Properties Of Solids And Liquids Question 247
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
Options:
A) Double
B)Slightly less than double
C)Slightly less than four times
D)Slightly more than four times
Show Answer
Answer:
Correct Answer: C
Solution:
[c] work done to form a bubble of radius R $ W _{1}=8\pi R^{2}T _{1} $ .
Work done to form a bubble of radius 2R $ W _{2}=8\pi {{(2R)}^{2}}T _{2}=32\pi R^{2}T _{2}$
$\therefore \frac{W _{1}}{W _{2}}=\frac{T _{1}}{4T _{2}} $ .
If surface tension of soap solution is same, then $ W _{2}=4W _{1} $ .
But in the problem the temperature of solution is increased, so its surface tension decreases. $ \therefore W _{2}<4W _{1} $
