# Question about the 0th law of thermodynamics

• QuasarBoy543298
In summary, the equilibrium between systems A and C can be described by the equality PcVc = f(A1,..., An), while the equilibrium between systems B and C can be described by the equality PcVc = g(B1,...,Bk). The 0th law of thermodynamics states that if A and B are in equilibrium with C, then they are also in equilibrium with each other. However, different pairs of Pc and Vc can result in the same value of PcVc. This does not only apply to ideal gases, but to general systems as well. Another combination, such as PN, can also be used to describe equilibrium between A and B. A thorough explanation of this concept can be found in "
QuasarBoy543298
assume I have 3 systems a,b and c.
the equilibrium between a and c can be described by the equality PcVc = f(A1,..., An)
and the same for b and c - PcVc = g(B1,...,Bk).
why does the equality g(B1,..., Bk) = f(A1,..., An) describes an equilibrium between A and B?
the 0th law states that if A and B are in equilibrium with c **for the same value of the thermodynamics coordinates of C**
then they are in equilibrium with each other, but I can find different pairs of Pc and Vc that will result in the same value of PcVc.

Last edited by a moderator:
Isn’t PV proportional to T? So this just describes three systems with the same temperature.

I'm not talking about ideal gas but on general systems.
you can take another combination as well, such as PN, and the question stays the same.

A persuasive representation which – to my mind – addresses your question can be found in “The Principles of Chemical Equilibrium“ (see pages 9-13) by Kenneth Denbigh.
https://archive.org/details/ThePrinciplesOfChemicalEquilibrium/page/n30

## What is the 0th law of thermodynamics?

The 0th law of thermodynamics states that if two systems are in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other. This means that if two objects have the same temperature as a third object, then they also have the same temperature as each other.

## Why is it called the 0th law?

The 0th law is called as such because it was the last law of thermodynamics to be discovered and added to the other three laws. It was also considered the most fundamental law, and therefore given the designation of "zeroth."

## How does the 0th law relate to temperature?

The 0th law is directly related to temperature because it states that the concept of temperature is based on the idea of thermal equilibrium. When two systems are in thermal equilibrium, they have the same temperature. This allows for the measurement and comparison of temperatures between different systems.

## What are the practical applications of the 0th law?

The 0th law has many practical applications, including the use of thermometers to measure temperature, the design of heating and cooling systems, and the understanding of heat transfer in various processes. It also allows for the creation of temperature scales, such as Celsius and Fahrenheit, which are based on the concept of thermal equilibrium.

## Is the 0th law always true?

Yes, the 0th law is always true and is considered a fundamental law of thermodynamics. It has been extensively tested and has been found to hold true in all known cases. It is a crucial concept in the study of thermodynamics and is used to understand and predict the behavior of various systems.

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