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

The temperature of the ball is $T = 200^{{}^{{}^{\circ}}}\text{C} = 473 \text{ K}$.

The temperature of the surroundings is $T_0 = 57^{{}^{{}^{\circ}}}\text{C} = 330 \text{ K}$.

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

Since the ball absorbs all incident radiation, it behaves as a perfectly black body, giving an emissivity $e = 1$.

According to the Stefan-Boltzmann law, the net rate of heat flow is given by:

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

Substituting the given values:

$P = (6.0 \times 10^{-8}) \times 1 \times (20 \times 10^{-4}) \times (473^4 - 330^4)$

$P = 12 \times 10^{-11} \times (5.005 \times 10^{10} - 1.186 \times 10^{10})$

$P = 12 \times 10^{-11} \times (3.819 \times 10^{10})$

$P \approx 4.58 \text{ W}$

Since $T > T_0$, the net heat flow is from the ball.