Law Behind Thermal Equilibrium

There were already two laws of thermodynamics when the zeroth law or the thermal equilibrium law was conceived in the 18th century. According to OpenStax, an educational initiative maintained by Rice University, this new law, which offered a formal definition of temperature, actually replaced the prior regulations and should legitimately be at the top of the list. This presented a problem: the original statutes were well-known by their given numbers, and renumbering them would conflict with the existing material and generate significant confusion.

Ralph H. Fowler, a scientist, devised a solution to the problem. He stated the new law as the “zeroth law.” (1939, Cambridge University Press). The zeroth rule states that “the temperature of two systems is the only thing you need to know to tell which way heat will flow between them,” according to David McKee, a physics professor at Missouri Southern State University.

Let’s know more about this thermal equilibrium law! But before that, let’s discuss what thermal equilibrium is in thermodynamics!

Thermal Equilibrium In Thermodynamics

Thermal equilibrium in thermodynamics is an essential topic related to temperature. The term “thermal equilibrium” refers to a condition in which two things that can exchange heat maintain a steady temperature throughout time. Heat can be conveyed in various ways, including when two items are in direct contact or when heat is radiated from a source such as a lamp or the sun. If the overall temperature of two items changes over time, they are not in thermal equilibrium, but they can approach it if the hotter object transfers heat to the colder one.

Consider a colder object coming into contact with a hotter object, such as ice in a hot cup of coffee. The ice (later water) and the coffee will achieve a halfway temperature between the ice and the coffee after some time. Though the two objects were not in thermal equilibrium initially, they gradually approached—and eventually achieved—thermal equilibrium, the temperature that lies halfway between hot and cold.

Formula Of Thermal Equilibrium

Now that we have discussed thermal equilibrium in thermodynamics, let’s look at the formula of thermal equilibrium.

The thermodynamic potential (or a system) is minimised when it is in thermodynamic equilibrium. If an object is in thermodynamic equilibrium, it will also be in thermal equilibrium. One of several forms of thermodynamic potentials addressed in physics is the Helmholtz free energy, which reflects the total amount of usable work that might be taken from the system. The following is the Helmholtz free energy equation:

A = U – TS,

Where A = Helmholtz Free Energy (Joules, J)

U = Internal Energy (Joules, J)

T = Temperature (Kelvin, K)

S = Entropy (J/K)

The Thermal Equilibrium Law (Zeroth Law Of Thermodynamics)

Having understood the concept of thermal equilibrium in thermodynamics, it is important to go through the zeroth law of thermodynamics or the thermal equilibrium law.

One of the four laws of thermodynamics is the zeroth law, which states that if systems 1 and 2 are in thermal equilibrium with a system 3, this simply means that they are in thermal equilibrium with each other. This is, in simpler terms, the zeroth law of thermodynamics or the thermal equilibrium law.

The zeroth law, or the thermal equilibrium law, is a fundamental law in thermodynamics. Despite its importance, this law was not completely appreciated for a long time until Fowler and Guggenheim published it in 1935.

The incredible aspect is that the remainder of the thermodynamic laws (1st, 2nd, and 3rd) had already progressed to that point. This law could not be referred to as the fourth because it is the most fundamental. As a result, it is known as the zeroth law of thermodynamics.

“All heat is of the same kind,” Maxwell declared in 1871, which began the road of establishing this rule of thermodynamics. This is an essential thermodynamics mathematical approach. The transitive relationship law is another name for it.

This statement of the zeroth law of equilibrium demonstrates the transitive relationship between systems of chemical natures. Thermodynamic equilibrium is a transitive connection as well. It indicates that if body A is thermally in equilibrium with body B and B is in equilibrium with body C. Then A will be thermally in equilibrium with C. 

Conclusion

We have learned what exactly thermal equilibrium is in thermodynamics and the formula of thermal equilibrium. We also understood the law behind the concept of thermal equilibrium, i.e., the zeroth law of thermodynamics or the thermal equilibrium law. As per the zeroth law of thermodynamics, when two objects or systems are in the state of thermal equilibrium with a third object or system, they are considered to be in the state of thermal equilibrium.

When two bodies are brought into touch with one other and separated by a heat-permeable barrier, thermal equilibrium occurs, which means that no heat is transferred from one to the other. To put it another way, the zeroth law states that all three bodies have the same temperature.