Find the total time elapsed for a hollow copper sphere of inner radius `3cm` outer radius `6cm`, density `rho = 9 xx 10^(3) kg//m^(3)`, specific heat `s = 4 xx 10^(3) J//kg K` and emissivity `e = 0.4` to cool from `727^(@)C` to `227^(@)C` when the surrounding temperature is `0.K` (for inner surface `e = 1` Stefan's constant `sigma = 5.6 xx 10^(-8) W//m^(2)K^(4))`

Answer

`6.56 xx 10^(4)sec`

Explanation

`R_(i) = 3cm`
`R_(0) = 6cm`
`(dq)/(dt) = sigma eA (T^(4)-0^(4)) = ms (dT)/(dt)`
`overset(t_(2))underset(0)int dt =(ms)/(sigmaeA) overset(500)underset(1000)int (dT)/(T^(4))`
where `m = rho xx (4)/(3) pi (R_(0)^(3) -R_(i)^(3)) A = 4 pi R_(0)^(2)`