#### Problem 38E

38. When air expands adiabatically (without gaining or losing heat), its pressure $P$ and volume $V$ are related by the equation $P V^{1.4}=C$, where $C$ is a constant. Suppose that at a certain instant the volume is $400 \mathrm{~cm}^{3}$ and the pressure is $80 \mathrm{kPa}$ and is decreasing at a rate of $10 \mathrm{kPa} / \mathrm{min}$. At what rate is the volume increasing at this instant?