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I have just recently started learning some very basic thermodynamics and there is one question that has been driving me crazy:

Why do we even need the Zeroth law of thermodynamics?

The law states:

If a body A, be in thermal equilibrium with two other bodies, B and C, then B and C are in thermal equilibrium with one another. (Wikipedia)

This seems like the most obvious statement ever. How could B and C not be in thermal equilibrium?

While looking for an answer I came across a Khan Academy video that deals with this exact question. The lecturer in the video says:

"...yeah our universe is like that but think about it a little harder, you could problably think of a universe where it might not be like that." (Video)

This just confused me even more. If we follow that logic wouldn't we have to formulate something like Newtons Zeroth Law or Keplers Zeroth law too?

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    $\begingroup$ You need the zeroth law to define 'empirical' temperature. $\endgroup$ – Quantum spaghettification Mar 18 '16 at 20:06
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    $\begingroup$ Instead of calling it "obvious", call it "axiomatic." If we don't have axioms, then our reasoning has nothing to stand on. $\endgroup$ – Solomon Slow Mar 18 '16 at 20:35
  • $\begingroup$ From a physical perspective you don't "need" it. I would agree with James that the zeroth law is so obvious as to be superficial. One does "need" it in a mathematical sense as an axiom for the formalism but to be honest, it has zero physical content. As for Quantum's remark... forget everything you have ever heard about "empirical temperature". It's as useful as the phlogiston. $\endgroup$ – CuriousOne Mar 18 '16 at 21:37
  • $\begingroup$ Thank you for the answers guys. I think the "axiomatic explanation" somewhat does it for me. @CuriousOne if it has zero physical content, why is it mentioned in so many physics books? $\endgroup$ – bluemoon Mar 18 '16 at 22:10
  • $\begingroup$ @CuriousOne, it may be obvious to some, but only based on experience. That's why it does have physical content. Without experience, it is entirely possible to have a scheme where A is in equilibrium with B when the two are brought into contact, the same for A and C, but B and C are not in equilibrium when brought into contact so heat flows. The fact we never observed such strange behaviour is based on observation and is a law of physics. $\endgroup$ – Ján Lalinský Mar 18 '16 at 22:38
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How could B and C not be in thermal equilibrium?

A is in contact with B: nothing happens

      B
   .
A

A is in contact with C: nothing happens

A
   .
      C

B is in contact with C: lots of heat is being transferred to B

          B

          ↑

          C

We have not observed bodies that would behave this way. That is the content of the zeroth law.

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  • $\begingroup$ Sorry for the late reply. Thank you very much for your answer. $\endgroup$ – bluemoon Mar 20 '16 at 8:58
  • $\begingroup$ @bluemoon, you're welcome. $\endgroup$ – Ján Lalinský Mar 20 '16 at 12:35

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