Answer:
The ballon will brust at
<em>Pmax = 518 Torr ≈ 0.687 Atm </em>
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Explanation:
Hello!
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:
![R_{max} = \sqrt{\frac{A_{max}}{4 \pi}}](https://tex.z-dn.net/?f=R_%7Bmax%7D%20%3D%20%5Csqrt%7B%5Cfrac%7BA_%7Bmax%7D%7D%7B4%20%5Cpi%7D%7D)
Rmax = 10.001 cm
Therefore, the max volume will be:
![V_{max} = \frac{4}{3} \pi R_{max}^3](https://tex.z-dn.net/?f=V_%7Bmax%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20R_%7Bmax%7D%5E3)
Vmax = 4 190.05 cm^3 = 4.19 L
Now, from (*)
![P_{max} = P_1 \frac{V_1T_2}{V_2T_1}](https://tex.z-dn.net/?f=P_%7Bmax%7D%20%3D%20P_1%20%5Cfrac%7BV_1T_2%7D%7BV_2T_1%7D)
Therefore:
Pmax= P1 * (0.687)
That is:
Pmax = 518 Torr