Physics IA · B · The particulate nature of matter · topic 7 of 30

Cooling water: how well does Newton's law fit? · IB Physics IA idea: guide, sample graph and step-by-step plan

slow but rewarding: plan the calendar!

A cup of tea cools fast at first, then slowly. Newton's law says it should be an exponential. You're going to see how exactly that holds.

Difficulty●●○ Medium
KitBasic to standard: thermometer or data logger, beaker, lid
TimeAbout 10 hours
FitsSL and HL
  • ✓ you like exponential models
  • ✓ you can leave a logger running
  • ✓ you want to test a law and find its limits

The big idea

← where it STOPS working is your story

Newton's law of cooling says the rate of cooling is proportional to the temperature difference from the surroundings, so the excess θ = T − T_s falls exponentially: θ = θ₀e^(−kt). Plotting ln θ against time should give a straight line of gradient −k. The room temperature T_s matters a great deal, and the law only holds for modest temperature differences. The interesting result is where your data stops following the straight line.

Make it yours: pick one twist

Copying a classic won't show your choices. Pick one of these (or invent your own) and your IA becomes yours.

Swipe for more twists →

Change the starting temperature

Start at several temperatures and find k each time.

→ Tests whether k depends on how hot the water is; the law says it should not, so a clean test of its limits.
Change the container

Use a metal, glass and polystyrene cup of the same volume.

→ k changes with the container; your graph compares gradients, and the evaluation links k to heat transfer.
Change the surface area or the lid

Compare open and covered cups, or wide and narrow containers.

→ Isolates evaporation or area; the log graph will bend if evaporation matters.
Add insulation layers

Wrap the beaker in one, two and three layers.

→ k becomes a function of insulation thickness; your graph is k against the number of layers.
Use a data logger

Replace a thermometer and stopwatch with a temperature probe.

→ Many more points, smaller timing uncertainty, and a clearer view of where the exponential fails.
Change the context

A hot drink, a car engine or a baby's bottle.

→ Gives the introduction a purpose; the physics and graph stay the same.

Your Physics IA research question: run the check

Write your own question first. Then make sure it ticks every box:

  • Names one independent variable and its range (starting temperature, container or insulation) and how many values.
  • Names one dependent variable and how it is found (the cooling constant k from which graph, over which time range).
  • Says what stays fixed (volume, container, lid, room, stirring).
  • Says what you compare with (the exponential model, and what counts as a good fit).
  • Is narrow enough for about 10 hours, noting that one cooling run takes a long time.

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The set-up

One way to arrange it. Draw yours with the real container, probe position and how you measure the room temperature.

lid: stops evaporationprobe in the middlelogger: every 30 sroom probe

How your Physics IA could be laid out

The usual order for a topic like this, what each part needs to show, and roughly how much of your 3,000 words it takes. The words are all yours.

Research question and context~250
Your question; where cooling rate matters (drinks, buildings, engines); what you expect and why.
Background physics~450
Heat transfer to the surroundings; Newton's law and its exponential solution; why ln θ against t should be straight; where the law fails.
Variablestable
Independent, dependent and controlled variables, each with how you set, measure or hold it, and why it matters.
Method~400
Volume and container; how and when you read temperature; where the probe sits; how T_s is measured; lid; stirring; repeats.
Safety, ethics, environment~50
Short and specific: hot water, spills, a kettle.
Raw datatable
One table or an exported file extract: time, temperature, room temperature, units and uncertainties.
Processing~250
Excess temperature θ = T − T_s, its uncertainty, the logarithm and the uncertainty in it; one worked example.
Graphs and analysis~400
ln θ against t with error bars and fit; what the gradient is; where the data departs from a straight line.
Conclusion~400
Answer with numbers: your k, how well the data follows the model, and where it does not.
Evaluation~650, the biggest part!
Weaknesses ranked by their effect on your result, each linked to a realistic improvement.
Referencesnot counted
Every source for theory and method.

What your Physics IA graph could look like

ln θ, not ln T ✓

Made-up data, to show you the form of a strong graph, not the answer. Yours will look different. example only

05101520253035402.02.53.03.54.04.5Time t / min (± 1 s)ln(θ / °C), where θ = T − TsNewton's law: a straight lineroom temperature misjudged by 2 °Cyour data, with error barsa wrong room temperaturebends the line up late onILLUSTRATIVE · MADE-UP DATA
  • The log axis turns an exponential into a straight line, so a straight-line fit tests the law.
  • Error bars here are drawn at the late-time size. Early ones are much smaller, so work them out point by point.
  • The second line shows how an error in the room temperature changes the shape: say how you measured it.
  • Fit the straight part and say how you chose where the fit stops.
  • Another graph to consider: cooling rate (the gradient of T against t) against θ, which should be a straight line through the origin.

Which uncertainty matters most?

Rank by the effect on your result, here ln θ late in the run, when θ is small. The room temperature can matter far more than the stopwatch.

Room temperature (± 1 °C)6.3%Probe reading (± 0.5 °C)3.1%Temperature gradient in water (± 0.3 °C)1.9%Timing (± 0.5 s)0.03%biggest effect: discuss this first!% uncertainty in θ at 35 min, where θ is about 16 °CILLUSTRATIVE · MADE-UP NUMBERS

Your game plan

measure room temperature, always

Tick steps off as you go. We'll remember on this device.

0 of 11 done

  1. Read and predictFind Newton's law of cooling and its solution. Predict what a ln θ against t graph should look like and what k depends on.
  2. Trial run (1 lesson)Cool a beaker for 20 minutes. Is the probe in the right place? Does the room temperature drift? How long does the run take? Fix the problems now.
  3. Decide the run lengthA run must last until θ is small, not just to a convenient time. Decide how long, how often to record, and how you will measure T_s.
  4. Decide range and repeatsChoose at least 5 values of your independent variable and plan repeats; remember each run takes time, so plan the calendar.
  5. Collect the dataStart from the same volume each time. Record temperature and time, and the room temperature at the start and end. Note drafts, doors and so on.
  6. ProcessSubtract T_s, take logarithms and carry the uncertainty through. Decide what to do with the late points, where θ is small.
  7. Graph and fitPlot ln θ against t with error bars. Fit straight lines and read off k. Decide where the fit should stop.
  8. Compare with theoryIs the graph straight within your uncertainties, and over what range? What causes the departure, evaporation, radiation or a changing T_s?
  9. EvaluateRank the weaknesses by effect on k. Make each improvement specific to a weakness you found.
  10. Write, then cutWrite in the order of the layout and stay within 3,000 words. Tables, graphs and references do not count.
  11. Check before your teacher's draftRun through the checklist below, then get your RQ or draft checked. Your teacher reads one draft only.

Physics you'll need

Traps to avoid in this Physics IA

  • Stopping before the water reaches room temperature, so the late curve is never tested.
  • Ignoring the room temperature, or reading it once and assuming it stayed constant.
  • Heat loss through the thermometer or probe, or a thermometer touching the glass.
  • Evaporation from an open surface treated as if it were conduction and convection.
  • Not stirring, so the probe records a local temperature.
  • Taking logarithms of T, not of the excess T − T_s.
  • An evaluation that does not say why the law fails at large temperature differences.

More Physics IA ideas like this

Make sure it's yours

This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.

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