Experiment: Volume and temperature of a fixed mass of gas at constant pressure (Charles's law)

Aim

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

Variables

• Manipulated: Temperature of the gas, θ
• Responding: Length of the trapped air column (proportional to volume), L
• Constant: Pressure and the mass of the trapped gas

Apparatus & materials

• Capillary tube sealed at one end with a trapped air column and a concentrated sulfuric acid index
• Ruler
• Beaker of water
• Thermometer
• Stirrer
• Bunsen burner or hotplate
• Retort stand with rubber band

Procedure

1. Fasten the capillary tube beside a ruler and immerse it in a beaker of water, with the sealed end down and the acid index trapping the air column.
2. Stir the water and record the temperature θ and the length of the air column L when they are steady.
3. Heat the water gently, stirring all the time.
4. At each of several temperatures (for example 30, 40, 50, 60 and 70 °C), stop heating, stir, and record θ and L.
5. Allow time for the trapped air to reach the water temperature before each reading.
6. Record θ and L for each temperature.

Tabulating results

Record the temperature θ in °C and the length of the air column L in cm (L represents the volume, since the tube has uniform cross-section). Keep the decimal places consistent.

The graph

Plot L (volume, y-axis) against temperature θ in °C (x-axis). The straight line, when extended back to L = 0, cuts the temperature axis near −273 °C (absolute zero).

Analysis

At constant pressure the volume is directly proportional to the absolute (kelvin) temperature, so V / T = constant. Extrapolating the line to zero volume gives absolute zero at about −273 °C.

Heat · Graph skills

Sample results and what they show

These are example readings for a fixed mass of gas at constant pressure. The length L of the trapped air column stands in for the volume because the capillary tube has a uniform cross-section.

• θ = 30 °C, L = 25.0 cm
• θ = 40 °C, L = 25.8 cm
• θ = 50 °C, L = 26.6 cm
• θ = 60 °C, L = 27.5 cm
• θ = 70 °C, L = 28.3 cm

The air column lengthens steadily as the water is heated, gaining about 0.8 cm for every 10 °C rise, so the gas expands on heating at constant pressure. If you add 273 to each Celsius reading to get the absolute temperature T, the ratio L/T is almost the same each time, roughly 0.083 cm K⁻¹.

That constant ratio is the real message of the experiment: the volume is proportional to the absolute temperature, not to the Celsius value. Notice L does not double when θ doubles in °C, which is why the Kelvin scale is needed.

Reading the graph and finding the answer

Plot L on the y-axis against θ in °C on the x-axis. The points fall on a straight line with a positive gradient that does not pass through the origin, because 0 °C is not the true zero of temperature.

Take a large triangle using two well-separated points on the best-fit line, for example (30 °C, 25.0 cm) and (70 °C, 28.3 cm):

• gradient = (28.3 − 25.0) cm ÷ (70 − 30) °C = 3.3 cm ÷ 40 °C = 0.0825 cm °C⁻¹

This gradient is the rate at which the column expands per degree. Extend the line backwards until L = 0; it meets the temperature axis at about −273 °C, which is absolute zero.

This confirms V/T = constant. Remember the SPM Physics 4531 papers give no formula sheet, so you must recall the Charles's law relationship V/T = constant yourself.

Choose axis scales that spread the plotted points across more than half of the grid, and draw the best-fit line so the points are balanced evenly on both sides of it. If one point is clearly off the line, treat it as an anomalous reading, ring it, and leave it out when drawing the line and taking the gradient.

Marks examiners look for

Precautions that protect the result:

• Stir the water continuously so its temperature is uniform.
• Wait for the trapped air to reach the water temperature before each reading.
• Keep the acid index thin and short so the pressure on the gas stays constant.
• Read L and θ at eye level to avoid parallax error.

For the Paper-3 science process skills, examiners award marks for: correctly stating the manipulated variable (θ), responding variable (L) and a fixed variable (pressure and mass of gas); tabulating with headings and units and consistent decimal places; plotting at least five points with labelled axes and a smooth best-fit line; and using a large triangle to find the gradient. State the relationship in words, that the volume increases linearly with temperature, and mention the extrapolation to absolute zero as your conclusion.

Repeat each reading and take the average to reduce random error, and quote the final answer to a sensible number of significant figures with its correct unit. In the discussion, name one source of error together with a matching improvement, and note that any point off the line was ignored so the conclusion rests on consistent data.

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