Question

A spherical black body of radius r radiates power P, and its rate of cooling is R. 

(a) P ∝ r 

(b) P ∝ r² 

(c) R ∝ r² 

(d) R ∝ 1/r

Answer 1

Correct Answer is: (b) P ∝ r² , (d) R ∝ 1/r

P = (4πr²)(σT⁴) = ms (- dT/dt) = - 4/3 πr³ ρs. dT/dt

Here, R = dT/dt.

 P ∝ r² and R ∝ 1/r.