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 100 cm3, the pressure is 150 kPa, and the pressure is increasing at a rate of 30 kPa/min. At what rate is the volume decreasing at this instant?

The volume is decreasing at a rate of 30 cm³/min.

Explanation:

From the question given above, pressure (P) and volume (V) are related by the following equation

PV = C

C => constant

If we make P the subject of the above, we shall have:

P = C/V

From the equation above (i.e P = C/V),

We can say that P is inversely proportional to V. This implies that as P is increasing, V will be decreasing and also, as P is decreasing, V will be increasing.

Considering the question given above, the pressure (P) is increasing at a rate of 30 kPa/min. Therefore, the volume will be decreasing at a rate of 30 cm³/min.