When air expands adiabatically (without gaining or losing heat), its pressure $\displaystyle {P}$ and volume $\displaystyle {V}$ are related by the equation $\displaystyle {P}{V}^{{{1.4}}}={C}$ where $\displaystyle {C}$ is a constant. Suppose that at a certain instant the volume is $\displaystyle {600}$ cubic centimeters and the pressure is $\displaystyle {95}$ kPa and is decreasing at a rate of $\displaystyle {12}$ kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

Preview Question 6   $\displaystyle \frac{\text{cm}^{{3}}}{\min}$

(Pa stands for Pascal -- it is equivalent to one Newton/(meter squared); kPa is a kiloPascal or 1000 Pascals. )