A certain super$-$insulation material having a thermal conductivity of $2\mathrm{.}0$ x $10-4$ W$/$m$\backslash$deg C is used to

insulate a tank of liquid nitrogen that is maintained at $-320\backslash$deg F$.85\mathrm{.}8$ Btu is required to vaporize

each pound mass of nitrogen at this temperature. Assuming that the tank is a sphere having an

ID of $2\mathrm{.}0$ ft$,$ estimate the amount of nitrogen vaporized per day for an insulation thickness of $1\mathrm{.}0$

inch and an ambient temperature of $70\mathrm{.}0\backslash$deg F