Zeroth Law of Thermodynamics: Thermal Equilibrium, Applications

There are four laws of thermodynamics, namely, Zeroth Law of Thermodynamics, the First Law of Thermodynamics, the Second Law of Thermodynamics, and the Third Law of Thermodynamics. The zeroth law was formulated by Ralph H. Fowler. It is important to note that the zeroth law was developed after the 3 laws of thermodynamics.

The Zeroth Law of Thermodynamics states that when two bodies are in thermal equilibrium with a third body, then this indicates that the two bodies are also in equilibrium with each other. Furthermore, the zeroth law is important as it establishes temperature to be a fundamental and measurable property of matter. Let us know more about Zeroth Law of Thermodynamics in this article. Continue reading to know more!

Zeroth Law of Thermodynamics: Overview

According to the Zeroth Law of Thermodynamics, when two bodies are each in thermal equilibrium with a third body, then this means that the two bodies are also in equilibrium with each other. Two bodies are said to be in thermal equilibrium when they are brought into contact with each other and separated by a permeable barrier to heat; we will not observe any heat transfer from one body to the other. This essentially means that the two bodies are at the same temperature. The most significant part of the Zeroth Law is that it establishes temperature to be a fundamental and measurable property of matter.

Thus, the systems are in thermal equilibrium if they do not transfer heat, even while they can do so, based on other factors surrounding them. For example, fruits kept in the fridge overnight are in thermal equilibrium with the air in the fridge: heat no longer flows from one source (the fruits) to the other source (the air) or back. But if the fruits are kept outside, there will be heat transfer between the outside air and the fruits. Zeroth law of thermodynamics holds even between those bodies in which the heat transfer occurs through radiation, i.e. the bodies are not in physical contact with each other.

Formally the Zeroth Law of Thermodynamics can be stated as:
Consider three systems \(A,\,B,\) and \(C\). Let the systems \(A\) and \(C\) be in thermal equilibrium. Separately, systems \(A\) and \(B\) are in thermal equilibrium; then zeroth law establishes that systems \(B\) and \(C\) will also be in thermal equilibrium.
Although the temperature is not mentioned explicitly, the formulation of this law necessitated a physical quantity that would be the same for all systems in thermal equilibrium. Thus, the temperature was established.

Visualising the Zeroth Law

It is imminent that we understand why this law was required. Consider that you have two separate systems, \(A\) and \(B\). An adiabatic wall (which will not allow the flow of heat) separates the two systems. Each system is separately in contact with a third system \(C\), via a conducting wall (which will allow the flow of heat). Across the conducting wall, heat exchange will occur between systems \(A\) and \(C\) and the system \(B\) and \(C\) until both \(A\) and \(B\) independently achieve thermal equilibrium with the system \(C\).

Now, replace the adiabatic wall between \(A\) and \(B\) with a conducting wall and the conducting wall between \(A\) and \(C\) and \(B\) and \(C\) with an adiabatic wall. Thus, system \(C\) is insulated from systems \(A\) and \(B\) while these two systems are in thermal contact. It is observed that no change takes place between the states of the system \(A\) and \(B\) implying that the two systems are already in thermal equilibrium. This result led to the formation of the Zeroth law of thermodynamics. This law states that ‘two systems, individually in thermal equilibrium with a third system, are in thermal equilibrium with each other too’.

Formulated by R.H. Fowler in 1931, the zeroth law was established after the first and second laws. But since its importance superseded the other two, it was numbered as the zeroth law.
The observations made from this law suggested that there must be a physical quantity that remains constant when the two systems are at thermal equilibrium. That physical quantity was later named “Temperature”.
That means, when system \(A\) and \(B\) and separately in thermal equilibrium with system \(C\), then:
\(T_A = T_C\) and \(T_B = T_C\)
Or, \(T_A = T_B\)
Where, \(T_A,\,T_B\) and \(T_C\) are respectively the temperatures of systems \(A,\,B\) and \(C\).

What is Thermal Equilibrium?

Temperature is one important variable that differentiates thermodynamics from other branches of science. Suppose a cup of water is kept in a fridge, and an identical cup of water is heated in a microwave. What is the key difference between the two cups? Their temperature. What will happen if the two cups are now kept in the open? Heat exchange will take place between the cups and their surroundings until the cups achieve their surroundings’ temperature. At this condition, when the temperature of the two bodies in contact becomes equal, the two bodies are said to be in thermal equilibrium.

