I keep getting the wrong answer to this related rate problem, so I would greatly appreciate it if someone could go over my work and tell me where I messed up and why. I'm not sure if I made a mistake early on in the problem, or if it's a little mistake somewhere at the end. Thanks a ton:
When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV1.4 = C, where C is a constant. Suppose that at a certain instant the volume is 750 cm3 and the pressure is 80 kPa and is decreasing at a rate of 10 kPa/min. At what rate is the volume increasing at this instant?
So I am given V = 750, P = 80, and dP/dt = -10.
PV^1.4 = C
1.4 lnPV = lnC
1.4 (1/PV) ( P(dP/dt) + V(dV/dt)) = 1/C (dC/dt)
[but since it is a constant, dC/dt goes to 0, right? Or is this wrong?]
1.4 (1/60000) ( 80(dV/dt) + 750(-10)) = 0
(2.333e-5) (80(dV/dt) - 7500) = 0
.0018667(dV/dt) - .175 = 0
.0018667(dV/dt) = .175
dV/dt = 93.75