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. `0.055^(@)C//s`
B. `0.066^(@)C//s`
C. `0.044 ^(@)C//s`
D. `0.03 ^(@)C//s`

Answer

B

Explanation

From Stefan's law of cooling :
`esigmaA(T^(4)-T_(0)^(4)) = ms(-(dT)/(dt))`
` implies 1 xx 5.8 xx 10^(-8) xx pi xx (0.08)^(2)xx (500^(4) - 300^(4))`
=` 10 xx 90 xx 4.2 xx(-(dT)/(dt)) implies (-(dT)/(dt)) = 0.067^(@)C//s`