Thus, thermal equilibrium is attained when two bodies in thermal contact no longer exchange heat energy with each other. To understand it better, take two thermodynamic bodies, \(A\) and \(B\) and consider the following cases:

Case 1: When two bodies \(A\) and \(B\), are connected with an insulating or adiabatic wall. If the pressure, volume and temperature of the two bodies \(A\) and \(B\), be \(P_1,\,V_1,\,T_1\) and \(P_2,\,V_2,\,T_2\) respectively. The pressure and volume of the two bodies remain unchanged over time. Since the wall between the two bodies is not conducting thus, there will not be any heat transfer between the two. The temperature of the two bodies remains different and unchanged. Thus, no heat exchange occurred between the two bodies; hence, the two thermodynamic bodies are not in equilibrium.

Case 2: When a conducting wall now separates the two bodies \(A\) and \(B\) and like the previous case, If the pressure, volume and temperature of the two bodies \(A\) and \(B\) be \(P_1,\,V_1,\,T_1\) and \(P_2,\,V_2,\,T_2\) respectively. Here, the pressure and volume of the two bodies vary. But over time, heat exchange takes place between these two thermodynamic bodies. After some time, the heat exchange stops and the temperatures of the two bodies become constant; let it be \(T\). At this point, the bodies are said to be in thermal equilibrium.

In conclusion, thermal equilibrium is achieved when a hot and cold body brought in contact across a conducting wall attain a constant temperature after the exchange of heat energy between them.

Relation Between 0th Law of Thermodynamics and Temperature

Let us look at the relation between 0th law of thermodynamics and temperature:

• The temperature of a body is a thermodynamic variable that determines the degree of hotness or coldness of a surface.
• A hot object is an object at a higher temperature, while a cold object is at a lower temperature. Temperature is a relative quantity, and we know that thermal equilibrium is achieved when two bodies in contact reach a constant temperature.
• The transfer of heat takes place from a hot object to a colder object, or in simple words, hot objects lose heat energy while cold objects gain heat energy.
• When this exchange of heat energy between two bodies placed in thermal contact, ceases; the bodies achieve a constant temperature and, thus, thermal equilibrium.

Applications of Zeroth Law of Thermodynamics

Let us look at some of the applications of zeroth law of thermodynamics:

1. A cup of hot tea, when left open, cools eventually. Tea loses its heat to the surroundings. Eventually, it attains thermal equilibrium when the temperature of surroundings becomes equal to the temperature of the tea, as suggested by the zeroth law of thermodynamics.

2. Mercury thermometer works on the zeroth law of thermodynamics. The mercury in the tube expands, and the height of the mercury level increases as the thermometer is placed over a hot surface, indicating the increased temperature.
3. A cold glass of water eventually cools down.
4. Fruits and vegetables kept inside the refrigerator achieve the fridge’s temperature when kept inside over a long time.

Summary About Zeroth Law of Thermodynamics

According to the Zeroth Law of Thermodynamics, when two bodies are each in thermal equilibrium with a third body, then this means that the two bodies are also in equilibrium with each other. Zeroth law of thermodynamics defines temperature. This law establishes that temperature is worth measuring because it will decide if the heat exchange will occur between objects. That means, when system \(A\) and \(B\) and separately in thermal equilibrium with system \(C\), then:
\(T_A = T_C\) and \(T_B = T_C\)
Or, \(T_A = T_B\)
Where \(T_A,\,T_B\) and \(T_C\) are respectively the temperatures of systems \(A,\,B\) and \(C\).

FAQs on Zeroth Law of Thermodynamics

Let us look at some of the interesting frequently asked questions about zeroth law of thermodynamics:

Q.1. State the 4 laws of thermodynamics.
Ans: The four laws of thermodynamics are as follows:
1. Zeroth Law of Thermodynamics
2. First Law of Thermodynamics
3. Second Law of Thermodynamics
4. Third Law of Thermodynamics

Q.2. What is the zeroth law of thermodynamics?
Ans: This law states that when two thermodynamic bodies are separately in thermal equilibrium with a third body, the two bodies will also be in thermal equilibrium with each other.

Q.3. What is temperature?
Ans: Temperature is a thermodynamic variable that expresses the degree of hotness and coldness of a body.

Q.4. What is thermal equilibrium?
Ans: Thermal equilibrium is attained between two thermodynamic bodies when there is no transfer of heat energy between them, i.e. they reach a constant temperature.

Q.5. What happens when two bodies attain thermal equilibrium?
Ans: Their temperature becomes equal.

Q.6. Who gave the Zeroth law of thermodynamics?
Ans: R.H fowler gave the zeroth law of thermodynamics.

Q.7. When was the zeroth law of thermodynamics formulated?
Ans: The zeroth law of thermodynamics was formulated by R.H. Fowler in 1931. It was established after the first and second laws of thermodynamics.

We hope this detailed article on Zeroth Law of Thermodynamics helps you in your preparation. If you get stuck do let us know in the comments section below and we will get back to you at the earliest.