A cylinder with a movable piston contains air under a 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 will be: (The surface tension is σ , and the temperature T is maintained constant)
Text Solution
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Let’s say, initially, the pressure due to air inside the bubble is P air .
⇒ P air – P 1 = 
..........(i)
Finally, the radius becomes half; so, volume becomes 
th and hence pressure becomes 8P air .
So,8P air – P 2 = 
.........(ii)
Solving (i) and (ii)
Get P 2 = 8P 1 + 
.
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