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Q.

Two soap bubbles combine to form a single bubble. In this process, The change in volume and surface area are respectively V and A. If P is the atmospheric pressure and T is the surface tension of the soap solution. The following relation is true

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a

$4 P V + 3 T A = 0$

b

$3 P V - 4 T A = 0$

c

$4 P V - 3 T A = 0$

d

$3 P V + 4 T A = 0$

answer is D.

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Detailed Solution

$\begin{aligned} P_{a} V_{a} + P_{b} V_{b} = P_{c} V_{c} \\ (P + \frac{4 T}{a}) (\frac{4}{3} π a^{3}) + (P + \frac{4 T}{a}) (\frac{4}{3} π b^{3}) = (P + \frac{4 T}{c}) (\frac{4}{3} π c^{3}) \\ 4 T (a^{2} + b^{2} - c^{2}) = P (c^{3} - a^{3} - b^{3}) \\ V = \frac{4}{3} π (a^{3} + b^{3} - c^{3}) \end{aligned}$
$\begin{aligned} And A = 4 π (a^{2} + b^{2} - c^{2}) \\ \frac{T A}{π} = - \frac{3}{4 π} V P \Rightarrow 4 T A + P V = 0 \end{aligned}$

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