$2-2$: A certain superinsulation material having a thermal conductivity of $2$ x $10-4$

W$/$m $$C is used to insulate a tank of liquid nitrogen that is maintained at $-196$C;

$199$kJ is required to vaporize each kilogram mass of nitrogen at this temperature.

Assuming that the tank is a sphere having an inner diameter $($ID$)$ of $0\mathrm{.}52$ m$,$ estimate

the amount of vaporized nitrogen per day for an insulation of thickness of $2\mathrm{.}5$ cm

and an ambient temperature of $21$C$.$ Assume that the outer temperature of the

insulation is $21$C and that the heat of vaporization of the nitrogen is not a function

of temperature. Since the tank$$s diameter is large compared to its thickness, treat

the wall as planar with the appropriate area.