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Two soap bubbles coalesce to form a single bubble . If V is the subsequent change in volume of contained air and S the change in total surface area , T is the surface tension and P atmospheric pressure ,which of the following relation is correct ?

$(a)\;4 \normalsize PV+3 \normalsize ST=0\qquad(b)\;3PV+4ST=0\qquad(c)\;2PV+3ST=0\qquad(d)\;3PV+2ST=0$

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Let the radius of two smaller soap bubble is r and larger bubble is R, than we know that
Surface tension $$\displaystyle T=P\frac{(R^{3} - 2r^{3})}{(4(2r^{2} - R^{2})}$$
Or, $$\displaystyle T= \frac{3P\delta V}{-4\delta A}$$
where  V  &  VA  are  the  change  in  volume  and  surface  area. Therefore,  .
$$3P\delta V+4T\delta A=0$$

answered Apr 7, 2015 by ashu.gaikwad.56

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