(5) Two large closely spaced concentric spheres (both are black body radiators) are maintained at temperatures of 200 K and 300 K respectively. The space in between the two spheres is evacuated. Calculate the net rate of energy transfer between the two spheres. [Given: \(\sigma = 5.672 \times 10^{-8} \, \text{W/m}^2\text{K}^4\)]

Another Explanation (5): Let \(T_1 = 200 \, K\) and \(T_2 = 300 \, K\) be the temperatures of the inner and outer spheres respectively. Since the spheres are black bodies, the net rate of energy transfer per unit area is given by Stefan-Boltzmann law: \(P = \sigma (T_2^4 - T_1^4)\) where σ is the Stefan-Boltzmann constant. Let's assume the area of the inner sphere is A. Then the total power transferred is: \(P_{total} = A \sigma (T_2^4 - T_1^4) = A \times (5.672 \times 10^{-8}) \times (300^4 - 200^4) \, W\) Without knowing the area A, we cannot calculate the exact numerical value. However, the expression for the net rate of energy transfer is: \(P_{total} = A \times 5.672 \times 10^{-8} \times (81 \times 10^8 - 16 \times 10^8) \, W = A \times 5.672 \times 10^{-8} \times 65 \times 10^8 \, W = 368.64 A \, W\)