Question

A solid spherical black body of radius r and uniform mass distribution is in free space. It emits power 'P' and it's rate of cooling is R, then -

• A. RP µ r²
• B. RP µ r
• C. RP µ 1/r²
• D. RP µ 1/r

Answer 1

Answer: (B)

RP µ r

Answer 2

Rate of radiation per unit area is proportional to (T⁴)

\ P µ AT⁴

̃ P µ r²

Also $ms\frac{dT}{dt}$ µ AT⁴

\ $\frac{dT}{dt}$ = R µ $\frac{1}{r}$

(because m = (Vp) µ r³ and A µ r²)\ PR µ r