Suspended inside a closed box maintained at 57^ ^ ^ C , a spherical...

The temperature of the enclosure is T = 57^{}^{{}^{\circ}} \text{C} = 57 + 273 = 330 \text{ K}.

The surface area of the ball is $A = 20 \text{ cm}^2 = 20 \times 10^{-4} \text{ m}^2$.

According to Prevost's theory of heat exchange, the radiation incident on a body placed inside an enclosure depends only on the temperature of the enclosure. The amount of radiation falling on the ball per second is given by:

$E = \sigma A T^4$

Substituting the given values:

$E = (6.0 \times 10^{-8}) \times (20 \times 10^{-4}) \times (330)^4$

$E = 120 \times 10^{-12} \times 1.186 \times 10^{10}$

$E \approx 1.42 \text{ J/s}$

The amount of radiation falling on the ball per second is approximately $1.4 \text{ J}$.