Required Practicals: Thermal Physics

AQA A-Level Physics includes several required practicals related to thermal physics. This lesson covers the practical skills, techniques, and analysis needed for the three key experiments: measuring specific heat capacity, verifying Boyle's law, and estimating absolute zero. Strong practical skills are tested in Paper 3 and also appear in context questions on Papers 1 and 2.

Spec mapping (AQA 7408 Required Practical 8 — Investigation of Boyle's law and Charles's law / determination of specific heat capacity): This lesson covers the practical skills assessed under RP8, including determination of specific heat capacity by an electrical method (using a heater of known power, measuring temperature rise vs energy supplied), verification of Boyle's law (pressure-volume relationship at constant temperature), and graphical extrapolation to absolute zero (using Charles's law or the pressure law). Candidates must be able to identify variables, evaluate uncertainty, propose improvements, and interpret graphs. (Refer to the official AQA specification document for exact wording.)

Synoptic links: RP8 integrates the gas laws (§3.6.2.2), specific heat capacity (§3.6.2.2), electrical energy E = IVt (§3.5), and uncertainty propagation (§3.1.3). The graphical extrapolation to absolute zero connects directly to the kelvin temperature scale (§3.6.2) and reinforces the thermodynamic interpretation of T = 0 K as the state of minimum mean molecular kinetic energy (§3.6.2.3). Practical evaluation skills assessed here recur in every AQA required practical across all topics, making RP8 a high-value preparation point for Paper 3.

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Required Practical: Specific Heat Capacity by Electrical Method

Aim

To determine the specific heat capacity of a solid material (typically aluminium or copper) using an electrical heater.

Apparatus

• Metal block with two holes (one for the heater, one for the thermometer)
• Electric immersion heater
• Thermometer (or temperature sensor with data logger)
• Ammeter and voltmeter (or joulemeter)
• Power supply
• Stopwatch
• Electronic balance
• Insulation (e.g. cotton wool or bubble wrap)
• Small amount of oil (for the heater hole, to improve thermal contact)

Method

1. Measure and record the mass of the metal block (m) using the electronic balance.
2. Place the block on an insulating mat. Wrap the block in insulation to reduce energy losses.
3. Insert the heater into one hole and add a small drop of oil to improve thermal contact.
4. Insert the thermometer into the other hole (also with a drop of oil).
5. Record the initial temperature (θ₁).
6. Switch on the heater. Record the ammeter reading (I) and voltmeter reading (V).
7. Start the stopwatch.
8. Record the temperature at regular intervals (e.g. every 30 seconds) for a set time (e.g. 10 minutes).
9. Switch off the heater.
10. Continue monitoring the temperature — it may continue to rise briefly as heat distributes through the block. Record the maximum temperature reached (θ₂).

Calculation

Energy supplied: E = VIt (or read from joulemeter)

Temperature change: Δθ = θ₂ − θ₁

Specific heat capacity: c = E / (mΔθ) = VIt / (mΔθ)

Worked Example

Question: An aluminium block of mass 1.00 kg is heated for 300 s with a heater running at V = 12.0 V and I = 4.00 A. The temperature rises from 21.0 °C to 37.2 °C. Calculate the specific heat capacity.

Solution:

E = VIt = 12.0 × 4.00 × 300 = 14 400 J

Δθ = 37.2 − 21.0 = 16.2 K

c = E / (mΔθ) = 14 400 / (1.00 × 16.2) = 889 J kg⁻¹ K⁻¹

The accepted value for aluminium is 900 J kg⁻¹ K⁻¹, so this result is within 1.2% — indicating a well-conducted experiment with good insulation.

