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 PV1.4 = C, where C is a constant. Suppose that at a certain instant the volume is 450 cm3 and the pressure is 80 kPa and is decreasing at a rate of 10 kPa/min. At what rate is the volume increasing at this instant? (Round your answer to the nearest whole number.)

Explanation / Answer

PV^1.4 = C => Differentiating, dP * V^1.4 + P*(1.4V^0.4) dV = 0 ; Given, V = 450cc ; P = 80Kpa ; dP = 10Kpa/min ; 10*(450^1.4) + 80*1.4*(450^0.4) dV = 0 => 51820.0132 + 1289.74 dV = 0 => dV = -40.178 cc/min ;

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