The adiabatic atmosphere obeys the equation

\[P / ho^{k}=\text { Constant }\]

where

$k$ is a constant

$ho$ is density

If the temperature decreases $0.3^{\circ} \mathrm{C}$ for every $100 \mathrm{ft}$ increase in altitude, what is the value of $k$ ? [Note: Air is an ideal gas; $g=32.2 \mathrm{ft} / \mathrm{s}^{2} ; R=1544 \mathrm{ft} \mathrm{lb}_{\mathrm{f}} /\left({ }^{\circ} \mathrm{R} \mathrm{lbmol}\right)$.