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TL;DR Charles' Law states that the volume of a fixed mass of gas is directly proportional to its absolute temperature at constant pressure: V∝T. In the standard O-Level practical, you heat a sealed air column in a capillary tube through a water bath, record length at several temperatures, convert to Kelvin, and plot a straight-line graph. Extrapolating the graph backward (dashed line) should reach −273,∘C, confirming absolute zero. Most marks are lost by using Celsius instead of Kelvin or not waiting for thermal equilibrium.
Charles' Law describes the behaviour of a gas when pressure and mass remain constant. It says:
The volume of a fixed mass of gas is directly proportional to its absolute (Kelvin) temperature, provided the pressure remains constant.
In symbols:
V∝T(at constant pressure)
This can be rewritten as:
TV=constantorT1V1=T2V2
The word "absolute" is critical. Temperature must be measured in Kelvin (K), not degrees Celsius. The conversion is:
T/K=θ/∘C+273
If you plot volume against Celsius temperature, the graph is still a straight line, but it does not pass through the origin. Only a Kelvin-scale graph gives the proportional relationship that passes through (0,0).
When pressure p and the amount of gas n are held constant, V=pnR⋅T, which is a straight-line relationship between V and T. Charles' Law is therefore a special case of the ideal gas equation.
2 | Apparatus needed
Item
Purpose
Capillary tube (sealed at one end)
Contains a trapped air column whose length represents the gas volume. Because the tube has uniform cross-sectional area, length is directly proportional to volume.
Concentrated sulfuric acid plug
Sits inside the capillary tube above the air column to seal the gas. Sulfuric acid also absorbs moisture so the trapped gas stays dry.
Ruler (mm scale)
Measures the length of the air column at each temperature.
Water bath (beaker of water)
Provides a controlled, uniform temperature environment around the capillary tube.
Thermometer (0--110 °C)
Reads the temperature of the water surrounding the tube.
Heat source (Bunsen burner or electric heater)
Raises the water bath temperature gradually.
Stirrer (glass rod)
Keeps the water temperature uniform so the gas inside the tube reaches the same temperature as the bath.
Retort stand and clamp
Holds the capillary tube vertically in the water bath.
3 | Step-by-step method
Set up the apparatus. Clamp the sealed capillary tube vertically inside the water bath so that the trapped air column is fully submerged. Place the thermometer alongside the tube, ensuring the bulb is at the same depth as the air column.
Record the initial readings. Before heating, record the room-temperature reading on the thermometer (θ in °C) and measure the length of the air column (L in cm) using the ruler. Read the ruler at eye level to avoid parallax error.
Heat the water bath slowly. Light the Bunsen burner or switch on the electric heater. Stir the water continuously.
Take readings at regular intervals. At every 10 °C rise (for example at 30 °C, 40 °C, 50 °C, 60 °C, 70 °C, 80 °C), remove the heat source, stir thoroughly, and wait at least one minute for the air column to reach thermal equilibrium with the water.
Record θ and L at each temperature. Aim for at least five or six pairs of readings spread across the available range.
Convert Celsius to Kelvin. Add 273 to each Celsius value to obtain the absolute temperature T.
Repeat if time permits. A second run with cooling readings (allowing the bath to cool and recording on the way down) provides a check on your data.
4 | Raw data table template
Copy this layout into your practical report. Fill in at least five rows.
θ / °C
T / K
L / cm
30
303
40
313
50
323
60
333
70
343
80
353
Column headings must include the quantity name and the unit separated by a forward slash, for example "T / K". This is a standard marking-scheme requirement - see the Practical Maths Toolkit for more on table and graph conventions.
5 | Plotting the graph
Axes
x-axis: Temperature in Kelvin (T / K).
y-axis: Length of air column (L / cm). Because the capillary tube has uniform bore, L is proportional to volume, so L serves as a proxy for V.
What you should see
Your plotted points should lie close to a straight line. Draw the best-fit line through the points.
Extrapolation to absolute zero
Extend the best-fit line backward (use a dashed line for the extrapolated section) until it meets the x-axis. The intercept on the temperature axis should be approximately 0,K (i.e. −273,∘C). This confirms that at absolute zero, the gas would theoretically occupy zero volume.
Pick two well-separated points on the best-fit line (not data points) and calculate.
