A house has well-insulated walls 19.5 $\mathrm{cm}$ thick (assume
conductivity of air) and area $410 \mathrm{m}^{2},$ a roof of wood 5.5 $\mathrm{cm}$
thick area $280 \mathrm{m}^{2},$ and uncovered windows 0.65 $\mathrm{cm}$
thick and total area 33 $\mathrm{m}^{2}$ . (a) Assuming that heat is lost
only by conduction, calculate the rate at which heat must
be supplied to this house to maintain its inside temperature
at $23^{\circ} \mathrm{C}$ if the outside temperature is $-15^{\circ} \mathrm{C}$ (b) If the
house is initially at $12^{\circ} \mathrm{C}$ , estimate how much heat must be
supplied to raise the temperature to $23^{\circ} \mathrm{C}$ within 30 $\mathrm{min}$ .
Assume that only the air needs to be heated and that its
volume is 750 $\mathrm{m}^{3} .(c)$ If natural gas costs $\$ 0.080$ per kilo-
gram and its heat of combustion is $5.4 \times 10^{7} \mathrm{J} / \mathrm{kg},$ how
much is the monthly cost to maintain the house as in part
(a) for 24 h each day, assuming 90$\%$ of the heat produced is
used to heat the house? Take the specific heat of air to be
0.24 $\mathrm{kcal} / \mathrm{kg} \cdot \mathrm{C}^{\circ} .$