A plastic bag is filled with hydrogen at atmospheric pressure and 26.0 o C. Assu
ID: 2253203 • Letter: A
Question
A plastic bag is filled with hydrogen at atmospheric pressure and 26.0 oC. Assume that the mass of the bag is negligible and take the temperature of the outside air to be 0 oC. With the help of this "balloon" we want to lift a 47.0 kg girl off her feet.
How large a volume of hydrogen (in m3) is required?
If hot air is used instead of hydrogen, what is the required volume of the balloon if the air inside can be maintained at 43.0 oC ?
The answer to the second question is NOT 30.92 m^3 or 42.7 m^3.
Explanation / Answer
The lift generated by a baloon is given by this formula
weight of the air it displaced - its own weight.
in the first question, the baloon is filled with hydrogen at 26C
lest assume the volume of the baloon to be V.
the density of hydrogen at 26C is 0.0826 kg/m^3.
density of air at 0C is 1.2922 kg/m^3
weight of the baloon = density*volume = 0.0826*V
weight of the air it displaced = 1.2922*V
lift generated = 1.2922*V - 0.0826*V
for this baloon to be able to lift a 47kg girl, the lift should equal her weight.
=> 1.2096*V = 47 => V = 47/1.2096 = 38.855 m^3
b)now the baloon is filled with hot air at 43C.
density of the air at 0C id 1.2922.
so using the equation D1*T1 = D2*T2 we can find the density of air at 43C
1.2922*273 = D2*316
D2 = 1.2922*273/316 = 1.1163 kg/m^3
the lift generated in this case assuming a baloon volume of V is:
1.2922*V -1.1163*V = 0.1759*V
this must equal the weight of the child.
so 0.1759*V = 47 => v = 47/0.1759 = 267.2 m^3
volume of the baloon required is 267.2 m^3
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