Checking direct proportionality
Direct proportionality means L=kT where k is a constant. Two checks confirm this:
The graph is a straight line that passes through the origin (when temperature is in Kelvin). If you started your x-axis at 0 K and the extrapolated line hits the origin, proportionality is verified.
Calculate L/T for each data pair. If all ratios are approximately equal, then L∝T.
T / K
L / cm
L/T / cm K−1
303
(your value)
313
(your value)
323
(your value)
333
(your value)
343
(your value)
353
(your value)
If the L/T values are consistent (within experimental tolerance), you can state that the results support Charles' Law.
7 | Sources of error and improvements
Source of error
Effect
Improvement
Heat loss from the water bath to the surroundings
The actual gas temperature may be lower than the thermometer reading, giving systematically short air-column lengths at high temperatures.
Insulate the beaker with a lid and lagging material.
Not waiting long enough for thermal equilibrium
The air column has not expanded fully, so L is too small for the recorded temperature.
Wait at least one minute after stirring before taking a reading. Remove the heat source during this pause.
Parallax error when reading the thermometer or ruler
Random error in recorded values of θ or L.
Read the scale at eye level, perpendicular to the scale.
Non-uniform bore of the capillary tube
Length is no longer proportional to volume.
Use a precision-bore capillary tube or calibrate the tube beforehand.
Air column not fully submerged in the water bath
Part of the gas is at room temperature rather than bath temperature.
Ensure the sealed end and the entire air column are below the water surface.
Evaporation of the sulfuric acid plug at high temperatures
The mass of trapped gas changes, invalidating the constant-mass assumption.
Keep the maximum temperature below 80 °C. Use a longer sulfuric acid plug.
8 | Planning question angle - designing the experiment in Paper 3
If Paper 3 gives you a planning question on Charles' Law, structure your answer around these headings:
Independent variable: Temperature of the gas (controlled by heating the water bath).
Dependent variable: Length of the air column (measured with a ruler).
Control variables: Pressure (atmospheric, kept constant by using an open-ended or consistently sealed setup), mass of gas (sealed tube, same air sample throughout).
Method outline: Describe the water-bath setup, how you heat in stages, how you ensure equilibrium, and how you take readings.
Safety precautions: Handle hot water carefully, use a heat-proof mat, do not overheat the water bath above 80 °C to avoid scalding and sulfuric acid vapour.
How to process results: Plot L against T (in Kelvin), draw a best-fit line, and check if it passes through the origin. Calculate L/T ratios to confirm proportionality.
Expected outcome: A straight line through the origin confirms V∝T (Charles' Law).
For a detailed walkthrough of planning-question structure, see the Paper 3 Marking Guide.
9 | Common exam mistakes
Mistake 1 - Using Celsius instead of Kelvin
This is the single most common error. If you plot L against θ in degrees Celsius, the graph is still a straight line, but it does not pass through the origin. You cannot claim direct proportionality from a Celsius graph. Always convert to Kelvin before plotting.
Mistake 2 - Not waiting for thermal equilibrium
Students rush to record readings immediately after heating. The thermometer may show 60 °C, but the air inside the capillary tube may still be at 55 °C. This produces points that fall below the best-fit line at higher temperatures.
Mistake 3 - Poor graph scale
Choosing a scale that squashes all your points into one corner of the graph paper wastes space and makes it impossible to draw an accurate best-fit line. Your plotted points should occupy at least half the available area on each axis. The Practical Maths Toolkit covers scale selection in detail.
Mistake 4 - Drawing a curve instead of a straight line
Charles' Law predicts a linear relationship. If your points suggest a curve, recheck your data for systematic error (such as incomplete equilibrium) rather than drawing a curve through them.
Mistake 5 - Forgetting units in table headings
Every column heading must include the quantity and the unit, separated by a slash. "Temperature" alone is not acceptable; use "T / K" or "θ / °C".
Mistake 6 - Confusing length with volume
Examiners accept length as a proxy for volume only when the capillary tube has a uniform cross-sectional area. State this assumption explicitly in your report: "Since the capillary tube has uniform bore, the length of the air column is proportional to its volume."
10 | Summary checklist
Before you hand in your report, confirm:
All temperatures are converted to Kelvin.
Table headings include quantity and unit (e.g. "T / K").
At least five data points are plotted.
The best-fit line is straight and drawn with a ruler.
The extrapolated section (toward the origin) is dashed.
You have stated the assumption that length is proportional to volume because of uniform bore.
Sources of error and improvements are specific, not generic.
