Math word problem?

Boyle's Law says that the volume of a gas varies inversely with the pressure. When the volume of a certain gas is 5 L, the pressure is 212 kPa (kilopascals). What is the volume when the pressure is 530 kPa?

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  • 3 years ago
    Best Answer

    Let V be the volume (in liters)

    Let P be the pressure (in kilopascals)

    If they varied *directly* then we would say that the volume (V) was equal to a constant (k) *times* the pressure (P).

    But they vary *inversely*. So the volume (V) is equal to a constant (k) *divided* by the pressure (P):

    V = k/P

    Plug in your first data point (V = 5, P = 212) and figure out k:

    5 = k/212

    k = 5 * 212

    k = 1060

    Now you have a complete equation:

    V = 1060/P

    Plug in your new pressure to figure out the new volume:

    V = 1060/530

    V = 2

    Answer:

    2 liters

    P.S. The shortcut equation would be

    5 * 212 = 530 * P

    1060 = 530P

    P = 2

  • 3 years ago

    Okay, if volume varies inversely with pressure, then we have an equation V = k/P where k is some constant that will make the equation true

    We know that when V=5, P=212

    5 = k/212

    5(212) = k

    1060 = k

    Now that we know k, we can use it to find any V

    V = 1060/P

    V = 1060/530

    V = 2

    the volume is 2 L when the pressure is 530 kPa

  • Glipp
    Lv 7
    3 years ago

    P1.V1 = P2.V2

    P1.V1 = 212 * 5 = 1060

    P2.V2 = 530 * V2 = 1060

    V2 = 1060/530 = 2L

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