Question
Sat February 19, 2011 By: Arun Iyer

Derive the expression for excess pressure for a bubble.

Expert Reply
Sun February 20, 2011
Dear student
 

Excess pressure inside a liquid drop and a bubble

 

 

We know that in small drops and bubbles, the effect of gravity is negligible on account of surface tension. Small drops do not collapse due to surface tension. This means that the pressure inside the drop is greater than the pressure outside. Let this excess pressure i.e., pi - po = p. Due to this pressure difference, let the radius increase from R to R + dR.

Outside force = pressure difference x surface area

 

 

Hence, to increase the surface area

 

 

Work done by the excess pressure is stored in the form of potential energy.

 

 

Increase in P.E. = surface tension x increase in surface area.

 

 

 

 

dW = increase in P.E.

 

 

 

 

 

 

hope this clarifies your doubt.

Regards

Team

Topperlearning 

 

 

 

 

 

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