(d) Calculate the maximum amount of heat which may be lost per second by radiation from a sphere of 5 cm in diameter at a temperature of 600 K when placed in an enclosure at a temperature of 300 K. Given that, \(\sigma = 5.7 \times 10^{-12} \, \text{watts/cm}^{-2}/(^\circ \text{C})^{-1}\).

The surface area of the sphere is \(4\pi r^2 = 4\pi (2.5)^2 = 25\pi \, \text{cm}^2\).

Using Stefan-Boltzmann's Law, the power radiated is given by:

\(P = \sigma A (T_1^4 - T_2^4)\)

Where:

• \(\sigma = 5.7 \times 10^{-12} \, \text{watts/cm}^2/K^4\)
• \(A = 25\pi \, \text{cm}^2\)
• \(T_1 = 600 \, K\)
• \(T_2 = 300 \, K\)

Substituting the values:

\(P = 5.7 \times 10^{-12} \times 25\pi \times (600^4 - 300^4) \approx 0.71 \, \text{watts}\)

Therefore, the maximum amount of heat lost per second by radiation is approximately 0.71 watts.