Zeroth law of Thermodynamics

Introduction

Two systems are said to be in thermal equilibrium if they are capable of heat transfer, but they don’t. In other words, we can say that two systems are in a thermal equilibrium state when they do not transfer heat even when they are in a position to do so. For example, food kept in a refrigerator is in thermal equilibrium with the air of the fridge as no transfer of heat flows from one source (food) to another source (air). The zeroth law of thermodynamics states that the temperature is worth measuring because it can tell whether the heat will move or not between the objects. However, this will be true regardless of the interaction between the objects. For example, in the case of radiation, the two objects do not interact, but the heat energy is still evolved from the system to surroundings. The zeroth law of thermodynamics was first given by scientist Ralph H. Fowler. It is one of the most important laws out of the four laws of thermodynamics. It is interesting to know that the zeroth law of thermodynamics was developed much later than the other three laws of thermodynamics.

Thermal Equilibrium

When two different bodies having different temperatures are brought into proximity or in contact with each other, they attain a common temperature after some time. This process is known as thermal equilibrium. Systems are said to be in thermal equilibrium if they do not tend to transfer heat even if they are capable of doing so.

The temperature can be defined as the energy of molecules in a substance. When two objects of different temperatures are kept together, the fast-moving molecules of one material will collide with the slow-moving material of other molecules. It will lead to the spreading of heat energy until both the objects have the same temperature.

If a system is in thermodynamic equilibrium, then we can say that the system has minimized its thermodynamic potential. Helmholtz free energy measures the total amount of useful work that can be extracted from a system. the equation can be written as A = U – TS; where 

A is the Helmholtz free energy;

U is the internal energy;

T is the temperature; and

S is the entropy.

Define zeroth law of thermodynamics

It implies the temperature is an indicator of thermal equilibrium. It states that if a system is in equilibrium with two separate systems, then all three systems will be in equilibrium. To understand, consider an example of 3 bodies – A, B, and C. According to the law, if A is in equilibrium with B and C, then bodies B and C will also be in thermal equilibrium. 

This law was named so because all other laws were developed and named before this law. However, after the development of this law, it was found that this law is more useful than the previous ones and hence was named the zeroth law of thermodynamics.

Zeroth law of thermodynamics with respect to temperature:

Here, the temperature is a variable whose value remains the same for two systems in equilibrium. For example, if TA = TB and TA = TC then TB = TC.

Consider two conducting bodies with adiabatic borders kept next to each other, and the wall between them is conducting. So, if the temperature of Body A is higher than body B, then the heat is transferred from the hot body to the cold body. By this mechanism, the temperature of the two systems is maintained.

Now suppose that these two bodies are not in thermal equilibrium, the body A will vibrate more than body B due to the higher kinetic energy, and the molecules of both the bodies will interact with each other. A heat transfer will occur when the high kinetic energy molecules collide with molecules of lower kinetic energy and transfer the heat to them. The movement of kinetic energy is just to maintain the temperature of both systems. The heat transfer is ceased at this stage, and the temperatures become equal.

Zeroth Law of Thermodynamics Applications

• Thermometer: The thermometer is the most common application of the Zeroth law of thermodynamics. Using a mercury thermometer, the zeroth law can easily be demonstrated as the area of the tube is always fixed, and the mercury level changes according to the temperature. The variation between the height of mercury indicates temperature change. However, different types of thermometers are used to measure different quantities. For example, a constant gas volume thermometer is used to measure the pressure; a constant pressure gas thermometer is used to measure volume; the electrical resistance thermometer measures the resistance; mercury in a glass thermometer is used to measure the length.
• Glasses containing water of different temperatures: Another illustration can be simply made by demonstrating two glasses of water, one with cold water and the other with warm water. Both the glasses will attain room temperature to attain thermal equilibrium.

Conclusion:

The Zeroth law of thermodynamics is one of the most important laws of the four laws of thermodynamics. It is named so because it was developed later, after the development of the other three laws of thermodynamics. It was observed that this law was more applicable than the other laws. So it was named the zeroth law of thermodynamics. The zeroth laws imply that the temperature is a measure/indicator of thermal equilibrium.

It states that if two bodies are in thermal equilibrium with each other and one of them is in thermal equilibrium with any third body, then all the three bodies will be in thermal equilibrium with each other. Even if two bodies are not in contact with each other, the process of heat transfer occurs through radiation.