Question

Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 400 cm3, the pressure is 160 kPa, and the pressure is increasing at a rate of 40 kPa/min. At what rate is the volume decreasing at this instant?

Answer 1

100 cm^3/min

Step-by-step explanation:

PV = C

V = 400 cm^3

P = 160 kPa

dP/dt = + 40 kPa/min

According to the question

PV = C

Differentiate both sides with respect to time

P x dV/dt + V x dP/dt = 0

160 x dV/dt = - 400 x 40

dV/dt = - 100 cm^3/min

The volume decreases by the rate of 100 cm^3/min.