Why Does a Hot Drink Cool Fastest at the Start? Cooling Curves and Newton's Law

Pour a hot drink and, for the first few minutes, it cools quickly. Later it seems to take forever to go from warm to room temperature. That isn’t your imagination. It’s a pattern you can measure, graph and explain.

The investigation

Question: How does temperature change as a cup of warm water cools?

You need: identical cups, card lids with a thermometer hole, a wool sock or foam sleeve, a thermometer reading to 0.1 °C (digital probe or alcohol-filled, never mercury), a timer and a kitchen scale.

Hot water safety: use warm water, not boiling, at about 60 °C at most, handled by an adult.

Set up three cups with the same amount of warm water: one open, one with a lid and one with a lid and a wool sleeve.
Record the temperature of each every minute for 20 to 30 minutes.
Graph temperature against time for each cup on the same axes.

What the graph shows

Each curve starts steep and flattens out as it approaches room temperature. The open cup drops the fastest, the lidded cup is slower, and the lidded, wool-wrapped cup is slowest.

Why the curve flattens

Newton’s law of cooling says the rate of heat loss is roughly proportional to the temperature difference between the object and its surroundings. At the start, a cup at 60 °C in a 20 °C room has a 40 °C difference, so heat leaves quickly. When it’s down to 30 °C, the difference is only 10 °C, so heat leaves much more slowly. The closer to room temperature, the slower the cooling. Strictly, the cup never reaches room temperature exactly. It just gets closer and closer.

Newton’s law is an approximation. It works well for small temperature differences and slow cooling, and less well when other effects dominate.

What the lid and wool do

The lid reduces evaporation, which carries away a lot of energy. Water molecules that escape from the surface take energy with them.
The wool slows conduction and convection by trapping air.

You can estimate evaporation by weighing the open cup before and after: the mass lost is water that evaporated. Each gram evaporated carries away a lot of energy, so this is often the largest effect in the open cup.

Practical lesson

If you want a drink to stay hot, use a lid and insulation. If you want a hot drink to cool quickly, spread it out, stir it or pour it into a wider cup. Adding cold milk early or late changes how long you wait, which is a good follow-up experiment.

The full activity is Why does a hot drink cool fastest at the start? from the Hot Stuff: Heat, Temperature and Cooling unit, which also asks Does hotter always mean more heat? and How do you keep a drink hot for the longest? Sign up for three lessons free.