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Pressures insides two soap bubbles are 1.01 and 1.02 atmospher

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Pressures insides two soap bubbles are 1.01 and 1.02 atmospheres. Ratio between their volumes is :-

102:101

(102)^{3} : (101)^{3}

8:1

2:1

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Text solutionVerified

The excess pressure inside a soap bubble is given by the expression:

δ P = \frac{4 T}{R}

Hence,

\frac{Δ P _{1}}{Δ P _{2}} = \frac{R _{2}}{R _{1}}

Δ P_{1} = P_{in} - P_{a} = 1.01 - 1 = 0.01

atm

Δ P_{2} = P_{in} - P_{a} = 1.02 - 1 = 0.02

atm

Therefore,

\frac{R _{2}}{R _{1}} = 0.01/0.02

Hence, their volumes will be in the ratio:

\frac{V _{1}}{V _{2}} = \frac{R _{1}^{3}}{R _{2}^{3}}

= \frac{0.0 2 ^{3}}{0.0 1 ^{3}} = 8 : 1

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Question Text	Pressures insides two soap bubbles are 1.01 and 1.02 atmospheres. Ratio between their volumes is :-
Answer Type	Text solution:1
Upvotes	150