The question was formed recently due to a conversation with a fellow tea-drinker. Does tea in a large cup cool off quicker – or slower – than in a small cup? I thought previously that the greater area in the larger teacup would cause a quicker cool-off than the small area of a smaller teacup. However, the volume is also larger, so how does that effect the cool-off?

One possible alternative is to consider the growth of area versus volume. Since area grows by O(n^2), but volume grows by O(n^3), it might seem that the larger the container, the more energy that needs to irradiate through a smaller area. In general, this theory holds with for instance animals – mice needs to eat much more often than elephants, because they have a much larger skin surface compared to their volume. An elephant the size of a mouse would die – it would never be able to feed itself quickly enough the replace the heat loss through the skin.

So, the following experiment was set up. Hot water at a starting temperature of 96 C was poured into different containers:

• Cup A – a small, paper cup for holding “Glögg”. Diameter 6cm, 1x water content.
• Cup B – a large McDonalds coffee mug (official McD size: “medium”). Diameter 9cm, 2x water content.
• Cup C – a medium-size ceramic coffee mug. Diameter 8cm, 1.3x water content.
• Cup D – a large (=tall) glass. Diameter 7cm, 2x water content.

Sample data was collected over 15 minutes using a steak thermometer. (Not the world’s most precise, mind you.)

The results are as follows (time is in UTC):

Surprisingly, the container that held its best was the McDonalds coffee mug. The water in the McDonalds mug was consistently hotter than in the others.

Not surprisingly, the small paper Glögg cup was a total failure – dropping down below the measurable 55 degrees Celsius on the steak thermometer, and had to be estimated to about 52.

Unfortunately, it seems that the data collected so far fails to support any conclusive theory. It seems to be largely dependent on the materials of the container, as well as “other factors”, not determined by this study.