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 some constant.

Suppose that at a certain instant the volume is $\displaystyle {V}={490}$ cubic centimeters and the pressure is $\displaystyle {P}={77}$ kPa. At that moment, the pressure is decreasing at a rate of $\displaystyle {7}$ kPa/minute. (Remember 'decreasing' means $\displaystyle \frac{{{d}{P}}}{{{\left.{d}{t}\right.}}}$ is negative).

At what rate is the volume increasing (with respect to time) at that instant?

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

(You don't need to worry about the units in this scenario, but Pa stands for Pascal -- it is equivalent to one Newton/(meter squared); kPa is a kiloPascal or 1000 Pascals.)