This JEE Mains 2025 Physics Radiation Question appeared in the 22nd Jan Shift 1 paper. It tests your understanding of Stefan–Boltzmann Law and thermal radiation concepts. Let’s solve it step by step.
🧠 Question:
Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in the same atmosphere. The temperature of the smaller body is 800 K and the temperature of the bigger body is 400 K. If the energy radiated from the smaller body is E, what is the energy radiated from the bigger body? Assume surroundings have negligible effect.
Options:
- 256 E
- E
- 64 E
- 16 E
✅ Step-by-Step Solution:
Concept Used: Stefan–Boltzmann Law
The power radiated by a body is given by:
P = σ × ε × A × T4
For spherical bodies, surface area A = 4πr2
So energy radiated E ∝ r2 × T4
Let:
- r1 = 0.2 m, T1 = 800 K (smaller body)
- r2 = 0.8 m, T2 = 400 K (bigger body)
Energy ratio:
Ebig / E = (r22 × T24) / (r12 × T14)
= (0.8 / 0.2)2 × (400 / 800)4
= 42 × (1/2)4 = 16 × 1/16 = 1
✅ Final Answer: Option (2) E
📺 Video Solution:
📘 Related Concept:
To revise the Stefan–Boltzmann Law in detail, read this Wikipedia article.
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