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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

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Double

Slightly less than double

Slightly less than four times

Slightly more than four times

answer is C.

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Detailed 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 temperature of solution is increased so its surface tension decreases. $∴ W_{2} < 4 W_{1}$

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