Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible),

Solution

Physics sir · 3 steps

Four times the radius gives 16 times the area, but half the temperature gives one-sixteenth.

1. What power depends on. By the Stefan-Boltzmann law, the power radiated is P = eσ A T⁴. Same material means the same emissivity e. For a sphere A = 4π r², so P ∝ r² T⁴.

   E_(big)/Eₛₘₐₗₗ = (r₂/r₁)²(T₂/T₁)⁴

2. Put in numbers. The area factor is (0.8/0.2)² = 4² = 16. The temperature factor is (400/800)⁴ = (1/2)⁴ = 1/16.
3. So. The ratio is 16 × 1/16 = 1, so the bigger body also radiates E. That is option (c).

The idea to keep. For radiation, always write P ∝ A T⁴ and take each ratio separately. For spheres, area goes as r², and the fourth power on T usually decides the answer.

Answer from the NTA final answer key. Solution by PrepWiser.