calculus related rates

posted by Bill

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= ……………………………

1. Steve

PV = k
V dP/dt + P dV/dt = 0

dP/dt = -(P/V) dV/dt

Now just plug in your numbers.

By the way, this is true only if the temperature remains constant. More generally,

PV = kT

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