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 10 minutes with negligible heat transfer with the surroundings, the air in an initially deflated balloon achieves a termperature of 80oF and a volume of 49,100 ft3. 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 ft3 and a temperature of 210oF. Air at 77oF and 14.7 lb/in2 surrouds the balloon. The net rate of heat transfer is 7x103 Btu/h. Ignoring effects due to kinetic and potential energy, modeling 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 power required by the fan, in hp.
(b) the time required for full inflation of the balloon, in minutes.