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.