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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 310 cubic centimeters and the pressure is 81 kPa and is decreasing at a rate of 14 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant

Answer 1

PV^1.4 = C

V^1.4(dP/dt) + 1.4V^-3/4(dV/dt)P = 0

dV/dt = -V(dP/dt) / [1.4P]

dV/dt = -310(-14) / [1.4(81)]