There are two thin spheres A and B of the same material and same thickness. They behave like black bodies, Radius of A is double that of B and Both have same temperature T. When A and B are kept in a room of temperature `T_0 (lt T)`, the ratio of their rates of cooling is (assume negligible heat exchange between A and B).

Options

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

Answer

B

Explanation

The rate of heat loss by a thin hollow sphere of thickness `Deltax`, mean radius r and made of density `rho` is given by
`mS=(dT)/(dt)=epsilonsigmaA(T^4-T_0^4)`
`(rho4pir^2Deltax)S(dT)/(dt)=-epsisigma4pir^2(T^4-T_0^4)`
`(dT)/(dt)=(epsisigma(T^4_T_0^4))/(SDeltax)` is independent of radius Hence the rate of cooling is same for both spheres.