Zeroth Law of Thermodynamics: The Thermal Equilibrium Law

The zeroth law of thermodynamics states that;

“If two bodies are in thermal equilibrium with a third body, they are in thermal equilibrium with each other as well”

The law of thermal equilibrium, the zeroth law is an important law in thermodynamics. Despite such importance, this law was not fully realized for soo long, until 1935, when Fowler and Guggenheim, wrote it as,

…..we introduce the postulate, “If two assemblies are each in thermal equilibrium with a third assembly, they are in thermal equilibrium with each other”……

The amazing part is that the rest of the thermodynamic laws (1st, 2nd, and 3rd) had reached rather an advanced stage till that time. With this law being the most basic one of all others, it could not be named as the fourth. That is why, it has an unusual name, the zeroth law of thermodynamics.

The journey of writing this law of thermodynamics started in 1871 when Maxwell stated, “All heat is of the same kind”. This law is an important mathematical approach for thermodynamics. It is sometimes also termed, the transitive relationship law.

Explanation of Zeroth Law of Thermodynamics

Let’s assume that there are three bodies A (iron), B (copper), and C (body of water). Now, if the iron block (body A) is in thermal equilibrium with that of the copper block (body B), and block iron block (body A) is also in thermal equilibrium with the body of water (body C), it is then essential for the copper block (body B) to be in same thermal equilibrium with the body of water (body C).

Thermal Equilibrium

Thermal equilibrium exists when the temperature of two bodies is the same. As ‘heat is the flow of energy from a body of higher temperature to a body of lower temperature, provided that the bodies are connected’. When this gradient balances out and no further transfer of heat energy takes place, this condition is termed thermal equilibrium.

If two bodies X and Y are in thermal equilibrium with a third body Z, the bodies X and Y are thus in thermal equilibrium with each other as well.

Transitive relationship 

The transitive relationship is a mathematical relationship, which says that;

The relationship between a homogeneous relation of R on the set X is transitive if all,

a,b,c ∈ X

Now, if

(a,b) ∈ R & (b,c) ∈ R

then it is essential that

(a,c) ∈ R

This statement of the zeroth law of equilibrium proves the transitive relationship between systems of chemical natures. Thermal equilibrium is a also transitive relationship. It means if body A is in thermal equilibrium with body B, and B is in thermal equilibrium with body C, then A becomes thermally in equilibrium with C.

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Significance of Zeroth Law of Thermodynamics

One of the most significant properties in thermodynamics of all, the thermal equilibrium principle is brought into light by the zeroth law of thermodynamics.

Although discovered late, this law is the fundamental basis of the first and second laws of thermodynamics.

Zeroth law of thermodynamics and the concept of temperature

Zeroth law of thermodynamics justifies the concept of temperature, and with that said, it also justifies the use of a thermometer.

Applications of Zeroth Law of Thermodynamics

The most important application of the zeroth law of thermodynamics is that it is the basic principle of the thermometer.

Suppose that, a glass capillary tube contains a uniform thermal coefficient conducting liquid such as mercury (Hg). When this capillary is brought into contact with let’s say a cup of tea, we can see that there is no physical relation between tea and mercury, but an indirect and a transitive relationship exists there. This is where the zeroth law of thermodynamics comes into play.

Example of zeroth law of thermodynamics - Tea in cup with thermometer - cross section

According to this figure, tea is in contact with the glass tube of the thermometer (in black), which is further in contact with liquid mercury (in red). It can easily be said that the tea and glass tube, being in direct contact, are in thermal equilibrium. The same case goes for the glass tube and mercury.

Now according to the above stated law, when a body is in thermal equilibrium with another body which happens to be in thermal equilibrium with a third body, the first and third bodies are also in thermal equilibrium.

So, the elevation, and if properly graduated, the temperature shown by mercury is in fact, the temperature of the tea.

The consequences of the Zeroth Law of Thermodynamics 

The consequences of the zeroth law of thermodynamics are that:

  • When hotter and colder objects are placed in thermal contact, they tend to be in thermal equilibrium and a transfer of heat takes place.
  • Two systems tend to be in thermal equilibrium if they are separated by a wall permeable to heat.
  • Symmetric or mutual equilibrium.
  • Transitive relationship.

Key Takeaway(s)

The zeroth law of thermodynamics based on experience is stated as;

“Two systems in thermal contact are not in complete equilibrium until and unless they have a thermal equilibrium, i.e. they have the same degree of hotness (the temperature).”

Concepts Berg

What is the importance of the zeroth law of thermodynamics?

Zeroth law of thermodynamics states that if two bodies are in thermal equilibrium with a third body then they are in thermal equilibrium with each other. Thermal equilibrium means the same temperature. When two bodies are in thermal equilibrium then there will be no heat transfer between them. So, the zeroth law of thermodynamics is used for temperature measurements. 

What is an example of the zeroth law of thermodynamics?

When a hot cup of tea and a cold glass of water are placed on the same table. Both have different temperatures. When they are brought in contact with each other, heat flows from a hot body to a cold body. After some time, both have the same temperature. We can say that they are now in thermal equilibrium with each other. This is an everyday example of the zeroth law of thermodynamics. 

How is the zeroth law of thermodynamics applied to thermometers?

Zeroth law of thermodynamics is used for the calibration and measurements from a thermometer. The thermometer is placed in contact with some object. This indirect relation between mercury (or any other such liquid) and the object whose temperature is to be measured, separated by a glass tube work as suggested by the zeroth law of thermodynamics. Details have been explained above.

How does a thermometer obeys the zeroth law of thermodynamics?

A thermometer obeys the zeroth law by being in thermal equilibrium with the object whose temperature is to be measured, with being in no direct relation.

What is the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created nor destroyed but it can be converted from one form into another. In other words, the energy of the universe is always constant.

What are the applications of the zeroth law of thermodynamics?

  • The Zeroth law of thermodynamics is used for temperature measurements by a thermometer. 
  • It is used to compare the temperature of different objects.
  • It is used to calibrate the thermometers.

Why is the zeroth law of thermodynamics called zeroth law? Why did they didn’t start counting from one?

This law came after the first and second law of thermodynamics but this is a most fundamental law than the other two. So, it was given the strange name, the zeroth law of thermodynamics.

Why is the zeroth law of thermodynamics called zeroth law instead of first?

The first and second laws of thermodynamics came first and the zeroth law of thermodynamics came after that. Fawler put forward the zeroth law and realized that thermal equilibrium had to be defined before the first law. So he gave this law named as zeroth law. 

What is the significance of the zeroth law of thermodynamics? Is it not trivial?

The zeroth law of thermodynamics is in no way trivial. It is required to validate the 1st and 2nd laws of thermodynamics. The first law and second law of thermodynamics are used to define the ordering of temperature while the zeroth law defines the equality of temperature.

What is Newton’s relation with zeroth law?

Newton had nothing to do with the zeroth law of thermodynamics. His laws somehow get involved in the study of thermodynamics, i.e. the relationship of gravity, gravitational constant, the relative action/reaction mechanism for the thermal equilibrium and its annulment, etc.

Is zeroth law of thermodynamics only valid for three objects?

No, it is valid for every object which is in equilibrium. It deals with thermal equilibrium and does not matter how many objects are present.

Reference books

  • ATKINS’ PHYSICAL CHEMISTRY (Eighth Edition) by Peter Atkins and Julio de Paula

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