Teach lesson
Gay-Lussac: how far the model goes
Compare measured data, a linear fit, and an extrapolation to decide what each one can support.
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Learning Outcomes
Interpret a linear model inside the measured range without overstating an extrapolation.
Explain why one real run does not exactly prove absolute zero.
Write a conclusion that separates evidence, model, and limitations.
Student activity preview
Activity Content
Preview only. In a class session, students can fill in responses and submit their work to the teacher.
How far would you trust a straight line?
5 min
Imagine that a straight line fits measurements taken between 24 °C and 45 °C. Is that enough reason to trust it more than two hundred degrees outside that interval? In this activity you will observe how pressure and temperature change while a fixed-volume ethanol sample is heated, then separate measured data, a fitted model, and an extrapolation: extending the model beyond the measured range.
Before seeing the fit, would you trust a prediction made more than two hundred degrees outside the measured data?
Anchor the model in real data
12 min
Open the lab and observe the real heating run. Before starting, prepare two notes: near 00:30 and 03:30, record temperature in °C and pressure in kPa. Then compare those measurements with the graph and fit included in the activity.
Open the Gay-Lussac lab
The sealed sample always contains the same total amount of ethanol, and the container keeps a fixed volume. The ideal model also treats the gas-phase amount as fixed; the lab records temperature and pressure, not the amount in each phase.
Open the lab from this activity's lab button.
On the configuration screen, select the only available sample: 0.014 mol of ethanol.
Start one observation, which takes about 4 minutes. During the run, record approximate temperature and pressure at the times shown in the following table.
Return to TEACH and complete that table before continuing with the analysis.
Lab readings
The times are already provided. Copy observed readings into the °C and kPa columns. Units appear in the headings.
| Run time (min:s) | Temperature °C | Pressure kPa |
|---|---|---|
After completing the table, describe the joint temperature-pressure trend in one sentence. Do not copy all four values again.
Separate measuring from extrapolating
10 min
Ideal model. Kelvin is an absolute scale: 0 K corresponds to -273.15 °C. In the ideal-gas model, P/T(K) is constant for a fixed amount of gas at fixed volume.
From measurement to extrapolation. To extrapolate is to extend a model beyond the measured range. The fit to all 61 readings from about 24 °C to 45 °C gives P(kPa) ≈ 0.37624 T(°C) + 78.436. The figure shows the data, the fit inside the interval, and part of its extension; it does not mark the P = 0 intercept.
Measured data, fit, and extrapolation
Blue points are measurements. The green segment is the fit inside the measured range, and the dashed amber segment is part of the same fit extended beyond the data. The figure does not show where it reaches P = 0; you will calculate that. The lower zoom makes the points and fit between 24 °C and 45 °C inspectable.
Calculate the intercept. Use a calculator. In P ≈ 0.37624 T + 78.436, substitute P = 0, solve for T, and show the operation. Round the intercept to 0.1 °C.
Compare distances. Calculate positive differences and complete: |24 − intercept T| = ___ °C; |−273.15 − intercept T| = ___ °C. Round both to 0.1 °C.
Conclusion with limits
13 min
A strong scientific conclusion says exactly what the evidence allows. A classmate claims: “Because the line crosses P = 0, this lab has proved absolute zero exactly.” Evaluate that claim in the following fields.
Verdict. Is the claim that the lab has proved absolute zero exactly justified?
Complete one sentence: From 24 °C to 45 °C, the data do support... Limit the answer to what is visible inside the measured interval.
Measurement or extrapolation. Correct this sentence: “the lab measured zero pressure at the calculated intercept.” Include the approximate intercept and its distance from absolute zero.
Physical mechanism. If ethanol is cooled far enough, some gas may condense. Explain which quantity in the model would stop being fixed and why this can make the extended line fail.
Measurement improvement. Propose one concrete change that would make the investigation more reliable and explain in one sentence how it would reduce a limitation.