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If we are going to define (empirical) temperature from the zeroth law, we need a definition of heat that does not depend on the concept of temperature, else this would produce a cyclic argument.

Does anyone know a good definition of heat that is not vague like 'energy in transit', but also does not bring in the concept of temperature? (A source would be helpful).

Note: I have looked in many, many places for such a definition but all the ones I have found fall into the 'temperature' or 'vague' categories.

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    $\begingroup$ Are you satisfied that one can precisely define internal energy and work? If so, heat can be defined as anything that isn't one of those. $\endgroup$ – joshphysics Jun 15 '16 at 15:42
  • $\begingroup$ possible duplicate (though also unanswered): physics.stackexchange.com/q/78783/64170 $\endgroup$ – Ross Presser Jun 15 '16 at 15:43
  • $\begingroup$ @joshphysics I am happy we can precisely define internal energy but I am not so sure about work, due to e.g. energy associated with magnet and electric fields. $\endgroup$ – Quantum spaghettification Jun 15 '16 at 15:46
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    $\begingroup$ I think part of this has to be cyclic/postulated, because there is no fundamental difference between heat and work. Heat is just work where you've decided to ignore the degrees of freedom performing the work. Flipping this around it means that you don't have to worry about the "true" definition of work, so Josh's answer works. $\endgroup$ – knzhou Jun 15 '16 at 16:01
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    $\begingroup$ Temperature isn't defined by the zeroth law but by the second law, which, at the same time, also completes the definition of heat. Can you explain why you are worried about the zeroth law? $\endgroup$ – CuriousOne Jun 15 '16 at 16:59

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