3 Basic Concepts (Zeroth Law)

There are a bunch of basic notions that are often lumped together and called the zeroth law of thermodynamics. These notions are incomparably less fundamental than the notion of energy (the first law) and entropy (the second law), so despite its name, the zeroth law doesn’t deserve priority.

We can divide the world into some number of regions that are disjoint from each other.

If there are only two regions, some people like to call one of them “the” system and call the other “the” environment, but usually it is better to consider all regions on an equal footing. Regions are sometimes called systems, or subsystems, or zones, or parcels. They are sometimes called objects, especially when they are relatively simple.

There is such a thing as thermal equilibrium.

You must not assume that everything is in thermal equilibrium. Thermodynamics and indeed life itself depend on the fact that some regions are out of equilibrium with other regions.

There is such a thing as temperature.

There are innumerable important examples of systems that lack a well-defined temperature, such as the three-state laser discussed in section 11.4.

Whenever any two systems are in equilibrium with each other, and they each have a well-defined temperature, then the two temperatures are the same. See section 10.1 and chapter 23.

This is true and important. (To be precise, we should say they have the same average temperature, since there will be fluctuations, which may be significant for very small systems.)

Equilibrium is transitive. That is, if A is in equilibrium with B and B is in equilibrium with C, then A is in equilibrium with C. See chapter 23.

This not always true. To understand how it sometimes goes wrong, we must keep in mind that there are different types of equilibrium. If A equilibrates with B by exchange of electrons and B equilibrates with C by exchange of ions, interesting things can happen. In particular, we can build a battery. When the battery is sitting there open-circuited, all of the components are essentially in equilibrium ... local pairwise equilibrium ... but the two terminals are not in equilibrium, as you will discover if you wire up a load.

We can establish equilibrium within a system, and equilibrium between selected pairs of systems, without establishing equilibrium between all systems.

This is an entirely nontrivial statement. Sometimes it takes a good bit of engineering to keep some pairs near equilibrium and other pairs far from equilibrium. See section 11.11.

If/when we have established equilibrium within a system, a few variables suffice to entirely describe the thermodynamic state (i.e. macrostate) of the system.¹ (See section 2.7 and section 12.1 for a discussion of microstate versus macrostate.)

This is an entirely nontrivial statement, and to make it useful you have to be cagey about what variables you choose; for instance:

Knowing the temperature and pressure of a parcel of ice gives you more-or-less a complete description of the thermodynamic state of the ice.
Knowing the temperature and pressure of a parcel of liquid water gives you more-or-less a complete description of the thermodynamic state of the water.
Meanwhile, in contrast, knowing the temperature and pressure of an ice/water mixture does not fully determine the thermodynamic state, because you don’t know what fraction is ice and what fraction is water.

In addition to all these thermo-related concepts, we must also comply with all the “non-thermal” laws of physics, including conservation of momentum, conservation of charge, et cetera. This is discussed in chapter 5.

Some thermo books recombine ideas in such a way that this assertion becomes part of the first law. That comes to the same thing; I don’t much care what you call things. Most books just gloss over this point entirely, which is unfortunate.