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Tutorial Exercise 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 900 cm3, the pressure is 150 kPa, and the pressure is increasing at a rate of 40 kPa/min. At what rate is the volume decreasing at this instant?

Differentiating both sides of PV = C with respect to t gives us

Answer 1

Differentiating both sides of PV = C with respect to t gives us ...

... P'V +PV' = 0

Filling in the given numbers gives us ...

... (40 kPa/min)(900 cm³) + V'(150 kPa) = 0

Solving for V' gives ...

... V' = -(40 kPa/min)(900 cm³)/(150 kPa)

.. V' = -240 cm³/min

The volume is decreasing at the rate of 240 cm³/min.