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 P V = C , where C is a constant. Suppose that at a certain instant the volume is 500 cm 3 , the pressure is 200 kPa , and the pressure is increasing at a rate of 30 kPa/min . At what rate is the volume decreasing at this instant?

Answer 1

-75 cm^3/min

Step-by-step explanation:

Given from Boyle's law;

PV=C

From product rule;

VdP/dt + PdV/dt = dC/dt

but dC/dt = 0, V= 500 cm^3, P= 200kPa, dP= 30kPa/min

PdV/dt = dC/dt - VdP/dt

dV/dt = dC/dt - VdP/dt/ P

substituting values;

dV/dt = 0 - (500 * 30)/200

dV/dt = -75 cm^3/min