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Maths in a minute: Thermodynamics

Tea and nineteenth century physics

As I sadly drink my now-cold cup of tea, I can cheer myself up with the fascinating area of physics known as thermodynamics. Everyone knows that if you leave a hot cup of tea sitting on a table, or indeed leave any object in cooler surroundings, it will inevitably cool down. Thermodynamics, the theory of heat and heat flow, was developed mostly during the 19th century when it was discovered that temperature is a bulk property of molecules and atoms in motion. Atoms that move around fast, as they do in a hot cup of tea, produce a warm temperature. Colder temperatures come from atoms that move very little, as is the case in a rigidly frozen block of ice tea.

cup of tea

This cup of tea will soon be cold. Image: Petr Kratochvil, public domain.

An important concept in this context is that of entropy. This can again be illustrated using tea, which is made up of many, many molecules in random motion. We don't see those molecules, in fact, the tea would look much the same to us if we re-arranged them slightly. Loosely speaking, the entropy of the cup of tea counts the number of ways in which you could arrange the molecules that would leave the cup of tea looking the same macroscopically. It's defined in the same way for any other system made up of microscopic parts, and there even is a relatively simple formula that tells you how to calculate it. (You can find out more in our brief introduction Maths in a minute: Entropy.)

There are four fundamental laws of thermodynamics:

Zeroth law: If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other. (Two systems are in thermal equilibrium if, when they are connected by something that can transfer heat, there isn't any net flow of heat energy between them.)

First law: Energy cannot be created or destroyed. It can only change form or be transferred from one object to another.

Second law: The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. (You can read more about the second law and it's implications in our brief introduction Maths in a minute: The second law of thermodynamics.)

Third law: As temperature approaches absolute zero (the lowest theoretically possible temperature, -273.15 degrees celsius), the entropy of a system approaches a constant minimum.

Thermodynamics plays a part anywhere where temperature, heat, work and energy are involved, so it's not so surprising to see it plays a role in weather forecasting and the evolution of planets, moons and even black holes. But that is not all: Thermodynamics has also led to new ways to approach fundamental questions about understanding information, time and life.

You can read more about applications of thermodynamics on Plus.

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