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Given r₁ = 12 cm, r₂ = 6 cm, T₁ = 500 K and T₂ = 2 × 500 = 1000 K, P₁ = 450 watt. Rate of power loss P ∝ T⁴. Find P₂.

1. P₂ = n²T₂⁴ / n²T₁⁴
2. P₂ = n²T₁⁴ / n²T₂⁴
3. P₂ = T₁⁴ / T₂⁴
4. P₂ = T₂⁴ / T₁⁴

Correct answer: P₂ = T₂⁴ / T₁⁴

Solution

The rate of power loss is proportional to the fourth power of temperature, i.e., P ∝ T⁴. Therefore, the ratio of power losses is P₂ / P₁ = (T₂ / T₁)⁴. Rearranging gives P₂ = P₁ × (T₂ / T₁)⁴. This matches option D.

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