# Zeroth Law of Thermodynamics and thermal equilibrium

This post is on Zeroth Law of Thermodynamics. To discuss this we will begin with a briefing on the definition of Thermodynamics and the concepts of Thermal Equilibrium in the context of Thermodynamics.

The Zeroth Law of Thermodynamics throws light on a major condition of thermal equilibrium among systems.

## Thermodynamics – define it

Thermodynamics is the branch of physics that deals with the concepts of heat and temperature and the inter-conversion of heat and the other forms of energy.

## What is the Equilibrium in Thermodynamics?

And Equilibrium in Thermodynamics is availed when the variables of the systems don’t change with time. For example, say a gas inside a closed rigid container is insulated from its surroundings. And as a result, say, its pressure, volume, temperature, mass, and composition remain unchanged. In this case, we can say that the gas has attained a state of equilibrium.

## Zeroth law of Thermodynamics – statement

This states that if two systems are in thermal equilibrium with a third system separately then they (the first 2 systems) are in thermal equilibrium with each other as well.

## Understanding Zeroth law of Thermodynamics with a 2 step process

Let’s discuss this in detail. We will a 2 step process to understand the basic concepts.

### Step 1: Thermal Equilibrium in Thermodynamics

Let’s take 3 systems, A, B, and C.

System A and System B are isolated by an adiabatic wall (no conduction of heat), but each of these A and B, is individually isolated to a 3rd system C by a conducting wall.

As time passes, after some time A will come to thermal equilibrium with C and similarly, system B will have the same equilibrium state with C separately.

Now, understanding the fact that thermal equilibrium means temperature equality, we can write the following equations, as per the above law stated:

Ta = Tc …………….. (1) and
Tb = Tc …………………….(2)
[ Ta, Tb, and Tc are the temperature of the systems A, B, and C respectively.]

### Step 2: Thermal Equilibrium in Thermodynamics

Now if we interchange the nature of the 2 walls, i.e. between A and B now the wall would be conducting and the other wall between C and the other 2 systems become adiabatic, then what is going to happen?

The wall separating C from others is adiabatic, there is no possible interaction with C. But there is ample scope of heat transfer now between A and B.

But, it is found that there is no further change of states for A and B. That means they are now in Thermal Equilibrium with each other.

That means as per the Zeroth Law of Thermodynamics, we can say, Ta = Tb.

### zeroth law of Thermodynamics: Summing up

So summing up the above 2 steps we can write,

If Ta = Tc …………….. (1) and
Tb = Tc …………………….(2)

then Ta = Tb …………(3) [ at thermal equilibrium].

Equation (3) above is showcasing the zeroth law of Thermodynamics which states if two systems are in thermal equilibrium with a third system separately then the first 2 systems are in thermal equilibrium with each other as well.

## Interesting Related Post:

First Law of Thermodynamics

Thermal Conductivity – definition, dimension, concepts, values

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