How Fast Does Volume Increase When Pressure Decreases in Adiabatic Expansion?

[Neil6790]

Homework Statement

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 450 cubic centimeters and the pressure is 81 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?

Homework Equations

I have no idea what any relevant equations would be.

The Attempt at a Solution

I don't know really where to start but I figured the kPa would be 71 and then 61 and so on... Maybe I take the derivative of the entire thing but that's an option

 

[tnutty]

You have :

PV^(1.4)=C

Try differentiate it. If you do you will see it become a algebra problem where you will
be solving for dv.

 

[blake knight]

I agree with tnutty, try differentiating it implicitly with respect to t(time).