A hot-air balloon achieves its buoyant lift by heating the airinside the balloon

Question

A hot-air balloon achieves its buoyant lift by heating the airinside the balloon, which makes it less dense than the air outside.Suppose the volume of a balloon is 1600 m3 and the required lift is2200 N (rough estimate of the weightof the equipment and passenger). Calculate the temperature of theair inside the balloon which will produce the required lift. Assumethat the outside air temperature is 0°C and that air is anideal gas under these conditions.
1°C
What factors limit the maximum altitude attainable by this methodfor a given load? (Neglect variables like wind.)

Explanation / Answer

Let the density of hot air inside the balloon be d. Then to lift up the ballon (The density of dry air is 1.290 kilograms perm3 at 0 deg celcius) we need to have from newtons second law(the net force on the bodymust be upwards) (wt. of displaced air >= wt. of equipment + wt. of airinside balloon) 1.290 x 1600 m3 x9.81 m/s2 >= (2200 N +d x 1600 m3 x 9.81 m/s2) => d

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