Question

A spherical body of radius ‘r’ radiates power ‘P’ at T kelvin. If the radius s halved and the temperature doubled the power radiated in the same time ‘t’ will be ______.

Options

• `P/2`

• 2P

• 4P

• 8P

Answer 1

A spherical body of radius ‘r’ radiates power ‘P’ at T kelvin. If the radius s halved and the temperature doubled the power radiated in the same time ‘t’ will be 4P.

Explanation:

Radiated power by a blackbody (P) = `Q/t`

For any two bodies of radii R₁ and R₂, kept at temperatures T₁ and T₂, the power radiated, or rate of loss of heat by them, can be given as:

`Q_1/Q_2 = (R_1/R_2)^2 xx (T_1/T_2)^4`

In the case of non-spherical bodies, `(R_1/R_2)^2` can be replaced by `(A_1/A_2)` where A₁, A₂ are areas of the given bodies.

∴ `P_1/P_2 = (r_1/r_2)^2 xx (T_1/T_2)^4` 

= `(r_1/(r_1/2))^2 xx (T_1/(2T_1))^4`

∴ `P_1/P_2 = 4 xx 1/16`

⇒ P₂ = 4P₁