The work done in stretching a surface of a membrane is converted to its surface energy, given by E=yA, for each surface of the membrane. Here y is called the surface tension of the membrane, and A is the area of the surface area. Consider a balloon of radius R. What is the change in surface energy when the radius changes by dR? Hence derive an expression for the pressure due to surface tension.
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Answer:
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Explanation:
Let Surface Tension be T.
Initial surface = 4ΠR
2
Final Surface area = 1000×4Πr
2
& Initial Volume = final volume
3
4
ΠR
3
=1000×
3
4
Πr
3
R = 10r
So,
Final surface area = 1000×4Π×
100
R
2
=40ΠR
2
So, Workdone = Change in Surface energy
= TΔA=(40−4)ΠR
2
T
ChangeinSurfaceenergy=36Πr
2
T
.
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