A black metal foil is warmed by radiation from a small sphere at temperature `T` and at a distance d it is found that the power received by the foil is `P` If both the temperature and the distance are doubled the power received by the foil will be .

Options

A. `16 P`
B. `4 P`
C. `2 P`
D. P

Answer

B

Explanation

We use `s=(P)/(4pir^(2))=(4piR^(2)sigmaT^(4))/(4pir^(2))`
`implies (s_(1))/(s_(2))=(T_(1)^(4))/(r_(1)^(2))xx(r_(2)^(2))/(T_(2)^(4))`
`implies (s_(1))/(s_(2))=(T_(1)/(2T_(1)))^(4)xx((2r_(1))/(r_(1)))^(2)`
`implies (s_(1))/(s_(2))=(1)/(2^(4))xx2^(2)`
`implies(s_(1))/(s_(2))=(1)/(4)`
`implies s_(2)=4s_(1)=4P`