Suspended inside a closed box maintained at 57^ C , a spherical ball with a surface area of 20 cm ^2 absorbs all incident radiation. Determine the amount of radiation falling on the ball per second. Use a Stefan constant of 6.0 10⁻⁸ W m ⁻² K ⁻⁴ .

Step-by-step solution

The temperature of the enclosure is T = 57^ C = 57 + 273 = 330 K . The surface area of the ball is A = 20 cm ^2 = 20 10⁻⁴ 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 = A T^4 Substituting the given values: E = (6.0 10⁻⁸) (20 10⁻⁴) (330)^4 E = 120 10⁻¹² 1.186 10¹⁰ E 1.42 J/s The amount of radiation falling on the ball per second