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In a cylinder-piston arrangement, the air is under a pressure P 1 . A soap bubble of radius r lies inside the cylinder. Soap bubble has surface tension T . The radius of soap bubble is to be reduced to half. Find the pressure P 2 to which air should be compressed isothermally.

Options

  1. AP 1 + 4 T r
  2. B4 P 1 + 1 2 T r
  3. C8 P 1 + 2 4 T r
  4. DP 1 + 2 T r

Correct answer

C. 8 P 1 + 2 4 T r

Step-by-step solution

Using P i V i = P f V f (for the air bubble) we have P 1 + 4 T r 4 3 π r 3 = P 2 + 4 T r / 2 4 3 π r 2 3 Solving this, we get P 2 = 8 P 1 + 2 4 T r

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