# Zeroth Law of Thermodynamics: Thermal Equilibrium

### Zeroth Law of Thermodynamics:

Before the zeroth law of Thermodynamics was put forward, there had already existed 3 laws of Thermodynamics. These are:

Scientists came to a realization that these 3 sets of laws are incomplete with regards to temperature. They envisaged the need for a law that will introduce a formal definition of temperature.

Due to the nature and importance of this law, it needed to supersede the three existing laws. At that time, the three laws (named respectively as 1st, 2nd and 3rd laws of Thermodynamics) were already popular in the academic world. Since these three laws are widely known by their numbers, a numbering confusion came up.

An alternative of calling this new law 'the fourth law of Thermodynamics' wouldn't be ideal due to its position and importance. It was a scientist named Ralph Fowler who termed the new law 'Zeroth Law'. This was a naming caveat that has become popular to this very day.

The Zeroth Law of Thermodynamics states that if two separate bodies are in thermal equilibrium with another body, then they are also in equilibrium with each other. To better understand what the zeroth law meant, we need to comprehend what thermal equilibrium is. This is explained below:

• Two bodies 'A' and 'B' are said to be in thermal equilibrium if each body can transfer heat to each other when placed closed together but ended up not transferring any heat to each other.

This will imply that both bodies are at equal temperature.

Now, according to the zeroth law, assuming we have three bodies namely X, Y and Z. If X = Y and Z = Y, then X = Z.

From the above expression, it will be observed that: if X and Y are in thermal equilibrium and Z and Y are in thermal equilibrium, therefore, X and Z must be in thermal equilibrium too.

So we can see that according to the zeroth law, temperature is a quantity worth measuring.

When we put a pot of water on a cooking gas, we will notice the transfer of heat from the cooking gas to the pot and subsequently, the water. The water begins to get warm during this process.

As heat transfer continues, the water becomes warmer and eventually becomes hot. A point will be reached when the water starts to boil. Recall that the boiling boiling point of pure water is 100OC.

Thermal equilibrium for the pure water is reached at 100OC because the water cannot become hotter through boiling; instead, it evaporates as water vapour.

Although, temperature is not directly mentioned in the zeroth law, the law actually points us towards the existence of temperature as a quantity.

It can therefore be stated that temperature is the quantity that remains constant (the same) for all systems in thermal equilibrium.

The above explanations are summarized in the image below:  