The Helium Balloon Pop · AI Generator #GEN-3712A761

Physics · thermodynamics

Problem

A child's helium balloon is accidentally released indoors at ground level where the temperature is T1=22°CT_1 = 22°\text{C} and pressure is P1=1.0  atmP_1 = 1.0\;\text{atm}. The balloon then floats up and gets stuck against the ceiling where, due to poor insulation, the temperature drops to T2=15°CT_2 = 15°\text{C}. The balloon was initially filled to a volume of V1=2.5  LV_1 = 2.5\;\text{L} and will pop if its internal pressure exceeds Pmax=1.15  atmP_{\text{max}} = 1.15\;\text{atm}. Assuming the balloon material is perfectly flexible (so internal pressure always equals external pressure) and the helium behaves as an ideal gas, what is the maximum volume the balloon can have at the ceiling before it pops?

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