It is usually said that the best formulation of the first law of thermodynamics is that work is path independent on adiabatic paths. From there, you can define the state function of internal energy and define heat as the deficit between internal energy and work. However, to define an adiabatic path you already need a definition of heat so how do we define an adiabat properly in this formulation?

  • $\begingroup$ your question is not clear In an adiabatic process, no heat is transferred $\endgroup$ – Abdelrhman Fawzy Dec 2 '18 at 9:56
  • $\begingroup$ Yes, I know. To define an adiabat, you need a definition of heat. However, to define heat, you need the first law for which you need an adiabat in this formulation at least. My question is how to reconcile this. $\endgroup$ – Aakash Lakshmanan Dec 2 '18 at 10:04
  • $\begingroup$ in zeroth law we define adiabat wall it's wall if we have two system A and B with different states if they put together by adiabat wall they can have any state (will not be in equilibrium) adiabatic work defined as work done by or on the system when the system is in adiabatic container and first law for adiabatic system become: if a closed system caused to change from initial to final state by adiabatic means only then the work done on the system is the same for all adiabatic paths connecting them $\endgroup$ – Abdelrhman Fawzy Dec 2 '18 at 10:29
  • $\begingroup$ So we need to have a notion of being adiabatically confined then, right? What does that mean in relation to other thermodynamic ideas like in the zeroth law? I know you mentioned it but I don't really understand your explanation. $\endgroup$ – Aakash Lakshmanan Dec 2 '18 at 10:32
  • $\begingroup$ Also, surely, you can have an adiabatic process if you don't have adiabatic walls so how can you use walls in the definition of such a process? $\endgroup$ – Aakash Lakshmanan Dec 2 '18 at 10:32

The solution of this apparent conundrum is quite simple. Even without any knowledge about heat, a thermodynamic system has confining walls between system and outside world. Simply by playing with the walls, by changing the material they are made of end their size, one can find that with some materials, the work required to bring the system from a state $A$ to a state $B$ depends less and less on the exact path in thermodynamic space. Those walls can be defined adiabat (made by thermal insulators) and the transformation is called adiabatic. At this point the usual definition of heat from the adiabatic work can follow in a logically consistent way.

  • $\begingroup$ From a logical standpoint though in terms of phrasing definitions/postulates, this simply shifts the burden of definition from adiabatic process to adiabatic walls, right? $\endgroup$ – Aakash Lakshmanan Dec 2 '18 at 11:25
  • $\begingroup$ The first law conveys in one statement a huge amount of experimental findings. The formulation throught adiabatic work is a statement about the existence of walls which allow to get a path-independent work, i.e. there are walls which allow a meaningful definition of the energy of a thermodynamic system. Said in a different way, the law ensures the existence of adiabatic process which allow to define a thermodynamic energy. As such, it can be recast in the form of statement on the existence of the internal energy for every thermodynamic system. $\endgroup$ – GiorgioP Dec 2 '18 at 11:35
  • $\begingroup$ So, in a sense, the first law both asserts the existence of adiabats and their relationship to the work functions defined for the system? $\endgroup$ – Aakash Lakshmanan Dec 2 '18 at 11:55
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    $\begingroup$ Yes, that's the way the first principle is introduced in advanced thermodynamics textbooks like Callen's "Thermodynamics and an Introduction to Thermostatistics". $\endgroup$ – GiorgioP Dec 2 '18 at 12:34

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