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Historically, why was it necessary to define the Zeroth Law of Thermodynamics after defining the other Laws? In our current understanding of science, the way we study it in schools, it seems obvious. So, what is so special about Zeroth Law? Why is it defined as a Law? What knowledge were we lacking without defining it? What was the need to define it?

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    $\begingroup$ In what way is en.wikipedia.org/wiki/Zeroth_law_of_thermodynamics#History deficient? $\endgroup$ – kimchi lover Dec 12 '19 at 17:23
  • $\begingroup$ Because we study it in schools it seems obvious??? Does studying something in schools make it cease to be a law? People wonder how it was established that all heat is of the same kind even today, just recently on this site for example, What is the history behind defining temperature as measure of hotness?. As can be seen from the link above, Fowler added the "zeroth law" to fill in a logical gap in a textbook's exposition of this point. $\endgroup$ – Conifold Dec 13 '19 at 1:16
  • $\begingroup$ @Conifold: you understood it wrong. I never said that whatever we study in school it's obvious. I said "the way" we study it in schools it seems obvious and there is a huge difference between them, which you fail to understand. in schools it is directly taught as the temperature between two bodies is same then they will be in thermal equilibrium and that is what is called zero of Thermodynamics and I think in teaching it like this we are missing a lot of details on the history of how it was developed and why it has certain importance. $\endgroup$ – Devansh Mittal Dec 13 '19 at 5:27
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If two unequal thermally insulated cylinders are connected with a pipe with a piston in it, then these two cylinders are said to be in "Mechanical Equilibrium" if the piston does not move and we conclude that the "Pressure" in both of them is same.

Similarly, if two bodies are brought in contact with each other and there is no exchange of heat between them then we say that these two bodies are in "Thermodynamic Equilibrium" and hence there must be a property which these bodies must be sharing analogous to "Pressure" by the virtue of which there is no exchange of heat in between them, and this property is defined by Zeroth Law of Thermodynamics as "Temperature". Zeroth Law of Thermodynamics defines the thermodynamic property - "Temperature".

The reason it is called Zeroth Law and not the first law because it was defined after having defined the First and Second Laws of Thermodynamics. By the time scientists felt the need for Zeroth Law of thermodynamics, the First and Second Laws had become so popular that it was not possible to change their names or numbering, so this law was defined as Zeroth Law.

It is worth noting down these different laws of thermodynamics define different thermodynamic properties.

Zeroth Law defines Temperature.

First Law defines Internal Energy and Energy Conservation.

The Second Law defines the idea of Entropy.

Third Law defines the idea of Zero Kelvin Temperature and also establishes that it cannot be achieved.

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Without the Zeroth Law it would not be possible to measure the temperature of objects or substances using another object, i.e. a "thermometer".

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