A shop air $(=0\mathrm{.}24$ Btu$/$lbm$-$R$,=0\mathrm{.}172$ Btu$/$lbm$-$R$)$ compressor rated at $1-(1)/(2)$ horsepower is operating steadily while dissipating $600$ Btu$/$hr of heat to the surroundings. If the air temperature is increased by $50$ degrees $($F$)$ with an exit volume flow rate of $45$ cfm $($cubic feet per minute$)$ determine the density of air $($lbm$/$ft$3)$ exiting the compressor.