Question

Two spheres of the same material have radii 1m and 4 m and temperatures 4000 K and 2000 K respectively. The energy radiated per second by the first sphere is

(a) greater than that by the second

(b) less than that by the second

(c) equal in both cases

(d) the information is incomplete to draw any conclusion

Answer 1

Correct option (c) equal in both cases

Explanation:

The energy radiated per second E, by a body of surface area A, at temperature T K is given by,

E = K σAT⁴ (Stefan’s Law), where K is relative emissivity

E₁ = energy radiated per sec. by first sphere

= Kσ(4π(1)²)(4000)⁴ = Kσπ (1024 × 10¹²)J

Similarly, E₂ = Kσ [4π(4)²] (2000)⁴ 

= K σπ(1024 × 10¹²)J 

∴ E₁ = E₂