The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is 
times the volume of the bubble B, then, the value of n is _______.
Text Solution
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The excess pressure inside a soap bubble is determined by the formula:
where 
is the excess pressure, T is the surface tension of the soap film, and 
is the radius of the bubble.
Given that the excess pressure inside bubble A is half that inside bubble B, we have:
This implies:
Now, considering the volumes of the bubbles, the relationship between volume and radius for a sphere is given by:
Thus, the ratio of the volumes of bubbles A and B is:
Therefore, the volume of bubble A is 
times the volume of bubble B.
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