Experiment: Pressure and volume of a fixed mass of gas at constant temperature (Boyle's law)

Aim

To investigate the relationship between the pressure and the volume of a fixed mass of gas kept at constant temperature.

Variables

• Manipulated: Pressure of the trapped gas, P
• Responding: Volume of the trapped gas, V
• Constant: Temperature and the mass of the trapped gas

Apparatus & materials

• Boyle's law apparatus (glass tube with trapped air column, oil reservoir and Bourdon pressure gauge)
• Foot pump
• Ruler scale on the tube

Procedure

1. Set up the Boyle's law apparatus so the trapped air column is clearly against the scale and the gauge shows the pressure.
2. Record the initial pressure P and the volume V (read as the length of the air column).
3. Use the foot pump to raise the pressure a little, then wait for the reading to settle so the temperature is constant.
4. Record the new pressure and the corresponding volume.
5. Repeat to obtain five or six pairs of readings over a range of pressures.
6. Record P, V and calculate 1/V and the product PV for each pair.

Tabulating results

Record the pressure P (e.g. in kPa), the volume V (in cm³ or as column length), the derived value 1/V, and the product PV. A near-constant PV column supports the law.

The graph

Plot P (y-axis) against 1/V (x-axis). A straight line through the origin shows P is inversely proportional to V.

Analysis

Because P is inversely proportional to V at constant temperature, PV = constant. The straight-line graph of P against 1/V confirms Boyle's law.

Heat · Graph skills

Sample results and what they show

These are example readings, not a mark scheme. For the trapped air column, as the pressure P was raised to 100, 150, 200, 250 and 300 kPa the volume (read as column length) fell from about 40.0 cm to 13.3 cm.

The clear pattern is that as P goes up, V comes down, but not by the same amount each step. Doubling P from 100 kPa to 200 kPa halves V from 40.0 cm to 20.0 cm; trebling P to 300 kPa cuts V to a third, about 13.3 cm.

That is the signature of an inverse proportion. Working out PV for each pair gives about 4000, 4005, 4000, 4000 and 3990 kPa·cm, nearly constant, which is the numerical statement of Boyle's law.

Change the pressure slowly and pause between readings, so any heat from compression leaks away and the temperature stays constant.

Reading the graph and finding the answer

A P–V graph is a curve, which is hard to test by eye, so plot P / kPa on the y-axis against 1/V / cm⁻¹ on the x-axis instead. This straightens the relationship: a straight line through the origin confirms P is inversely proportional to V.

Take the gradient from a large triangle on the best-fit line. Using (0.0250 cm⁻¹, 100 kPa) and (0.0752 cm⁻¹, 300 kPa): gradient = (300 − 100) kPa ÷ (0.0752 − 0.0250) cm⁻¹ = 200 kPa ÷ 0.0502 cm⁻¹ = 3984 kPa·cm.

The gradient equals the constant PV, matching the near-constant PV column in the table. A line that curves away from a straight fit, or misses the origin, usually means the temperature drifted or there was a small gas leak.

Marks examiners look for

State the variables: manipulated P / kPa, responding V (the column length in cm), with the temperature and the trapped mass of gas kept constant. Keeping the temperature constant is the fair-test heart of the experiment, so 'wait between readings' is a precaution worth marks, not a throwaway line.

Tabulate P / kPa, V / cm, the derived 1/V / cm⁻¹ and the product PV / kPa·cm, with units in the headings and consistent decimals; a PV column that stays nearly constant is strong supporting evidence. Read the air-column length at eye level to avoid parallax, and check for leaks before starting.

On the graph, draw a single best-fit straight line and comment that its passing through the origin shows the inverse proportion. A conclusion that states PV = constant at constant temperature, backed by both the straight line and the steady PV column, secures the analysis mark.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)