Question

A spherical ball of surface area 20 cm² absorbs any radiation that falls on it. It is suspended in a closed box maintained at 57°C. (a) Find the amount of radiation falling on the ball per second. (b) Find the net rate of heat flow to or from the ball at an instant when its temperature is 200°C. Stefan constant = 6.0 × 10⁻⁸ W m⁻² K⁻⁴.

Answer 1

(a)
Area of the ball, A = 20 × 10⁻⁴ m²
Temperature of the ball, T = 57°C = 57 + 273 = 330 K
Amount of heat radiated per second = AσT⁴
= 20 × 10⁻⁴ × 6 × 10⁻⁸ × (330)⁴
= 1.42 J

(b)
Net rate of heat flow from the ball when its temperature is 200$°\mathrm{C}$ is given by

$$\begin{gathered} eA\sigma \left(T_1^4-T_2^4\right) \\ =20\times {10}^{-4}\times 6\times {10}^{-8}\times 1\left({\left(473\right)}^4-{\left(330\right)}^4\right)[\because e=1] \\ =4.58\mathrm{W} \end{gathered}$$