Question

Two black metallic spheres of radius 4m, at 2000 K and 1m at 4000 K will have ratio of energy radiation as

• A. 1 : 1
• B. 4 : 1
• C. 1 : 4
• D. 2 : 1

Answer 1

Answer: (A)

1 : 1

Answer 2

Q = σ A t T⁴ ⇒

$\frac{Q_{1}}{Q_{2}} = \frac{A_{1}}{A_{2}}\left( \frac{T_{1}}{T_{2}} \right)^{4} = \frac{\pi r_{1}^{2}}{\pi r_{2}^{2}}\left( \frac{T_{1}}{T_{2}} \right)^{4} = \left( \frac{4}{1} \right)^{2} \times \left( \frac{2000}{4000} \right)^{4} = 16 \times \frac{1}{16} = 1:1$.