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AP EAMCET2006PhysicsMechanical Properties of Fluids

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 :

Options

  1. A4 P V+3 T A=0
  2. B3 P V-4 T A=0
  3. C4 P V-3 T A=0
  4. D3 P V+4 T A=0

Correct answer

D. 3 P V+4 T A=0

Step-by-step solution

Let radii of two soap bubbles are a and b respectively and radius of single larger bubble is c . As excess pressure for a soap bubble is 4 T r and external pressure P . P_i=P+ 4 T r So, P_a=P+ 4 T a , P_b=P+ 4 T b and P_c=P+ 4 T c ...(i) and V_a= 4 3 a^3, V_b= 4 3 b^3 and V_c= 4 3 c^3 ...(ii) Now as mass is conserved. _a+ _b= _c i.e., P_a V_a R T_a + P_b V_b R T_b = P_c V_c R T_c ( as P V= R T) As temperature is constant, i.e., T_a=T_b=T_c So, P_a V_a+P_b V_b=P_c V_c which in the light of Eqs. (i) and (ii) becomes,

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