? asked in Science & MathematicsMathematics · 3 years ago

Math Question?

Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 300 cm3, the pressure is 80 kPa, and the pressure is increasing at a rate of 40 kPa/min. At what rate is the volume decreasing at this instant?

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  • 3 years ago
    Best Answer

    .

    Given: P’(t) = 40kPa/min, V = 300cm³, P = 80kPa

    PV = C

    P*V’(t) + V*P’(t) = 0

    V’(t) = -V*P’(t)/P

    V’(t) = -(300cm³)(40kPa/min) / (80kPa)

    V’(t) = -150cm³/min

    Volume is decreasing at a rate of 150cm³/min

  • 3 years ago

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