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12 January, 10:55

13. The volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 210 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 70 cubic inches.

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  1. 12 January, 12:21
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    4.67 pounds

    Step-by-step explanation:

    In order to find the answer we need to use the following formula:

    V=k/P where:

    V=volume

    P=pressure of the gas

    k = constant of proportionality

    The above equation establishes that the volume is inversely proportional to the pressure of the gas.

    Now, the problem gave us two situations, which are:

    For a time 1, we have V1=210 cubic inches and P1=14 pounds, using the equation we have:

    V1=k/P1

    210 cubic inches=k * (14 pounds) which can be written as:

    (210 cubic inches) / (14 pounds) = k

    For time 2, we have V2=70 cubic inches and P2=P2 using the equation we have:

    V2=k/P2

    70 cubic inches=k*P2, using 'k-value' from above:

    (70 cubic inches) = [ (210 cubic inches) / (14 pounds) ]*P2

    (70 cubic inches) * (14 pounds) / (210 cubic inches) = P2

    4.67 pounds = P2
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