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As far as I understand it, the first principle of thermodynamics is a mere definition of the quantity “Heat”: $$\text d Q: = \text d L + \text d U.$$ This is somewhat the point of view taken in Fermi's introductory book "Thermodynamics":

[...] $$\Delta U + L=0$$If the system is not thermally isolated, the first member of [eqn.] will be generally not equal to zero [...] Substitute the [eqn.] with the more general: $$\Delta U + L = Q.$$ [...] Now we will call $Q$, by definition, the quantity of heat received by the system during the transformation.

(if you want to read the full text you might want to google “Fermi Thermodynamics"... pag. 17).

I think that this point is logically sound and I have a quite good understanding of some of the above structure starting from here (e.g. the second principle). On the other hand I feel as I'm missing something.

To give an example, from mechanics, this is how I understand Newton's equation:

It is a matter of fact that the positions and the velocities of a mechanical system fully determine the accelerations of the system. Hence, the dynamic of each system follows second order differential equations: $$\ddot x = F(x,\dot x, t).$$

An other example might be the second law of thermodynamics, that (in Clausius' form) is simply the statement of the fact that heat doesn't flow spontaneously from a cold body to an hotter one.

Since I find strange that something that is called a “principle” is a mere definition (after all, there's no assumption involved in making a definition), I ask: what are the experimental facts behind the first principle of thermodynamics?

Note: I understand that this is really about my personal understanding, however I think that this question can be useful to others. Furthermore, if something isn't clear and if I can improve my question, let me know.

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Thermodynamics is a phenomenological description of macroscopic systems, and it's laws are based on empirical observations.

The first law, first states that a state function called internal energy $U$ exists for macroscopic systems (an experimental fact), that can be thought of as the analog of potential energy in mechanics, for macroscopic systems; then defines heat intake of the system:

1) For an adiabatically isolated macroscopic system (i.e., when the only sources of energy are mechanical), the amount of work required to change the state of the system only depends on the initial and final states. (an observational fact)

2) When the adiabatic constraint is removed the amount of work is no longer equal to the change in the internal energy, and their difference is defined as the heat intake of the system: (definition of heat) $$\delta Q=dU-\delta W$$ Here, $\delta Q$ and $\delta W$ are not separately functions of state, but their sum (internal energy) is. Note that $\delta W$ is the work done on the system.

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  • $\begingroup$ Thank you for the answer, good point. The existence of substances that are adiabatic with good approximation is necessary to define operationally the internal energy $U$ (if we are taking a pure thermodynamics point of view, I suppose). $\endgroup$ – pppqqq Nov 19 '13 at 16:42
  • $\begingroup$ To elaborate on what Mostafa said, you can take $dU = \Delta W$ to the bank, as it is in a way a statement of the work-energy theorem. Note that work is never a state function, because, well, it's just work. But whatever quantity of work we can't account for, we lump into heat. So if you push a block up a ramp, then the energy of the block changes according to the state function, but some amount of $\Delta W$ may be unaccounted for as friction, hence $\Delta Q$. $\endgroup$ – lionelbrits Nov 20 '13 at 12:37

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