Boyle's law: P ∝ 1/V at constant T
Boyle's law: for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume, , i.e. (or ). Two mark-scheme conditions are non-negotiable: constant temperature and fixed mass of gas. Units: in Pa, in m³. To test data, multiply each P and V pair — if the products are approximately equal, the data support the law.
P–V is a hyperbola; P vs 1/V is a line
Two graphs. P against V: a rectangular hyperbola — P falls as V rises, and the curve never touches either axis. Every point has the same product. P against : rearranging gives , form , so a straight line through the origin with gradient (unit Pa·m³). "Proportional" means the line passes through the origin — one that misses it shows only a linear relationship.
Verify Boyle's law with PV products
Trap a fixed mass of gas at constant temperature, change the pressure and record the new volume, then compute for each pair. If the products are approximately equal (within experimental error), the data support Boyle's law. Use at least two pairs plus a comparative statement. Keep units consistent — convert kPa to Pa and cm³ to m³, or use the same non-SI units throughout; never mix them in one product.
Drawn from real examiner reports.
Boyle's law only at constant temperature
Boyle's law applies ONLY at constant temperature. If a gas is compressed AND heated (or cooled), is invalid — the combined gas law is needed. Watch for tyres heated by braking, or gas warmed while squeezed: check the temperature is unchanged before using Boyle's law.
June 2024 Paper 2P Q8(a) — examiner noted systematic errors when candidates applied gas-law formulae without converting or verifying temperature units, showing confusion about which law requires which constant condition.
Definition needs constant T, fixed mass
Writing only "pressure is inversely proportional to volume" loses a mark — the mark scheme requires the conditions "at constant temperature, for a fixed mass of gas". Those words after the relationship are non-negotiable. State the relationship AND both conditions.
PV: approximately equal, not exact
Real data always carries measurement error, so the products come out approximately — not exactly — equal. Writing "the values are not equal, so Boyle's law fails" loses the conclusion mark. Say "the products are approximately constant, within experimental error, supporting Boyle's law".
June 2024 Paper 2PR Q9(c) — candidates scored 2 of 3 for calculating PV constants but not the third mark because they expected exact equality and gave no comparative statement acknowledging experimental variation.
P–V graph is a hyperbola, not a line
Describing the P against V graph as "a straight line with negative gradient" scores zero — that would mean , a different relationship. Inverse proportionality gives a rectangular hyperbola that never touches the axes. Do not confuse it with the P vs graph.
P vs 1/V must pass through the origin
On a P against graph the line must go through the origin — that is what confirms proportionality. A positive y-intercept implies a non-zero pressure at infinite volume (), which is nonsense. A line that misses the origin shows only linearity, not proportionality.
Don't mix pressure or volume units
Convert consistently before computing : kPa to Pa (×1000), cm³ to m³ (), or keep the same non-SI units on both sides so they cancel. Mixing Pa with cm³ in one product, or leaving the final answer in kPa when Pa is asked, loses the unit mark.
Calculation scaffold for P₁V₁ = P₂V₂
(1) State and check temperature is constant. (2) Substitute known values (consistent units). (3) Rearrange for the unknown. (4) Evaluate and give the unit (Pa or m³). A correct substitution scores even if the final value slips.
Confirm the law with two PV products
For "do the data confirm Boyle's law", pick at least TWO P–V pairs, compute for each, then state they are "approximately equal" and conclude the data support the law. One product alone, or demanding exact equality, does not gain the conclusion mark.
Answering the graph questions
"Sketch P–V" → a hyperbola not touching the axes, axes labelled with quantity and unit. "What P vs graph confirms Boyle's law?" → a straight line through the origin. "What does its gradient represent?" → the constant (Pa·m³).
Explain P rise by wall collisions
For "why compressing a gas raises pressure": the same number of molecules in a smaller space hit the walls more frequently → greater force per unit area → higher pressure. At constant temperature the speed is unchanged; only the collision rate rises.
where:
Conditions (both required for any credit): constant temperature; fixed mass of gas.
Equivalently: (a constant), or at constant temperature.
| Symbol | Quantity | SI unit |
|---|---|---|
| Pressure | Pa (pascal) | |
| Volume | m³ | |
| Boyle's law constant () | Pa·m³ |
State Boyle's law (give the full mark-scheme definition).
A gas is trapped in a sealed syringe at a pressure of and a volume of . The plunger is pushed in at constant temperature until the volume is . Calculate the new pressure of the gas.
