Aparticular balloon can be stretched to a maximum surface area of 1257 cm2. the balloon is filled with 3.1 l of helium gas at a pressure of 754 torr and a temperature of 294 k . the balloon is then allowed to rise in the atmosphere. assume an atmospheric temperature of 273 k and determine at what pressure the balloon will burst. (assume the balloon to be in the shape of a sphere)

The ballon will brust at

Pmax = 518 Torr ≈ 0.687 Atm

Explanation:

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To solve this problem we are going to use the ideal gass law

PV = nRT

Where n (number of moles) and R are constants (in the present case)

Therefore, we can relate to thermodynamic states with their respective pressure, volume and temperature.

--- (*)

Our initial state is:

P1 = 754 torr

V1 = 3.1 L

T1 = 294 K

If we consider the final state at which the ballon will explode, then:

P2 = Pmax

V2 = Vmax

T2 = 273 K

We also know that the maximum surface area is: 1257 cm^2

If we consider a spherical ballon, we can obtain the maximum radius:

Rmax = 10.001 cm

Therefore, the max volume will be:

Vmax = 4 190.05 cm^3 = 4.19 L

Now, from (*)

Therefore:

Pmax= P1 * (0.687)

That is:

Pmax = 518 Torr

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