 300^4)$

$P = 1.8 \times 10^{-8} \times 4\pi \times 10^{-4} \times (10^{12} - 81 \times 10^8)$

$P = 7.2\pi \times 10^{-12} \times 10^{12} (1 - 0.0081)$

$P = 7.2 \times 3.1416 \times 0.9919$

$P \approx 22.4 \text{ W}$

The closest value among the given options is $22 \text{ W}$.