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 670 cubic centimeters and the pressure is 97 kPa and is decreasing at a rate of 7 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

Question

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 670 cubic centimeters and the pressure is 97 kPa and is decreasing at a rate of 7 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

Steve · Answer

PV^1.4 = C V^1.4 P' + 1.4PV^.4 V' = 0 (60^1.4)(-7) + (1.4)(670)V' = 0 V' = 2.3 cc^3/min

Bu · Answer

Where did the 60 come from in your equation?