Two copper spheres of radii 6 cm and 12 cm respectively are suspended in an evacuated. Each of them is at a temperature `15^(@)C` above the surroundings. The ratio of their of loss of heat is

Options

A. `2 : 1`
B. `1 : 4`
C. `1 : 8`
D. `8 : 1`

Answer

B

Explanation

The two spheres have the same material. Similarly their temperature are `15^(@)C` above the surrounding. i.e. they are at the same temperature.
`therefore` According to Stefan's law rate of loss of heat or
`((dQ)/(dt))propAT^(4)`
`thereforeR_(1)/R_(2)=A_(1)/A_(2)(T_(1)/T_(2))^(4)` but `T_(1)=T_(2)`
`thereforeR_(1)/R_(2)=A_(1)/A_(2)=(4piR_(1)^(2))/(4piR_(2)^(2))=(6/12)^(2)=1/4`