According to Boyle’s Law, if the temperature of a confined gas is held fixed, then the product of the pressure P and the volume is a constant. Suppose that, for a certain gas, PV = 800, where P is measured in pounds per square inch and V is measured in cubic inches.
(a) Find the average rate of change of P as V increases from 200 in to 250 in3.
(b) Express V as a function of P and show that the instantaneous rate of change of V with respect to P is inversely proportional to the square of P.