When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV^{1.4}=C where C is a constant. Suppose that at a certain instant the volume is 430 cubic centimeters and the pressure is 89 kPa and is decreasing at a rate of 13 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

Answer 1

PV^1.4 = C
using the product and chain rules,
V^1.4 dP/dt + 1.4PV^.4 dV/dt = 0

now just plug in your numbers