In 1992, a Danish study concluded that a standard toy balloon, made from latex a

Question

In 1992, a Danish study concluded that a standard toy balloon, made from latex and filled with helium, could rise to10,000 m (where the pressure is 1/3 of that at sea level) in the atmosphere before bursting. In the study, a number of balloons were filled with helium, and then placed in a chamber maintained at 20°C. The pressure in the chamber was gradually reduced until the balloons exploded, and then the researchers determined the height above sea level corresponding to that pressure. Assume each balloon was filled with helium at +20°C and at about atmospheric pressure. Determine the balloon's volume just before it exploded, if its volume when it was first filled was 540 cm3.

___cm3

Please show all work!

Explanation / Answer

Here, there are two states of the balloon. The initial state is at +20C, 1 atm and has a
given volume. The second is at -20C, 1/3 atm and the volume is the variable of interest.
Thus, since the number of particles in the balloon remains constant:

P1V1/T1 = P2V2/T2

Solving for V2
V2 = P1*V1*T2/(T1*P2)

V2 = (1atm*253K*V1)/(1/3atm*293K)
V2 = 2.6*V1
V2 = 1404 cm^3

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