Sources of Error and Improvements

Source of Error	Type	Effect on c	Improvement
Energy lost to surroundings	Systematic	Measured c is too high (temperature rise is smaller than expected, so c = E/(mΔθ) gives a larger value)	Insulate the block thoroughly
Poor thermal contact	Systematic	Temperature reading lags behind true block temperature	Use oil in thermometer and heater holes
Non-uniform temperature distribution	Random	Temperature reading may not represent the whole block	Allow time for heat to spread; use a data logger to monitor continuously
Reading thermometer before equilibrium	Random	Final temperature may be inaccurate	Continue monitoring after switching off; record the maximum temperature
Assuming all electrical energy goes into heating	Systematic	Overestimates energy used for heating	Difficult to eliminate completely; good insulation minimises the error

Graphical Analysis

If you plot temperature against time, you can use the initial gradient of the line (before significant heat losses occur) to calculate c:

Gradient = Δθ/Δt = P/(mc) (where P = VI is the heater power)

Therefore: c = P / (m × gradient)

This method can give a more accurate result than using the total time and total temperature change, because it uses data from early in the experiment when heat losses are smallest.

Exam Tip: In exam questions about this practical, always discuss heat losses as the main source of systematic error. State that the measured value of c will be higher than the true value because some energy was lost to the surroundings, making the temperature rise smaller than expected.

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Required Practical: Boyle's Law Verification

Aim

To verify that pressure is inversely proportional to volume for a fixed mass of gas at constant temperature.

Apparatus

• Boyle's law apparatus (sealed tube containing a column of gas above oil, connected to a pressure gauge and hand pump)
• Alternatively: a large gas syringe with a pressure sensor
• Ruler or scale for reading the gas column length
• Pressure gauge (Bourdon gauge or digital sensor)
• Thermometer (to check constant temperature)

Method

1. Note the initial volume (or length of gas column) and pressure.
2. Use the hand pump to increase the pressure in small steps.
3. After each increase, wait for the temperature to return to the starting value (compression heats the gas temporarily).
4. Record the pressure (p) and volume (V) at each step.
5. Repeat for at least 6–8 data points over a wide range of pressures.
6. Also take readings while decreasing the pressure (to check for systematic errors such as friction).

Analysis

Method 1: Plot p against 1/V

If Boyle's law holds, p ∝ 1/V, so a plot of p against 1/V should give a straight line through the origin.

Calculate 1/V for each data point and plot the graph.

A straight line through the origin confirms Boyle's law.

Method 2: Plot pV against p

If pV = constant, a plot of pV against p should give a horizontal straight line.

Method 3: Plot log(p) against log(V)

If p ∝ V^n, then log(p) = −n log(V) + constant.

For Boyle's law, n = −1, so the gradient should be −1.

Worked Example — Data Analysis

A student records the following data:

p (×10⁵ Pa)	V (cm³)	1/V (cm⁻³)	pV (×10⁵ Pa cm³)
1.00	50.0	0.0200	50.0
1.25	40.2	0.0249	50.3
1.50	33.5	0.0299	50.3
2.00	25.0	0.0400	50.0
2.50	20.1	0.0498	50.3
3.00	16.8	0.0595	50.4

The pV values are approximately constant (50.0–50.4 × 10⁵ Pa cm³), confirming Boyle's law within experimental uncertainty.

Sources of Error

Source of Error	Type	Improvement
Gas not at constant temperature after compression	Systematic	Wait for temperature to return to room temperature between readings
Friction in piston/syringe	Systematic	Take readings increasing and decreasing pressure; use average
Air leak from system	Systematic	Check all seals; use silicon grease
Parallax error reading scale	Random	Read scale at eye level; use digital sensor
Gas column includes dead volume	Systematic	Account for volume of tubing and fittings

Exam Tip: The most common pitfall in Boyle's law experiments is not allowing the gas to cool between compressions. Fast compression heats the gas, causing the volume to be larger than it should be at constant temperature. Always state that you waited for thermal equilibrium after each change.

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Required Practical: Estimating Absolute Zero

Aim

To estimate the value of absolute zero by extrapolating the relationship between the volume (or pressure) of a fixed mass of gas and its temperature.

