Boyle's law: pressure and volume of a gas — GCSE Physics practice questions

Question 1

A nurse seals the nozzle of a plastic syringe holding 80 cm³ of air at a pressure of 100 kPa. The plunger is then pushed in slowly until the volume of the air is 20 cm³. The temperature of the air does not change.

What is the new pressure of the air?

Accepted Answer

C: 400 kPa. pV is constant, so 100 kPa × 80 cm³ = p₂ × 20 cm³, giving p₂ = 400 kPa. The volume is divided by 4, so the pressure is multiplied by 4.

Question 2

Scientists live for a few days in a small laboratory on the sea bed. The air in the laboratory is at the same pressure as the water outside, a total of 250 kPa (this includes the pressure of the atmosphere).

A scientist seals 1800 cm³ of this air in a large, loosely filled plastic bag and takes it up to the surface, where the pressure is 100 kPa. The temperature of the air does not change.

What is the volume of the air in the bag at the surface?

Accepted Answer

C: 4500 cm³. pV is constant for the fixed mass of air: 250 kPa × 1800 cm³ = 100 kPa × V₂, so V₂ = 4500 cm³. The pressure falls to 0.4 of its value, so the volume grows by a factor of 2.5.

Question 3

A student compresses some gas in a sealed cylinder from 200 cm³ to 100 cm³. At the start, the pressure is 150 kPa.

The graph shows the pressures predicted by pV = constant (dashed curve) and the pressures measured (solid curve).

Which statement explains the difference between the two curves?

Accepted Answer

A: The gas became warmer as it was compressed.. The measured pressures are higher than pV = constant predicts, and more so the more the gas is compressed. If the gas warmed up (for example because it was compressed quickly, doing work on it), its particles would move faster and hit the walls harder and more often, giving extra pressure. A leak or a cooler gas would make the measured curve lie below the prediction.