Question

A point source s of light is emitting a power p. A sphere of radius r is situated at a distance r from source s(r << r), has a mass m and specific heat capacity c, assuming that the sphere absorbs all the radiation incident on it. The time in which temperature of sphere rise by cc is:

Answer 1

2R²MCθ / Pr²

Explanation:

A point source S of light is emitting a power P.

A sphere of radius r is situated at a distance R from source S. (r<<R)

The sphere has a mass M and specific heat capacity C.

IR = P / 4πR²

So Power =  P / 4πR² * 2πr² = Pr² / 2R²

Now Pr² / 2R² * t = MCθ

Therefore T = 2R²MCθ / Pr²

The time in which temperature of sphere rises by θ∘C = 2R²MCθ / Pr²