Apparatus

• Capillary tube sealed at one end with a trapped column of dry air
• Water bath
• Thermometer
• Ruler
• Heat source (Bunsen burner or electric heater)
• Stirrer

Method (Volume Method — Charles's Law)

1. Set up the capillary tube vertically in the water bath, sealed end up.
2. A small bead of sulfuric acid (or mercury) traps a column of dry air in the sealed end.
3. Heat the water bath to about 80 °C, then allow it to cool slowly.
4. Record the temperature (θ) and the length of the air column (L) at regular temperature intervals as the bath cools (every 5–10 °C).
5. The length of the air column is proportional to the volume (since the cross-sectional area of the tube is constant): V ∝ L.

Alternative Method (Pressure Method — Pressure Law)

1. Use a sealed flask of air connected to a pressure gauge.
2. Immerse the flask in a water bath.
3. Heat to various temperatures and record pressure and temperature.
4. Plot p against θ (°C).
5. Extrapolate to find the temperature at which p = 0.

Analysis

Plot L (or V) against θ (in °C). The data should form a straight line (Charles's law: V ∝ T).

Extrapolate the line backwards (towards lower temperatures) until it crosses the horizontal axis (L = 0 or V = 0). The x-intercept gives an estimate of absolute zero in °C.

If the experiment is well-conducted, the intercept should be close to −273 °C.

Worked Example — Estimating Absolute Zero

A student records the following data:

Temperature (°C)	Length of air column (mm)
20	52
30	54
40	56
50	58
60	60
70	62
80	64

The gradient of the line = (64 − 52) / (80 − 20) = 12/60 = 0.20 mm °C⁻¹.

The equation of the line is: L = 0.20θ + c

At θ = 20, L = 52: 52 = 0.20 × 20 + c → c = 52 − 4 = 48

So: L = 0.20θ + 48

Setting L = 0: 0 = 0.20θ + 48 → θ = −48/0.20 = −240 °C

This estimate of absolute zero (−240 °C) is lower than the true value (−273 °C). The discrepancy could be due to experimental errors such as uneven heating, heat losses, or the air not being completely dry.

A better result would typically give −250 to −280 °C.

Sources of Error

Source of Error	Type	Improvement
Non-uniform temperature in water bath	Random	Stir the water bath continuously
Rapid cooling (readings taken before equilibrium)	Systematic	Allow plenty of time between readings; cool slowly
Water vapour in the air column	Systematic	Use concentrated sulfuric acid to keep the air dry
Air column length measured inaccurately	Random	Use a ruler with mm divisions; avoid parallax
Limited temperature range	Affects extrapolation	Use the widest possible range (e.g. 10 °C to 90 °C)
Capillary tube not vertical	Systematic	Clamp carefully; check with spirit level

Exam Tip: The key weakness of the absolute zero experiment is the long extrapolation from the measured data range (~10–90 °C) back to −273 °C. Small errors in the gradient have a large effect on the extrapolated intercept. Always discuss this when evaluating the experiment.

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General Practical Skills Tested

Planning

• Identify independent, dependent, and control variables.
• Choose appropriate apparatus and justify your choices.
• Consider the range and number of readings needed.

Data Collection

• Record data to an appropriate number of significant figures.
• Repeat readings and calculate means where possible.
• Identify and exclude anomalous results with justification.

Data Analysis

• Plot graphs with correctly labelled axes, appropriate scales, and best-fit lines.
• Calculate gradients and intercepts from graphs.
• Use logarithmic plots to test power-law relationships.
• Calculate percentage uncertainties and combine them correctly.

Evaluation

• Identify systematic and random errors.
• Suggest realistic improvements.
• Discuss the reliability and validity of results.

Uncertainty Calculations

Percentage uncertainty in a single measurement: % uncertainty = (absolute uncertainty / measured value) × 100%

Combining uncertainties:

• For addition/subtraction: add absolute uncertainties.
• For multiplication/division: add percentage uncertainties.
• For powers: multiply percentage uncertainty by the power.