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?

dV/dt = 100 cm³/min

Step-by-step 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