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.

Question

When air expands adiabatically (without gaining or losing heat), its pressure  and volume  are related by the equation  where  is a constant. Suppose that at a certain instant the volume is  cubic centimeters and the pressure is  kPa and is decreasing at a rate of  kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

Answer 1

I'm assuming this is supposed to say the PV^1.4 = C

If we take the derivative with respect to time (using the chain rule and the product rule) we get:

(-7)(420^1.4) + (99)(1.4)(420^0.4)dV/dt = 0

-32934 + 1552.6dV/dt = 0

dV/dt = 32934/1552.6

dV/dt = 21.2 cm³/min