A copper ball of diameter `d = 1.2cm` was placed in an evacuated vessel whose walls are kept at the absolute zero temperature. The initial temperatures of the ball is `T_(0) = 300K`. Assuming the surface of the ball to be absolutely balck, find how soon its temperature decreases `eta = 2.0` times.

Explanation

In time `dt` after the instant `t` when the temperature of the ball is `T`, it loses
`pid^(2) sigmaT^(4)dt`
Joules of enegry. As a result its temperature falls by `-dT` and
`pid^(2) sigmaT^(4) dt=- (pi)/(6)d^(3)rhoCdT`
where `rho =` density of copper, `C =` its sh.heat
Thus `dt =- (C rhod)/(6 sigma)(dT)/(T^(4))`
or `t_(0)(C rhod)/(6 sigma) underset(T_(0))overset(T_(0)//eta)int - (dT)/(T^(4)) = (C rhod)/(18 sigma T_(0)^(3)) (et^(3) - 1) = 2.94` hours.