(Solved): The procedure to inflate a hot-air balloon requires a fan to move an initial amount of air into th ...

The procedure to inflate a hot-air balloon requires a fan to move an initial amount of air into the balloon envelope followed by heat transfer from a propane burner to complete the inflation process. After a fan operates for 20 minutes with negligible heat transfer with the surroundings, the air in an initially deflated balloon achieves a temperature of \( 80^{\circ} \mathrm{F} \) and a volume of \( 49,100 \mathrm{ft}^{3} \). Next the propane burner provides heat transfer as air continues to flow into the balloon without use of the fan until the air in the balloon reaches a volume of \( 65,425 \mathrm{ft}^{3} \) and a temperature of \( 210^{\circ} \mathrm{F} \). Air at \( 77^{\circ} \mathrm{F} \) and \( 14.7 \mathrm{lbf} / \mathrm{in}^{2}{ }^{2} \) surrounds the balloon. The net rate of heat transfer is \( 2 \times 10^{6} \mathrm{Btu} / \mathrm{h} \). Ignoring effects due to kinetic and potential energy, modeling the air as an ideal gas, and assuming the pressure of the air inside the balloon remains the same as that of the surrounding air, determine: (a) the magnitude of the fan power, in hp. (b) the time required for full inflation of the balloon, in min. Part A Your answer is correct. Determine the magnitude of the fan power, in hp. \[ \dot{W}_{\text {fan }}=\quad \mathrm{hp} \] Attempts: 1 of 3 used Part B Your answer is incorrect. Determine the time required for full inflation of the balloon, in min.