$2095*($USE $79\mathrm{.}5$W$/$m$/$K for iron conductivity and $\mathrm{.}2$W$/$m$/$K for rubber.$)*$

A one person research submarine has an exterior spherical iron hull that is $1\mathrm{.}50$ meters in outer radius, $2\mathrm{.}00$ cm thick, and whose interior surface is lined with an equal thickness of rubber. If the submarine is used in Arctic waters $($temperature $OC)$ and the total rate of thermal energy release within the sub $($including the occupant $)$ is $1500$ Watts, find the equilibrium temperature of the interior. $($NOTE: solve problem by first deriving an expression for $R_{\text{s}\text{p}\text{h}\text{e}\text{r}\text{e}}$ and making use of it in your solution. Also, neglect both interior and exterior boundary layer resistances in your solution.$)$