Zeroth Law of Thermodynamics a Very Important Concept

Zeroth Law of Thermodynamics

The zeroth law of thermodynamics establishes the concept of temperature by introducing the term “thermodynamic equilibrium”. It says:

“If two bodies are in thermal equilibrium each with a third body, then they are also in thermal equilibrium with each other”. By mere looking at this concept one may say it is quite intuitive. What else could be true otherwise? If A is in thermal equilibrium with B, and B is in thermal equilibrium with C then A has to be in thermal equilibrium with C. But the zeroth law of thermodynamics doesn’t rely on mere intuition like maths neither does.

The above definition of the zeroth law of thermodynamics is the transitive property of the systems. The transitive property or relation in mathematics is:

“If a=b and b=c then a=c”.

But the real question is, doesn’t it happen all the time? The answer is no. There is also a relation in mathematics which we call “Intransitivity or antitransitivity”. Suppose we have a tournament and we are in a knockout stage. Team A has defeated team B, and Team B has defeated Team C. In this case we cannot say that Team A has also defeated team C. Both these teams might haven’t played with each other. This is an example of intransitive relation.

Zeroth Law of Thermodynamics and Temperature

We know that by establishing the concept of thermal equilibrium, we introduce a thermodynamic property “temperature” as well. Because, when we say that the two systems are in thermal equilibrium with each other an important question arises; What is the property that describes whether the two systems are in equilibrium or not? We call that property “temperature”. Since Sommerfeld and Fowler said, “every physical quantity has to have a numerical value” .i,e. we should be able to measure it. In the case of thermal equilibrium, they termed it as temperature. Thus they formulated their postulate as:

If for a particular system or a body, any of the physical property changes by the application of heat, it must be observed and utilised for the measurement of temperature“. Read more:

Temperature generally tells us about the degree of hotness or coldness of a body. It is a macroscopic property that tells us about the average kinetic energy of the molecules of a particular system.

Zeroth Law of Thermodynamics


To measure temperature, the zeroth law of thermodynamics enabled the scientist to develop a thermometer. A thermometer is usually a device that measures a specific property of a system that changes with temperature. The property that changes with the temperature could be the length, pressure, volume, resistance, electrical conductivity etc.

For example, a mercury glass tube is one of the widely used thermometers. The mercury is filled in a glass tube of a constant crosssection. The length of the entire tube is calibrated with respect to the temperature from 0 degrees (referenced to the freezing point of water) to 100 degrees (referenced to the boiling point of water).

Mercury expands and contracts with the rise and fall of the temperature respectively. The change, expansion or contraction of mercury is thus converted into the numerical value that is the visible scale on the glass tube.

There are several other types of thermometers such as Resistance Temperature Devices (RTDs), Thermocouples, Infrared thermometers etc.

Why do we call it the zeroth law of thermodynamics?

Saadi Carnot postulated the second law of thermodynamics in 1824 while he discussed the working of steam engines. After which Hermann Helholts and William Thompson came up with the first law in 1848. Since both these laws were firmly established prior to the naming or numbering of the Zeroth Law. But the scientists realized that the concept of thermal equilibrium was the most fundamental and essential. Peter Atkins calls zeroth law an afterthought in his famous book “Four Laws That Drive the Universe”.

But as the first and second laws were so embedded in our thoughts that an attempt to renumber them was impossible. So later in 1931 Sommerfeld and Fowler coined the term “Zeroth Law of Thermodynamics” to acknowledge its fundamentality.

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