Question

Calculate the energy radiated in one minute by a perfect black sphere of radius 5cm and maintained at 127°c.​

Answer 1

We have to calculate the energy radiated in one minute by a perfect body sphere of radius 5cm and maintained at 127°C.

solution : rate of energy radiated by a black body is given by, P = σAT⁴

where σ is Stefan's Boltzmann's constant. i.e., σ = 5.67 × 10^ -8 Watt/m²/K⁴

here, surface area of sphere, A = 4πr²

= 4 × 3.14 × (5 × 10¯² m)

= 314 m²

Temperature, T = 127°C = 127 + 273 = 400K

Therefore, P = 5.67 × 10^-8 × 314 × (400)⁴ watt

= 455777.28 × 10^-8 × 10^8 watt

= 455777.28 watt ≈ 4.56 × 10⁵ watt

so energy radiated by the black body, E = P × t

= 4.56 × 10⁵ × 60 sec

= 27.36 × 10⁶ J

Therefore the energy radiated by the black body is 27.36 MJ

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