Consider a $400$ mm by $400$ mm window in an aircraft.

For a temperature difference of $90$C from the inner to the outer surface of the window,

a$.)$ Calculate the heat flow rate through L$=12-$mm$-$thick polycarbonate,

b$.)$ soda lime glass,

c$.)$ and aerogel windows, respectively.

The thermal conductivities of the aerogel, soda lime glass and polycarbonate are k ag $=0\mathrm{.}04$ W$/$m$.$K

kgl $=1\mathrm{.}4$ W$/$m$.$K and kpc $=0\mathrm{.}21$ W$/$m$.$K$,$ respectively.

d$-$f$.)$ If the aircraft has $130$ windows and the cost to heat the cabin air is $ $1/$kW$.$h$,$ compare the

costs associated with the heat loss through the windows for an $8-$hour intercontinental flight.