'Two spherical soap bubbles of radii r1 and r2 coalesce to form a bubble of radius R. If the surface tension of soap solution is T, atmospheric pressure is P, the change in volume of the air enclosed is V and the change in surface area is 'A'. Complete the expression using above statement, 3PV + ___ = 0

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AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 3)
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  1. 8TP
  2. 4TP
  3. 2TA
  4. 4TA

Answer (Detailed Solution Below)

Option 4 : 4TA
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Detailed Solution

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CONCEPT

The excess pressure inside a soap bubble of radius R and surface tension T is

Also when the two spherical soap bubbles coalesce to form a new soap bubble temperature of the soap bubble remains constant.

By applying the following equation

CALCULATION:
Absolute pressure inside the soap bubble of radius r1

Absolute pressure inside the soap bubble of radius r2

Absolute pressure inside the resulting soap bubble is r3

Now applying the equation

⇒ 3PV + 4TA = 0 

Hence the completed expression is 

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