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A cylinder with a movable piston contain...

A cylinder with a movable piston contains air under a pressure `P_1` and a soap bubble of radius 'r'. The pressure `P_2` to which the air should be compressed by slowly pushing the piston into the cylinder for the soap bubble to reduce its radius by half will be : `x[P_1 +3S//r]`, where S is the surface tension

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Knowledge Check

  • In a cylinder-piston arrangement air is under a pressure P_(1) and constant temperature t. A soap bubble lies insie the cylinder, surface tension is T. The soap bubble is to be reduced to half its size, the required pressure P_(2) to which air should be compressed by slowly pulling the piston into the cylinder is

    A
    `8P_(1)+(24T)/(r)`
    B
    `8P_(1)+(3T)/(r)`
    C
    `8P_(1)+(2T)/(r)`
    D
    `8P_(1)+(12T)/(r)`

  • A soap bubble of radius R is surrounded by another soap bubble of radius 2R, as shown. Take surface tension = S.

    A
    Then the pressure inside the smaller soap bubble in excess of the atmospheric pressure is zero
    B
    Then the pressure inside the smaller soap bubble in excess of the atmospheric pressure is 6S/R
    C
    Then the pressure inside the larger soap bubble in excess of the atmospheric pressure is 4S/2R
    D
    Then the pressure inside the larger soap bubble in excess of the atmospheric pressure is 4S/R

  • Air is pushed into a soap bubble of radius r to double its radius. If the surface tension of the soap solution is S, the work done in the process is

    A
    `8pir^(2)S`
    B
    `12pir^(2)S`
    C
    `16pir^(2)S`
    D
    `24pir^(2)S`

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