When air expands adiabatically (without gaining or losing heat), its pressure P

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 390 cubic centimeters and the pressure is 77 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? please explain how you got to the answer because it is vital for my exam. best explanation will get points. thank you

Explanation / Answer

PV^1.4=C , 1.4PV^.04dV/dt +V^1.4dP/dt , dV/dt=- -.714286V/P*(dP/dt)

When V=390, P=77 and dP/dt= -7,
We have (-.714286*(390)/(77))(-7)= 25.32cm^3/min ,

so the volume is increasing at a rate of 25.32 cm^3/min

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