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 380 cubic centimeters and the pressure is 89 kPa and is decreasing at a rate of 10 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

asked by ujkk

14 years ago

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1 answer

PV^k=C

take the derivative
kPv^(k-1) dV/dt+V^k dP/dt=0

solve for dV/dt

dV/dt= -V/Pk * dP/dt check that.

answered by bobpursley

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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 380 cubic centimeters and the pressure is 89 kPa and is decreasing at a rate of 10 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

1 answer

PV^k=C

take the derivative
kPv^(k-1) dV/dt+V^k dP/dt=0

solve for dV/dt

dV/dt= -V/Pk * dP/dt check that.

bobpursley · Answer

PV^k=C take the derivative kPv^(k-1) dV/dt+V^k dP/dt=0 solve for dV/dt dV/dt= -V/Pk * dP/dt check that.