Introduction to Thermodynamics

The physics of heat, energy, and why time runs one way

Thermodynamics is the branch of physics that deals with heat, energy, and how they move. It grew out of a very practical question in the 1800s — how to build better steam engines — but it turned out to contain some of the deepest laws in all of science. Thermodynamics governs car engines, refrigerators, power stations, weather, stars, and even why your cup of tea cools down but never spontaneously heats up. It is also the only branch of physics that tells us why time only runs forward.

Heat is not the same as temperature

Before the laws, we must clear up a common confusion. Temperature and heat are different things.

• Temperature is a measure of the average kinetic energy of the particles in a substance. Faster-jiggling particles mean a higher temperature. It is measured in degrees Celsius or in kelvin (K).
• Heat is energy transferred from one object to another because of a temperature difference. It is measured in joules (J).

A swimming pool of warm water contains far more total thermal energy than a cup of boiling water, simply because it has so many more particles — yet the cup is at a higher temperature. Heat is the flow; temperature is the level. For more on how that energy actually moves between objects, see heat and how it travels.

Internal energy

Every object stores internal energy — the total kinetic and potential energy of all its jiggling, vibrating particles. The hotter an object, the faster its particles move and the greater its internal energy. Thermodynamics is essentially the study of how this internal energy changes when heat flows in or out and when the object does work on its surroundings.

There are only two ways to change a system's internal energy:

1. Heating or cooling it (transferring heat).
2. Doing work on it or letting it do work (for example, a gas pushing a piston).

The first law of thermodynamics

The first law is simply the conservation of energy applied to heat and work:

ΔU = Q − W

where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. In words: the internal energy of a system rises by however much heat you put in, minus however much work it does pushing on the outside world.

Energy is never created or destroyed — it only changes form or moves around. If you heat a gas in a cylinder (Q is positive) and it expands to push a piston (W is positive), its internal energy may rise, fall, or stay the same depending on the balance. This is the same conservation principle that governs all of physics, explored more broadly in energy, work, and power.

Worked example. You add 500 J of heat to a gas, and the gas does 200 J of work pushing a piston outward. What is the change in its internal energy?

ΔU = Q − W = 500 − 200 = +300 J

The gas keeps 300 J as extra internal energy (it gets hotter) and spends 200 J doing useful work.

The second law of thermodynamics

The first law says energy is conserved — but it does not say which direction processes go. A smashed cup never reassembles, and a cold drink never warms your hand to make itself colder, even though energy would be conserved in both cases. The second law explains the one-way street of nature:

Heat flows naturally from hot to cold, never the reverse on its own. Equivalently: the total entropy of an isolated system always increases.

Entropy is a measure of disorder, or how spread out energy is. A neat, concentrated arrangement of energy (a hot object beside a cold one) has low entropy; once the heat has spread out evenly (everything lukewarm), the entropy is high. Nature relentlessly moves toward higher entropy because spread-out, disordered states are overwhelmingly more probable than neat, ordered ones.

This is profound. The reason you can tell a video of a smashing glass is being played forwards rather than backwards is entropy increasing. The second law gives time its "arrow".

You can make something more ordered locally — a freezer makes ice, your body builds ordered cells — but only by dumping even more disorder (waste heat) into the surroundings. The total entropy of the universe still goes up.

Heat engines and why nothing is perfect

A heat engine is any device that converts heat into useful work — a car engine, a jet, a power-station turbine. It works by taking heat from a hot source, converting some of it into work, and rejecting the rest to a cold sink.

The second law imposes a hard limit: some heat must always be thrown away to the cold reservoir. You can never turn all the heat into work. This is why no engine can be 100% efficient — not because engineers are careless, but because the laws of physics forbid it. A typical petrol car engine converts only about 25–30% of its fuel's energy into motion; the rest leaves as waste heat through the exhaust and radiator.

Efficiency is the fraction of input heat that becomes useful work. The best possible efficiency depends on the temperatures of the hot and cold reservoirs: the bigger the temperature gap, the more work you can extract. This is why power stations use very high-pressure, high-temperature steam.

Why thermodynamics matters

These laws are not just for engineers. They tell us why our Sun shines (and will eventually fade), why life needs a constant flow of energy to stay ordered, and why a perpetual-motion machine — one that runs forever creating free energy — is impossible. Every claim of a machine that beats the first or second law has always turned out to be wrong, and thermodynamics tells us it always will be.

Try it yourself! 🧪

Experiment 1 — Watch entropy spread. Fill a clear glass with water and let it go perfectly still. Gently add a single drop of food colouring without stirring. Watch over the next few minutes: the colour slowly spreads until it is evenly mixed. This is entropy increasing in real time — the dye molecules disperse from a concentrated (low-entropy) state to a spread-out (high-entropy) one all by themselves. And crucially, you will never see the dye spontaneously gather back into a single drop. That one-way behaviour is the second law.

Experiment 2 — Feel heat flow one way. Hold a metal spoon and place its bowl in a mug of hot water. After a minute the handle feels warm — heat has flowed from the hot water, up the spoon, toward your cooler hand. It flows hot to cold, never cold to hot. Now warm your hands on the mug: the heat enters your hands, never the reverse. You are feeling the second law of thermodynamics directly.