Applied mathematics and modelling · Maths EE idea · Accessible

Is Newton's law of cooling right?

A research question to start from

How well does Newton's law of cooling describe the cooling of a hot drink, and does adding a radiation term improve the model?

A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.

Why it works as a maths EE

A model you derive, test with your own data and then evaluate against an improved version.

Mathematics you would need

First-order differential equations
Exponential decay
Fitting parameters
Residual analysis

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Solve the ODE and fit it to your data.
Analyse residuals.
Fit a modified model and compare fairly.

Scope and difficulty

Accessible. Accessible; a careful evaluation reaches the top.

Pitfalls

IA-style data project with little theory.
Comparing models by eye.

Where to start reading

Search a library catalogue or a university's open lecture notes for: Newton's law of cooling validity radiation term; residual analysis. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

Plan this EEOpens the free EE planner with this question as a starting point. Sharpen the questionSix quick checks for a focused research question. Self-check a draftCheck a section against each criterion, free.