Question

I would really appreciate some help:
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 340 cubic centimeters and the pressure is 83 kPa and is decreasing at a rate of 12 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

Answer 1

\[P = 340 (cm^{3})=3.4\times10^{-4}(m^3)\]
\[V=83(kPa) \]
\[{dP \over dt} = 12 {(kPa/min)} = 0.2({kPa \over s})\]

Answer 2

\[V={nRT \over P}\]\[\ V^{1.4}=({nRT\over P})^{1.4} \]
\[V^{1.4}=(nRT)^{1.4}P^{-1+1.4}\]
\[V^{1.4} =C' P^{0.4 }\]
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im sorry but i cant figure out how to solve this problem
(and im not sure if anything i have written is helpful)