#$3.$ a$)$ Consider a tall building; let's assume a height of $1200ft.$ Is atmospheric pressure significantly less at the top of the building than at the bottom? Use the barometric distribution law $($assumes no temperature difference between top and bottom of the building$)$ to calculate the ratio of pressures $p($top$)/$p$($bottom$).$ For simplicity, assume a nitrogen atmosphere, and $298K.$

b$)$ Now, repeat the calculation, but comparing sea level to Mt$.$ Everest $($assume $28,000$ feet$).($This calculation is rather approximate, because in reality, $T$ is $25\%$ lower on top, but we will ignore that$).$