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# The zeroth law of thermodynamics and basic definitions

A thorough, lightweight introduction to the basic concepts along with an overview of the universal zeroth law of thermodynamics.

Thermodynamics is a major branch of physics that studies the properties of and relationships between temperature, energy, heat and work involved in a system. While the field itself is vast and employed in a number of areas, it helps to start traditionally with a simplified overview of what we talk about when we talk about thermodynamics and the three basic laws that govern all of thermodynamics.

# A statistical briefing

The term itself stems from thermo and dynamics meaning the movement of heat, which is studied in terms of the temperature and work done and the energies involved. That said, it is worth noting that thermodynamics is a lot more complex than it appears at first and the initial idea to confront is less thermal and more statistical.

Any body in the universe is made of a large number of atoms and molecules. The object as we look at it is the bigger picture, the net result of a lot of thinner actions occurring at a molecular level. While one molecule may move leftwards, for instance, the object will still move right if a majority of its other molecules move rightwards.

That is to say, studying the one molecule rarely gives us the correct idea of how an object, or system, may act. What we need instead, is an integration of all movements exhibited by the molecules or atoms, or — to state it simply — the total effect of each atom or molecule’s contribution towards the final status of a system.

Similarly, thermodynamics is an integration $not the mathematical kind, strictly speaking$ of vibrational and translational energies exhibited by molecules. What we study as thermodynamics, in other words, is the net picture of the system as a whole. We do this by understanding everything at the molecular level, but by observing and understanding the effects on the larger scale with the system as a whole.

We will see this in complete detail when we discuss the second law of thermodynamics.

# Definitions

Everywhere in thermodynamics are used a set of words, recurring, and it helps to know what they mean.

## System

#### A System is a definite portion of the universe considered for study.

Remember that a system is defined by the user: it can be you, a tortoise, the head of a pin or the solar system itself, depending on whose properties you need to study and what you feel is convenient.

Systems come in three types:

## Variables

#### Thermodynamic variables are those properties of a system which help us describe the system itself.

Common ones include temperature, volume, pressure and entropy $which we will talk about in the second law$.

Heat is generated by the vibration of molecules in a body or system. The average $kinetic$ energy of these vibrations is measured as a property known as temperature, which is often simply stated $albeit not entirely correctly$ as the measure of heat. Note how we start to find molecular and net pictures $statistical pictures$ appearing already.

Volume and pressure retain their universal definitions as in other fields.

These are also called state variables. More complex ones include Gibbs’ free energy, enthalpy, Helmholtz free energy and so on, all of which we will discuss and define as needed so as not to make the subject overbearing right at the beginning.

Thermodynamic state variables are known as conjugate variables because they are almost always defined in pairs. Defining a single variable $for example, pressure alone$ is quite useless; but defining multiple conjugate variables can tell us almost everything we need to know about the system $for example, pressure and temperature$. This is because often, knowing at least two of these variables, most other state variables may be mathematically determined.

## Equilibrium

#### Equilibrium is a state of a system wherein its defining properties remain unchanged in time so long as external factors remain unchanged or the system remains isolated.

This, once again, comes in three types, mainly because general equilibrium is rather hard to achieve. Thermal equilibrium is a state without a temperature change across parts of the system; mechanical equilibrium is when no unbalanced forces exist; and chemical equilibrium, as its name suggests, is a state where reactant and product concentrations are unchanged with time.

## Intensive and extensive properties

All of the state variables we have seen can be classified into two types: intensive and extensive variables. Extensive variables are additive, intensive variables are not.

Temperature and pressure, for instance, are intensive because the temperature $or pressure$ of a whole system is not the sum of its temperatures $or pressures$ in select portions.

Mass and volume are extensive because the total mass $or volume$ of a system may be defined as a sum of the masses $or volumes$ of arbitrarily divided parts of the system.

## Processes

When a system goes from an equilibrium condition under certain parametric values to another equilibrium condition defined by certain other parametric values, it is said to undergo a process.

The simplest example of this can be an object being heated from room temperature $one configuration$ to some, say, $a second configuration$. Processes can be, and often are, more complex with many state variables changing during the process path.

Once again, we classify these processes into three types: isothermal processes occur at a constant temperature, isobaric processes at a constant pressure, and isochoric processes at a constant volume. Isochoric processes are also called isometric processes.

The zeroth law of thermodynamics may seem obvious but is extremely fundamental
[Image courtesy: Onkel Tuca at da.wikipedia $Own work$ [Public domain], via Wikimedia Commons]

# The zeroth law of thermodynamics

Having defined all the basic definitions in thermodynamics, we can proceed to the so-called zeroth law. This is a simple, almost obvious law $which does not have to be obvious, if you think about it deeply$ which sets the stage for all of thermodynamics.

Although this law is so fundamental, it was not the first to be stated academically; it was formalised into a law only when we realised that all other existing laws actually take this for granted and would break down if it was not true.

#### If two systems are each separately in thermal equilibrium with a third, then all three systems are in thermal equilibrium with one another.

In their 1935 book, A treatise on heat, M.N. Saha and B.N. Srivastava state a form of this law which then led to Ralph Fowler and Edward Guggenheim giving it the name, “zeroth law”. This concept, of course, had been discussed since long before 1935 — only the formal label for this law arose then.

Around 1871, Maxwell had already discussed  this idea crudely; he stated, “all heat is of the same kind”. In addition, this law may be stated as A → B : B → C :: A → C form instead of the A → C : B → C :: A → B form stated above. Try it yourself.

In the next article in this series, we take a look at the first law of thermodynamics, its implications and drawbacks.

Cover image by Jenny Downing.

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V.H. Belvadi is a physics postgraduate specialising in solid-state physics and also interested in astroparticle physics. When he is free he makes photographs and short films, writes on his personal website, makes music, reads voraciously, or plays his violin.