Related Rates and Boyle's Law?

Boyle’s law for the expansion of a gas is PV = k, where P is the pressure (in pounds per unit of area), V is the volume of the gas, and k is a constant.

Find the expression that shows the rate of change of the pressure as related to the rate of change of the volume.

dP/dt= ……………………

Evaluate the rate of change of the pressure at the instant when the gas fills 2〖ft〗^3, the pressure is 3000 lb/〖ft〗^2 , and the gas is expanding at 2〖ft〗^3/min

dP/dt= ……………………………

How do I get the formula to solve this?

1 Answer

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  • M3
    Lv 7
    5 years ago
    Best Answer

    PV = k

    P = k/V

    dP/dt = -k/V² dV/dt ......... [ I ]

    When V = 2, P = 3000, so k = 6000

    dV/dt = 2, so plugging into [ I ],

    dP/dt = -(6000/4)*2 = -3000 ft³/min

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