$1\mathrm{.}8.$ A gas is compressed from atmospheric pressure to a pressure of $4$ atm $.$ Temperature changes from $300$ K to $400$ K $.$ Find the density after compression. Assume perfect gas behavior for gas with initial density of $1\mathrm{.}176k\frac{g}{m^3}.$

$1\mathrm{.}17.$ Using equations $(1\mathrm{.}21)$ and $(1\mathrm{.}22),$ calculate the temperature and pressure of the atmosphere at $9000$ m $.$ Compare the tabulated values with those presented in Table $1\mathrm{.}2.$

Problems $1\mathrm{.}21$ and $1\mathrm{.}22$ deal with standard atmosphere usage. The properties of the standard atmosphere are frequently used as the free$-$stream reference conditions for aircraft performance predictions. It is common to refer to the free$-$stream properties by the altitude in the atmospheric model at which those conditions occur. For instance, if the density of the free$-$stream flow is $0\mathrm{.}00199$ slugs $\frac{?}{f{t}^3},$ then the density altitude $(h_o)$ would be $6000$ ft