Newton’s Law of Cooling
Lesson notes
Overview
A hot drink cools fastest at first, approaching room temperature exponentially. This topic is rated intermediate and is number 66 of 227 in Physics. Builds on the basics with relationships, methods and trade-offs.
What you are seeing
The panel above shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.
In depth
A hot drink cools fastest at first, when it is far above room temperature, and more slowly as it approaches it. Newton’s law says that the rate of cooling is proportional to the temperature difference, giving T(t) = Tₐ + (T₀ − Tₐ)e^(−kt), an exponential approach. The constant k depends on the object and surroundings. It is a good approximation for small temperature differences, and it is used in forensic estimates of time of death.
Reading the relationship
The expression "T(t) = Tₐ + (T₀−Tₐ)e^(−kt)" is a compact summary of the idea. It uses the symbols T, t, Tₐ, T₀, e, k; name what each one stands for before you start. Notice that it contains an exponential, which changes by the same factor for every equal step. Then use the sliders to see how changing one quantity changes the others.
A guided exploration
1. Set every slider to its middle value and note the shape of the curve. 2. Move one slider at a time and describe whether the curve shifts, stretches or turns. 3. Find the value where the behaviour changes sharply, then connect it to the formula.
Try this
Predict the outcome first, then test extreme slider values to find where the pattern changes or breaks.
Common pitfalls
Check units and directions first. Many mistakes come from mixing up a scalar with a vector, or from using a formula outside the conditions where it holds.
How it connects
It builds on “Diffusion and Entropy”, the topic before it in Physics. Once you are comfortable, continue with “Specific Heat Capacity”.
Why it matters
Physics explains how the world moves, heats, shines and interacts, and the same principles power technology around you.
Where you might use it
- Revising “Newton’s Law of Cooling” before a class, exam or certification
- Designing vehicles, bridges and devices where motion, forces or waves must be predicted
- Understanding how sensors, lasers and communication links actually work
- Explaining everyday phenomena such as sound, light, heat and orbits
Frequently asked questions
What is Newton’s Law of Cooling?
A hot drink cools fastest at first, approaching room temperature exponentially. It is an intermediate topic in Physics.
How do I use the Newton’s Law of Cooling simulation?
The panel at the top shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. Move the sliders one at a time, then press Space to pause the animation and look closer.
What does the formula mean?
The expression T(t) = Tₐ + (T₀−Tₐ)e^(−kt) packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.
Who is this topic for?
Builds on the basics with relationships, methods and trade-offs. If the quiz feels hard, reread the lesson notes and try the previous topic first.
What should I learn before this?
Start with “Diffusion and Entropy”, the previous topic in Physics. Each topic in a subject builds on the ones before it.
How do I track my progress?
Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.