Physics · Heat transfer: conduction, convection and radiation

Two spheres of the same metal have radii and and temperature and respectively. T

Two spheres of the same metal have radii \( 1 \mathrm{m} \) and \( 4 \mathrm{m} \) and temperature \( 4000 K \) and \( 2000 K \) respectively. The ratio of the energy radiated per second by the first to the second is :

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

Step-by-step solution

Using Stefan-Boltzmann law, power radiated P = εσAT⁴. Since spheres are same metal, ε same. Area A ∝ r², so P ∝ r² T⁴. Ratio P₁/P₂ = (r₁/r₂)² × (T₁/T₂)⁴ = (1/4)² × (4000/2000)⁴ = (1/16) × (2)⁴ = 16/16 = 1. Hence ratio 1:1.
Practise more in this unitView MCQsSign up for full question bank