Boyle's law states that when a sample of gas is compressed at a constant temperature P and volume V are related by the equation PV=C, where C is a constant. Suppose that at a certain instant the volume is 600 cm3 and the pressure is 150 kPa and is increasing at a rate of 10 kPa/min. At what rate is the volume decreasing at this instant?
Help so greatly appreciated :] Having a VERY hard time with related rates problems so I don't have any idea where to start…
Best Answer
Hint:
You know $\frac{dP}{dt}=10$
Find $\frac {dP}{dV}$.
Then you get
$\frac {dP}{dV}=\frac{dP}{dt}.\frac{dt}{dV}$
or $\frac{dV}{dt}=\frac{dP}{dt}.\frac{dV}{dP}$
Aliter:
$PV=C$
Differentiate it with respect to $t$, you get $\frac{dP}{dt}.V+\frac{dV}{dt}.P=0$