Thermal equilibrium and the zeroth law

What is thermodynamics?

Narrated video. Transcript:

Put a pressure cooker on the stove. Heat flows in, the water boils, steam builds up, and the whistle is lifted. Heat has turned into work.

Thermodynamics is the branch of physics that deals with heat and temperature, and with the conversion of heat into other forms of energy, and back again.

It is a macroscopic science. It looks at a whole system, like the gas in a cylinder, and does not ask what each molecule is doing. That molecular picture is kinetic theory, in the next chapter.

Instead it uses a few measurable quantities called macroscopic variables: pressure, volume, temperature, mass and chemical composition.

The system is the part we study, such as the gas inside the cooker. Everything else that can exchange energy with it, the flame, the room, the air, is its surroundings.

Now watch a bullet fired from a gun. It flies very fast, but its temperature does not change because of that motion. The motion of the bullet as a whole is mechanics, not thermodynamics.

When the bullet hits a wooden block and stops, its ordered kinetic energy becomes the disordered jiggling of molecules. The bullet and the wood near it get hot.

So temperature is linked to the random internal motion of the molecules, not to the motion of the body as a whole. Keep this idea in mind for the whole chapter.

Thermal equilibrium and the zeroth law

Narrated video. Transcript:

In mechanics, a body is in equilibrium when the net force on it is zero. In thermodynamics, a system is in equilibrium when its macroscopic variables do not change with time.

Take a gas sealed in a rigid, insulated container. Left alone, its pressure, volume, temperature and composition stay fixed. It is in thermodynamic equilibrium.

Now a spark ignites a mixture of petrol vapour and air in a cylinder. The temperature and pressure jump and keep changing. The system is not in equilibrium until it settles into a new steady state.

Bring two systems A and B together, separated by a wall. If the wall is an insulator, like thick wood or thermocol, nothing happens. This is called an adiabatic wall.

Replace it with a conducting wall, like a thin copper sheet. This is called a diathermic wall. Energy flows from the hotter system to the colder one as heat, and their states change.

The flow stops when the states no longer change. A and B are then in thermal equilibrium with each other.

Now the key experiment. A and B are separated by an adiabatic wall, but each touches a third system C through a conducting wall. Wait until A and C, and B and C, are each in equilibrium.

Now make the wall between A and B conducting. Watch carefully. No heat flows at all. A and B are already in thermal equilibrium with each other.

This is the zeroth law of thermodynamics: two systems in thermal equilibrium with a third system separately are in thermal equilibrium with each other. R. H. Fowler named it in 1931, after the first and second laws were already numbered.

So there must be a quantity that is equal for systems in thermal equilibrium. That quantity is temperature. The third body C is just a thermometer: when it reads the same for A and B, they are at the same temperature.

Try it: three bodies and their walls

Interactive simulation. Things to try:

• Press Start (or Space). A and B exchange heat only through C, so both settle at C’s final temperature.
• Once all three match, tap the A–B wall to make it conducting. The heat flow across it stays at 0 W.
• Make every wall adiabatic and nothing changes: the bodies keep their own temperatures.
• A bigger heat capacity for C means C’s temperature hardly moves. That is why a good thermometer is small compared with what it measures.

Is heat flowing?

A thermometer reads 36 °C when kept in contact with body P, and also 36 °C when kept in contact with body Q. P and Q are now placed in contact through a copper sheet. What happens?

1. Heat flows from the larger body to the smaller one
2. No net heat flows between P and Q
3. Heat flows from the body with more internal energy
4. We cannot say without knowing their masses

Where do they settle?

Body A (heat capacity 1 kJ/K) at 80 °C is placed in contact with body C (heat capacity 2 kJ/K) at 20 °C through a conducting wall. Everything else is insulated. What is their common final temperature?

1. 30 °C
2. 40 °C
3. 50 °C
4. 60 °C

Summary

• Thermodynamic equilibrium: p, V, T, mass, composition do not change with time
• Zeroth law: A ~ C and B ~ C ⇒ A ~ B
• Thermal equilibrium: T_A = T_B

• Thermodynamics is a macroscopic science: it describes a system by p, V, T, mass and composition, not by individual molecules.
• Temperature is linked to the internal, disordered motion of molecules, not to the motion of the body as a whole.
• An adiabatic wall stops heat flow; a diathermic (conducting) wall allows it.
• Zeroth law: two systems each in thermal equilibrium with a third are in thermal equilibrium with each other.
• The zeroth law gives meaning to temperature: systems in thermal equilibrium have the same temperature, and a thermometer is the “third system”.