Question

Calculate the energy radiated in one minute by a perfectly black body of surface area 200 cm² when it is maintained at 127°C.

Answer 1

Given: A = 200 cm² = 200 × 10⁻⁴ m² = 0.02 m²

T = 127°C = (127 + 273) K = 400 K

t = 1 min = 60 s

σ = 5.67 × 10⁻⁸ W/m² K⁴

The total energy radiated is given by the Stefan-Boltzmann Law:

Q = σ AtT⁴

= (5.67 × 10⁻⁸) × 0.02 × 60 × (400)⁴

= (5.67 × 10⁻⁸) × 0.02 × 60 × (256 × 10⁸)        ...(400⁴ = 256 × 10⁸) 

= 5.67 × 10⁻⁸ × 307.2 × 10⁸

= 5.67 × 307.2

= 1741.82 J