5.1.1–5.1.4Newtonian World and AstrophysicsCore

Thermal Investigations and Gas Laws

Electrical energy measurements and gas-law graphs connect thermal theory to practical evidence. Account for energy losses and choose the variable held constant before interpreting the graph.

40 min 5.1 Thermal Physics

What you'll be able to do

Measure specific heat capacity and latent heat
Test Boyle’s law and constant-volume pressure–temperature behaviour
Estimate absolute zero and evaluate thermal controls

Specific heat capacity by electrical heating

Measure the mass of a block or liquid, supply a heater with measured current and pd, and record temperature against time. Electrical input is approximately VIt when V and I are steady. If losses are negligible, mcΔT equals this input; a temperature–time gradient gives c=P/(m gradient).

Insulate the apparatus, improve heater and thermometer contact, stir a liquid gently and record the surroundings. Some energy heats the heater, container and sensors as well as the sample. Heat losses increase as the sample warms above the room, so a longer run does not automatically improve accuracy.

Latent heat at a phase change

During a steady phase change, energy changes intermolecular potential energy while temperature remains approximately constant. For an electrical vaporisation method, measure mass lost over a known time at a steady boil and relate heater energy to mL. For melting, separate heater-induced melting from ambient melting where the method permits.

A mass-loss rate at two heater powers can help account for an approximately constant background heat loss: the power difference corresponds to the extra phase-change rate. Specify the model and do not assume every joule measured at the supply changes phase. Use the approved hot-liquid and electrical safety setup.

E=mc\Delta T,\qquad E=mL

Gas-law controls and an absolute-zero estimate

For Boyle’s law trap a fixed amount of gas, vary volume slowly and allow temperature to re-equilibrate; plot absolute pressure against 1/V. For the OCR constant-volume temperature investigation, keep gas amount and volume fixed, vary bath temperature, and measure absolute pressure after equilibrium.

A p against kelvin-temperature graph should be proportional in the ideal-gas model. Extrapolating p against Celsius temperature towards zero pressure estimates absolute zero near −273 °C. Include dead volumes and distinguish gauge from absolute pressure. This is a constant-volume pressure–temperature experiment, rather than the constant-pressure volume–temperature form of Charles’s law.

pV=\mathrm{constant}\ (T\text{ fixed}),\qquad p/T=\mathrm{constant}\ (V\text{ fixed})

Work through the reasoning

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.

Example 1A 0.50 kg block receives 6000 J and warms by 12 K. Estimate c, then explain the effect of heat loss.

c=E/(m\Delta T)=6000/[0.50(12)]=1000

J kg⁻¹ K⁻¹.

2If some input energy escaped, the actual energy raising the block’s temperature was smaller.

3Using all the input would therefore overestimate c.

Answer1000 J kg⁻¹ K⁻¹ as an uncorrected estimate; heat loss biases it high.

Example 2A constant-volume gas gives p=100 kPa at 300 K. Predict p at 330 K in the ideal model.

p_2/p_1=T_2/T_1

p_2=100(330/300)=110

kPa.

Answer110 kPa absolute.

Equation recap

E=mc\Delta T,\qquad E=mL

Equation recap

pV=\mathrm{constant}\ (T\text{ fixed}),\qquad p/T=\mathrm{constant}\ (V\text{ fixed})

Equation recap

Common mistakes to avoid

Using gauge pressure as absolute pressure.

Account for the atmospheric reference.

Assigning every joule of input to the specimen without considering the apparatus.

Evaluate container heating and losses.

Key takeaways

Electrical heating methods need an energy budget.
Phase changes can occur at nearly constant temperature.
The controlled variables determine which gas law is tested.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

Browse practice topics

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