Hot air balloons are held up buoyancy generated by the difference in density bet
ID: 2252688 • Letter: H
Question
Hot air balloons are held up buoyancy generated by the difference in density between hot air and cool air. Because the balloon is open at the bottom the pressure is the same inside and outside the balloon.
a) The density of air at STP is 1.29 g/1, and it is molar mass is about 14.5 grams. Assuming that air is as ideal gas, find the density at the 20 degree C and the same pressure. Hint: choose some arbitrary amount of air to consider (one mole would be handy), then find the ratio of the volumes at the two temperatures.
b) If we assume a balloon with a volume of 5000 cubic meters, and that we are able to maintain 20 degree C in the balloon while it is freezing outside, how much total weight (bag, basket, passangers, fuel and so on) can be lifted
Explanation / Answer
buoyancy.
a)
density d = PM/RT
d1*T1 = d2*T2
1.29*273 = d2*293
d2 = 1.202 gm/l
b)
weight of the balloon = volume*density
weight = 5000*1.202*9.8gm
= 58898 N
buoyancy force = volume*density of outside air
= 5000*1.29*9.8
= 63,210 N.
difference in force = buoyancy - weight of the balloon
= 63,210 - 58898
= 4,312 N
this difference in force can be used to balance the total weight.
so total weight that can be carried = 4,312 N
or 440 Kg of mass.
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