Question

14. Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the pressure P of the gas is inversely proportional to the volume V of the gas. Suppose that at a certain temperature the volume is 728 cm!, the pressure is 182 kPa, and the pressure is decreasing at a rate of 25 kPa/min. At what rate is the volume increasing at this instant?

Answer 1

dV/dt = 100 cm³/min

Explanation:

Given

V = 728 cm³

P = 182 kPa

dP/dt = - 25 kPa/min

dV/dt = ?

If we apply the ideal gas equation

P*V = n*R*T

where n*R*T is constant

we have

d(P*V)/dt = d(n*R*T)/dt

⇒ d(P*V)/dt = 0

⇒ V*(dP/dt) + P*(dV/dt) = 0

⇒ dV/dt = - (V/P)*(dP/dt)

Plugging the known values we obtain

⇒ dV/dt = - (728 cm³/182 kPa)*(- 25 kPa/min)

⇒ dV/dt = 100 cm³/min