First slide

Surface tension and surface energy

Question

A soap bubble of radius R is blown. After heating the solution a second bubble of radius 2R is blown. The work required to blow the second bubble in comparison to that required for the first bubble is

Moderate

A

Double
B

Slightly less than double
C

Slightly less than four times
D

Slightly more than four times

Solution

Work done to form a bubble of radius R
$W_{1} = 8 π R^{2} T_{1}$
Work done to form a bubble of radius 2R
$W_{2} = 8 π (2 R)^{2} T_{2} = 32 π R^{2} T_{2} ∴ \frac{W_{1}}{W_{2}} = \frac{T_{1}}{4 T_{2}}$
If surface tension of soap solution is same, then
$W_{2} = 4 W_{1}$
But in the problem the temperature W₂ of solution is increased.
So its surface tension decreases.
$∴ W_{2} < 4 W_{1}$

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