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Two concentric black (perfectly absorbing) spheres have radii R1 and R2 (R1 < R2) and are kept at temperatures T1 and T2 respectively. Find the rate of net radiative heat flow between them.

1. 4*pi*sigma*R1²*(T1⁴ - T2⁴)
2. 4*pi*sigma*R1*R2*(T1⁴ - T2⁴)
3. 4*pi*sigma*R2²*(T1⁴ - T2⁴)
4. 4*pi*sigma*(R1² + R2²)*(T1⁴ - T2⁴)

Correct answer: 4*pi*sigma*R1²*(T1⁴ - T2⁴)

Solution

Since both surfaces are black, the net radiative transfer between concentric spheres is set by the inner sphere's surface area, giving 4 pi sigma R1² (T1⁴ - T2⁴).

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