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Pressure needed to reduce size of soap bubble by half

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cylinder with the movable system contains air under pressure $p_1 $and a soap bubble of radius R .
The pressure $p_2 $to which the air should be compressed by slowly pushing the Piston into the cylinder for the soap bubble to reduce its size by half.
( the surface tension is T and temperature is maintained constant)

I tried it as $ 4T / R = p_i - p_1$

Then $ 4T / ( R/2) = p_i' - p_2$

where $p_i $ = internal pressure
and $ p_i'$ = new internal pressure

From here I am unable to do as no relation for $p_i $ and $ p_i'$

asked Apr 1, 2017 in Physics Problems by physicsapproval (2,320 points)

1 Answer

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Best answer

"Size" is ambiguous. It could mean radius or volume (or even surface area).

The gas inside the bubble obeys the ideal gas law. So if its volume is halved the internal pressure is doubled.

answered Apr 1, 2017 by sammy gerbil (28,876 points)
selected Apr 1, 2017 by physicsapproval
The answer given is $ 8 p_1 + 24T/R $ ;
So I think the question says radius as halved , using that internal pressure becomes 8 times , and that gives the correct answer using The ideal gas law point as stated in answer :)
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