Calculus world problem expansion of air How would I solve this problem?
The adiabatic law for expansion of air is $P(V)^{1.4}=C$ when P is pressure V is volume and C is a certain constant.At a given instant the volume is 30 cubic feet and the pressure is 60 psi. At what rate is the pressure changing if the volume is decreasing at a rate of 2 cubic feet per second?
I know that $\frac{dv}{dt}=-2$
$P(1.4)\frac{dv}{dt}+V^{1.4}\frac{dp}{dt}=0$
$60(1.4)(-2)+30^{1.4}\frac{dp}{dt}=0$
$-168+116.9417\frac{dp}{dt}$
$168=116.9417\frac{dp}{dt}$
$\frac{dp}{dt}=1.4366$ but would this be right.

Note:
$PV^{\gamma}=C \implies \dfrac{dP}{dt}\cdot V^{\gamma}+(\gamma)V^{(\gamma-1)} \cdot \dfrac{dV}{dt}\cdot P=0$
