$(20$ points$)$

A $450$ feet tall building has openings and cracks uniformly distributed along its height. The temperature inside the building is $70F$ when the outside temperature is $15F.$ The barometric pressure is $14\mathrm{.}696$ psia. Determine the outside$-$to$-$inside pressure difference, in inches of water, caused by stack effect at a height of:

a$)150$ feet

b$)425$ feet

c$)$ Comment on the results of parts a$)$ and b$)$ with respect to the inside$/$outside direction of air flow.

Use value of the gas constant for air, $R_{\text{a}\text{i}\text{r}}=53\mathrm{.}352ft.lb\frac{f}{l}b{m}_m.{?}^{0}R$