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Two soap bubbles are combined isothermally 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 S is the surface tension of the soap solution, the correct relation, among the following, is

Options

  1. A4 p V + 3 S A = 0
  2. B3 p V - 4 S A = 0
  3. C4 p V - 3 S A = 0
  4. D3 p V + 4 S A = 0

Correct answer

D. 3 p V + 4 S A = 0

Step-by-step solution

Let the radii of the two soap bubble be a and b , respectively, and radius of a single larger bubble be c . As excess pressure for a soap bubble is 4 S r and external pressure is p , p i = p + 4 S r So, p a = p + 4 S a ,         p b = p + 4 S b and p c = p + 4 T c ...(i) and V a = 4 3 π a 3 ,         V b = 4 3 π b 3 and V c = 4 3 π c 3   ...(ii) Now, as mass is conserved, μ a + μ b = μ c i . e . ,   p a V a R   T a + p b V b R &#16

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