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 330 cubic centimeters and the pressure is 79 kPa and is decreasing at a rate of 10 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

Answer 1

you have your formula:

pv^1.4 = c, so
you get

v^1.4 dp/dt + 1.4pv^.4 dv/dt = 0
Now just plug in your numbers:

(330^1.4)(-10) + (1.4)(330^.4)(79) dv/dt = 0
-33567.54 + 1125.02 dv/dt = 0
dv/dt = +29.84