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Question #42534

Difficulty: 8/10 | 🟢 Free

The Question

A solid sphere of radius $R$ and emissivity $\epsilon_1 = 0.5$ is maintained at a constant temperature $T_1 = 2T_0$ . It is completely enclosed by a concentric hollow sphere of radius $2R$ and emissivity $\epsilon_2 = 0.5$ maintained at a constant temperature $T_2 = T_0$ . The space between the spheres is evacuated. The net rate of radiative heat transfer from the inner sphere to the outer sphere is given by $k \pi R^2 \sigma T_0^4$ , where $\sigma$ is the Stefan-Boltzmann constant. Find the value of $k$ .

Options

A.
$\frac{80}{3}$
B.
20
C.
30
D.
15

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Emissivity and Absorptivity|Superposition Principle|Small Angle Approximation

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of radiative heat transfer between enclosed surfaces using the radiosity method, moving beyond the simplified Stefan-Boltzmann equation for a single body.

A common trap is blindly applying the effective emissivity formula for infinite parallel plates ( $\frac{1}{\epsilon_1} + \frac{1}{\epsilon_2} - 1$ ), which ignores the area ratio and view factor geometry of concentric spheres.

Another frequent mistake is assuming the outer sphere acts as a perfect blackbody ( $\epsilon_2=1$ ) because it is an enclosure, failing to account for the infinite series of reflections between the two non-black surfaces.

By requiring the full thermal resistance network, it forces a first-principles approach to radiative transport.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Thermal Properties of Matter - Class 11 Part 2
Concept	Emissivity and Absorptivity
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free