Practical: Investigating Gas Laws Revision Notes | A Level AQA Physics

1. Why These Practicals Matter

Gases behave in ways that feel almost counterintuitive until you see the pattern. Squeeze a gas into half the space and its pressure doubles. Heat it up and it expands. These are not just textbook curiosities — they are the foundations of thermodynamics, and AQA requires you to demonstrate them experimentally in Required Practical 8.

The two investigations — Boyle's law and Charles's law — each isolate one relationship by holding everything else fixed. That word fixed is doing a lot of work here, and getting the controlled variables right is where most marks are won or lost in exam questions about this practical.

2. Boyle's Law: Pressure and Volume at Constant Temperature

Picture a sealed syringe full of air. Push the plunger in and the same number of gas molecules are now crammed into a smaller space — they hit the walls more often, so the pressure rises. Pull the plunger out and the molecules spread into a larger volume, hitting the walls less frequently, so the pressure falls. That is Boyle's law in physical terms.

The key experimental challenge is keeping temperature constant throughout. Any compression of a gas releases a small amount of thermal energy, so you must allow time for the gas to return to room temperature between readings. Rushing this step is the most common source of systematic error in this investigation.

When you plot pressure against $\frac{1}{V}$, a straight line through the origin is your confirmation. The gradient of that line equals the constant $k = pV$. If your line does not pass through the origin, the most likely cause is a systematic error — either the volume scale was not zeroed correctly, or the temperature was not properly controlled.

3. Graphical Analysis and Calculating pV

Raw data from the Boyle's law experiment needs careful processing before you can draw conclusions. The table below shows the kind of data you might collect and how to check for consistency.

Notice that $pV$ remains constant at 2000 kPa cm³ across all readings. In a real experiment, small variations are expected due to measurement uncertainty, but the values should cluster closely around a constant. A large spread suggests poor temperature control or a leak in the apparatus.

Worked example: Checking Boyle's Law from Experimental Data

A student records the following data: when V = 30 cm³, p = 120 kPa. When V = 60 cm³, p = 58 kPa. Determine whether these readings are consistent with Boyle's law.

1. $pV_1 = 120 \text{ kPa} \times 30 \text{ cm}^3 = 3600 \text{ kPa cm}^3$ — Multiply pressure by volume for the first data point.
2. $pV_2 = 58 \text{ kPa} \times 60 \text{ cm}^3 = 3480 \text{ kPa cm}^3$ — Multiply pressure by volume for the second data point.
3. $\frac{|3600 - 3480|}{3600} \times 100\% \approx 3.3\%$ difference — A 3.3% discrepancy is small and could be attributed to measurement uncertainty or slight temperature variation. The readings are broadly consistent with Boyle's law.
4. $pV \approx \text{constant}$ within experimental uncertainty — Boyle's law is supported. To strengthen the conclusion, more data points across a wider range of volumes should be collected.

Answer: The two readings give pV values of 3600 and 3480 kPa cm³ — a 3.3% difference, consistent with Boyle's law within experimental uncertainty.

4. Charles's Law: Volume and Temperature at Constant Pressure

Now consider what happens when you heat a gas while keeping the pressure constant. The molecules gain kinetic energy and move faster. To maintain the same pressure — the same rate of collisions with the walls — the gas must expand into a larger volume. This is Charles's law, and it reveals a beautifully linear relationship between volume and absolute temperature.

The critical point here is that the temperature must be in kelvin, not degrees Celsius. If you plot V against temperature in °C, you get a straight line that does not pass through the origin — it intersects the temperature axis at approximately −273 °C. Convert to kelvin and the line passes through the origin, confirming direct proportionality.

Using column length rather than volume directly is perfectly valid because the cross-sectional area of the capillary tube is constant. Volume equals cross-sectional area multiplied by length, so if area is fixed, length is directly proportional to volume. This is a common simplification in this experiment and examiners expect you to justify it.

5. Processing Charles's Law Data

The data processing for Charles's law follows the same logic as Boyle's law: calculate the ratio $V/T$ for each data pair and check for constancy. The table below illustrates typical results from a capillary tube experiment.

Worked example: Verifying Charles's Law from Experimental Data

A student measures a trapped air column of length 6.20 cm at 40 °C and 7.10 cm at 90 °C. Check whether these results are consistent with Charles's law.

1. $T_1 = 40 + 273.15 = 313.15 \text{ K}$\n$T_2 = 90 + 273.15 = 363.15 \text{ K}$ — Always convert to kelvin before applying Charles's law. Adding 273.15 (or 273 as an approximation) to the Celsius temperature gives the absolute temperature. At A-level, using 273.15 is more precise.
2. $\frac{L_1}{T_1} = \frac{6.20 \text{ cm}}{313.15 \text{ K}} = 0.01980 \text{ cm K}^{-1}$ — Divide column length by absolute temperature for the first data point.
3. $\frac{L_2}{T_2} = \frac{7.10 \text{ cm}}{363.15 \text{ K}} = 0.01955 \text{ cm K}^{-1}$ — Divide column length by absolute temperature for the second data point.
4. $\frac{|0.01980 - 0.01955|}{0.01980} \times 100\% \approx 1.3\%$ difference — A 1.3% discrepancy is within typical experimental uncertainty for this apparatus. The results are consistent with Charles's law.
5. $\frac{L}{T} \approx \text{constant}$ within experimental uncertainty — Charles's law is supported. The small discrepancy is likely due to difficulty reading the column length precisely or slight non-uniformity in water bath temperature.

Answer: L/T values of 0.01980 and 0.01955 cm K⁻¹ — a 1.3% difference — are consistent with Charles's law within experimental uncertainty.

6. Comparing the Two Investigations

It helps to see both investigations side by side. The structure is the same — fix two variables, vary one, measure another — but the specific quantities and apparatus differ significantly.

One subtle but important difference: in the Boyle's law experiment, you actively change the volume and measure the resulting pressure. In the Charles's law experiment, you change the temperature and measure the resulting volume. The direction of causality in the experiment matches the independent variable you control.

7. Exam Technique and Common Mistakes

Questions on Required Practical 8 tend to fall into three categories: describing the method, explaining how variables are controlled, and analysing or evaluating graphical data. Each demands a different approach, and mixing them up is where marks are dropped.

When a question asks you to describe the method, give a clear sequence of steps — what you set up, what you change, what you measure, and in what order. Do not explain why at this stage; the command word is 'describe', not 'explain'. When asked to explain a control variable, always state what would happen to the results if that variable were not controlled.

For evaluation questions, the strongest answers follow a point–evidence–implication structure. Identify the source of error, state how it affects the data (does it cause a systematic shift or random scatter?), and then suggest a specific improvement with a reason. A vague 'repeat the experiment' without explaining what it improves will not score the evaluation mark.

Both investigations in Required Practical 8 are built on the same experimental logic: isolate one relationship by controlling everything else, collect sufficient data across a wide range, and use graphical analysis to confirm proportionality. Master that logic and you can answer any exam question on these practicals — whether it asks you to describe, explain, or evaluate.