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

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SUMMARY

The discussion centers on the relationship between pressure and volume during adiabatic expansion of air, governed by the equation PV^(1.4) = C. Given an initial volume of 450 cubic centimeters and a pressure of 81 kPa decreasing at 10 kPa/minute, participants suggest using implicit differentiation to find the rate of volume increase. The key takeaway is that differentiating the equation with respect to time will yield the necessary relationship to solve for the rate of change of volume (dv/dt).

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

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