The temperature of a spherical black body is inversely proportional to its radius . If its radius is doubled then the power radiating from it will be

Options

A. doubled
B. `(1)/(4) ` times of initial value
C. halved
D. four times of initial value

Answer

B

Explanation

Power radiating from a black body is given by
P=` sigma AT^(4) " " cdots(i)`
For a spherical body ,
`A = 4piR^(2) " " cdots(ii)`
and it is also given that
` T prop (1)/( R) or T = (k)/(R ) " " cdots (iii)`
From Eqs (i) , (ii) and (iii) we have
`P = sigma 4piR^(2). (k^(4))/(R^(4)) or P prop (1)/(R^(2))`
So when radius is doubled radiating power of sphere becomes one fourth.