Section 1 of 9The law
Boyle's law for a fixed mass of gas at constant temperature, the pressure is inversely proportional to the volume.
p ∝ 1/V, or pV = constant
so
p1V1 = p2V2
What the symbols mean: p1, V1 = pressure and volume before · p2, V2 = after; only for a fixed mass of gas at constant temperature
Use any consistent units for p and V, such as Pa and m3, or kPa and cm3.
Section 2 of 9Particle explanation
When a gas is compressed into a smaller volume, the molecules are packed more closely.
1
They have farther to travel before hitting a wall in a large container, and less far in a small one,
- so there are more collisions per second with each square metre of the walls.
2
Temperature is constant, so the speed and the force per collision do not change.
3
More collisions per second means greater pressure.
4
Halving the volume doubles the number of collisions per unit area per second and so doubles the pressure.
Section 3 of 9Graphs of Boyle's law
p against V
p against V a downward-sloping curve (a hyperbola). Both axes are positive and the curve never touches either axis.
p against 1/V
p against 1/V a straight line through the origin, showing that p is proportional to 1/V.
pV against p
pV against p a horizontal straight line, as pV is constant.
Curves at higher temperatures lie further from the axes: on a p–V graph, each curve is called an isotherm.
Section 4 of 9Practical measurement
Air trapped by a column of oil in a sealed glass tube is compressed using a foot pump or a hand pump.
Practical measurement
The pressure is read from a Bourdon gauge and the length of the trapped air column (proportional to volume if the tube has a uniform bore) is read from a scale.
Compression must be slow so that the gas stays at room temperature.
A set of readings of p and length l shows that p × l is constant, and a plot of p against 1/l is a straight line through the origin.
Section 5 of 9Everyday uses
Everyday uses
A bicycle pump: pushing in the plunger reduces the air volume and raises its pressure until it exceeds the tyre pressure.
Your lungs: the diaphragm moves down, volume increases and pressure falls below atmospheric, so air flows in.
A rising bubble in water expands as the water pressure above it falls.
Section 6 of 9Using the data to test the law
To check Boyle's law from a table of results, multiply p by V for every pair of readings.
1
If the products are constant (allowing for small experimental scatter), the law is verified.
2
Alternatively, compute 1/V for each reading and plot p against 1/V; a straight line through the origin confirms inverse proportion.
3
A common source of error is the dead volume in the tubing that connects the gauge to the trapped air: it adds a constant volume which makes the line miss the origin.
4
Reading the scale at eye level reduces parallax error.
Gauge pressure and absolute pressure
Some pressure gauges, such as tyre gauges, read pressure above atmospheric pressure.
Using the data to test the law
The pressure used in Boyle's law must be the total (absolute) pressure.
If a tyre gauge reads 2.0 × 105 Pa, the absolute pressure inside is about 3.0 × 105 Pa when atmospheric pressure is 1.0 × 105 Pa.
Always check whether the question states a gauge pressure or the actual pressure of the gas before using pV = constant.
Section 7 of 9Worked examples
Air in a syringe has volume 60 cm3 at 1.0 × 105 Pa. The plunger is pushed in slowly until the volume is 24 cm3. What is the new pressure?
p2 = p1V1/V2 = 1.0 × 105 × 60/24 = 2.5 × 105 Pa.
A gas cylinder of volume 0.020 m3 holds gas at 6.0 × 105 Pa. The gas is released into a large bag at atmospheric pressure of 1.0 × 105 Pa, at constant temperature. What is the volume of the gas in the bag?
V2 = p1V1/p2 = 6.0 × 105 × 0.020 / 1.0 × 105 = 0.12 m3.
Table: when V = 50 cm3, p = 1.2 × 105 Pa. When V = 80 cm3 what pressure should be recorded if Boyle's law holds?
pV = 1.2 × 105 × 50 = 6.0 × 106 Pa cm3. p = 6.0 × 106/80 = 7.5 × 104 Pa.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Boyle's law | pV is constant for a fixed mass of gas at constant temperature. |
| Inversely proportional | When one quantity doubles, the other halves. |
| Isotherm | Curve on a p–V graph for constant temperature. |
| Compression | Reduction in the volume of a gas. |
Section 9 of 9Exam technique
1
Using the law when temperature changesit is only valid at constant temperature.
2
Using p ∝ V instead of p ∝ 1/V.
3
Forgetting that gauge pressure may differ from absolute pressure by atmospheric pressure.
4
Compressing the gas too quickly in an experiment, which warms the gas.