Answer
The volume is increasing at a rate of $~~35.7~cm^3/min$
Work Step by Step
$PV^{1.4} = C$
$V^{1.4}~\frac{dP}{dt}+1.4~V^{0.4}~P~\frac{dV}{dt} = 0$
$1.4~V^{0.4}~P~\frac{dV}{dt} = -V^{1.4}~\frac{dP}{dt}$
$\frac{dV}{dt} = -\frac{V}{1.4~P}~\frac{dP}{dt}$
$\frac{dV}{dt} = -\frac{400~cm^3}{(1.4)(80~kPa)}~(-10~kPa/min)$
$\frac{dV}{dt} = 35.7~cm^3/min$
The volume is increasing at a rate of $~~35.7~cm^3/min$
