A metallic sphere having radius `0.08 m` and mass `m = 10 kg` is heated to a temperature of `227^(@)C` and suspended inside a box whose walls ae at a temperature of `27^(@)C`. The maximum rate at which its temperature will fall is:-
(Take `e =1`, Stefan's constant `sigma = 5.8 xx 10^(-8) W//m^(-2)K^(-4)` and specific heat of the metal `s = 90 cal//kg//deg J = 4.2 "Joules"//"Calorie")`

Options

A. `.055""^(@)C//sec`
B. `.066""^(@)C//sec`
C. `.044""^(@)C//sec`
D. `0.03""^(@)C//sec`

Answer

B

Explanation

`(-(dT)/(dt))=(sigmacA)/(mS)[T^(4)-T_(S)^(4)]`
Rate of temperature fall will maximum when (`T^(4)-T_(S)^(4)`) has amximum value i.e. T has max. value