When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV1.4=C where C is a constant. Suppose that at a certain instant the volume is 690 cubic centimeters and the pressure is 97 kPa and is decreasing at a rate of 9 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 rule,

dp/dt * v^1.4 + 1.4pv^0.4 dv/dt = 0
No wjust plug in your numbers and solve for dv/dt