(III) Show that inside a soap bubble, there must be a pressure ΔP in excess of that outside equal to ΔP = 4γ/r, where r is the radius of the bubble and γ is the surface tension. [Hint: Think of the bubble as two hemispheres in contact with each other: and remember that there are two surfaces to the bubble. Note that this result applies to any kind of membrane, where 2γ is the tension per unit length in that membrane.]
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