# Zeroth Law of Thermodynamics

## State the Zeroth Law of Thermodynamics

Zeroth law of thermodynamics tells us the concept of temperature. This law states that if two bodies are each in thermal equilibrium with a third one, then they are in thermal equilibrium with each other. So, what is thermal equilibrium?

Consider an isolated body filled with a gas, insulated with a boundary from its surroundings under an adiabatic process (a process where no heat transfer takes place).

Since no heat transfer takes place between the body and the surroundings, and all the macroscopic properties of the body, i.e., P, V, T, M, n remain constant.

Therefore, we can say that it is in thermal equilibrium with its surroundings, and the body has become an isolated system.

### Concept of Thermal Equilibrium

Consider two thermodynamic systems; both filled with gas are kept in an adiabatic environment, as shown below:

Let’s say one system is A with parameters pressure P1, volume V1, and temperature T1, another system is B with parameters P2, V2, T2.

Here, you can see these two systems are in contact with each other, and they are in thermal equilibrium even when their temperatures are different, i.e., T1 and T2. This happens because the boundary around these bodies is adiabatic.

This is the basic concept applied in this law, but if you want to understand what zeroth law exactly is, let’s move on to its explanation.

### Explain Zeroth Law of Thermodynamics

Suppose two bodies that are in contact with each other are kept inside an adiabatic boundary, and the wall between the two bodies is also adiabatic.

Consider two bodies A and B having a fluid inside them. The pressure,  volume, and temperature for body A and B be Pa, Va, Ta, and Pb, Vb, Tb, respectively.

Since no heat transfer takes place, i.e., in thermal equilibrium even if the temperatures T1 and T2 are different. This is exactly the zeroth law of thermodynamics.

So, if you are asked, can two bodies with different temperatures be in thermal equilibrium?

Your answer will be yes because the bodies are kept in an adiabatic frame. Therefore, their state remains constant.

### Application of Zeroth Law of Thermodynamics

Zeroth law is used for comparing the temperature of different objects. For getting an accurate temperature, we take a reference body and check certain characteristics that change in it.

Let’s understand the zeroth law of thermodynamics with the concept of temperature.

Consider two conducting bodies kept side-by-side, the boundary of these bodies is adiabatic. However, the wall between these two bodies is a conducting wall or a diathermic wall.

Let’s say fluid is kept in container A with pressure, volume, and temperature as Pa, Va, Ta, and the other body also have fluid with properties as Pb, Vb, Tb.

Assume the temperature of body A is greater than that of body B (Ta > Tb), so the heat flow occurs from the body of high temperature to the body of lower temperature. This is what happens in two conducting bodies with varying temperatures when kept in contact with each other, as you can see in the image above.

So, at present, these two bodies are not in thermal equilibrium; what happens is that the molecules of body A vibrate a lot because of higher kinetic energy, that the molecules of both the bodies interact with each other. Now, molecules with high kinetic energy hit the molecules with lower kinetic energy and transfer their energy to them, this is how heat transfer takes place.

Now, a time comes when their kinetic energies become equal. This means that the temperature also becomes equal, i.e., Ta = Tb. Now, heat transfer stops.

The state of these two bodies change, but after this change, no further change will occur. Therefore, the two bodies are in thermal equilibrium. This is the zeroth law of thermodynamics.

### Zeroth Law of Thermodynamics

Consider three bodies, A, B, and C, that is in contact with each other, as shown below:

Here, the bodies A and B are inside an adiabatic environment, while the wall between C and AB is conducting.

The zeroth law of thermodynamics follows the transitive relationship between three bodies in contact, as we saw in the set theory of mathematics that if two systems, i.e., after some time two bodies A and C will come in thermal equilibrium, and B and C also achieves thermal equilibrium, then the systems A and B should be in thermal equilibrium with each other.

But, the states of two bodies A and B remain constant as they are in the adiabatic boundary. However, they also come in thermal equilibrium.

This is the zeroth law of thermodynamics.

Q1: Write an Example of the Zeroth Law of Thermodynamics.

Ans: Consider a cup of hot water, and measure its temperature with the help of a thermometer. After some time, the thermometer reads 98°C. This is the stage when the water inside the cup and the thermometer show equal temperature, i.e., they are in thermal equilibrium with each other.

Q2: Why do we Study the Zeroth Law Before the First and the Second Law of Thermodynamics?

Ans: Zeroth law discusses the concept of temperature, which is fundamental to the first and the second law of thermodynamics. Therefore, the zeroth law establishes temperature as a valid concept. That’s why we study the zeroth law before these two laws.

Q3: What is the Importance of the Zeroth Law of Thermodynamics?

Ans: Zeroth law is an important concept of temperature. This is used on a large scale in a place where we need an accurate measurement of the temperature of an object.

For example, to measure our body temperature, we use a thermometer as a reference body, then a time comes when its reading scale shows your temperature, which means the thermometer and your body temperature have achieved thermal equilibrium.

Q4: What is the Application of Thermodynamics?

Ans: The real-life applications of thermodynamics are:

1. The heat engine transforms heat into work.

2. Generators transform the mechanical energy they acquire from the source into the electrical energy.