A $2\mathrm{.}5$m internal diameter double walled spherical tank is used to store iced water at $0$ C$.$ Each wall is $0\mathrm{.}5$ cm thick, and the $1\mathrm{.}5$ cm thick air space between the walls of the tank is evacuated in order to minimize heat transfer. The surfaces surrounding the evacuated space are polished SO that each surface has an emissivity of $0\mathrm{.}20.$ The temperature of the outer wall of the tank is measured to be $25$ C Assuming the inner wall of the steel tank to be at $0$ C$,$ determine: $($a$)$ The rate of heat transfer to the iced water in the tank $($b$)$ The amount of ice at $0$ C that melts during a $24$h period