Is it possible to apply thermodynamics to simple physical problems? Classical mechanics can not predict neither energies nor trajectories of many interacting particles and we use thermodynamics to understand (get the energies) those systems. Am i right? But what about the reverse? The question is: Can thermodynamics be applied when Newton's equations have solution? 
For example, a body falling down by the action of gravity, the problem of an elastic spring, or maybe two rigid particles that collide, etc.
What would you say about entropy, internal energy, enthalpy, gibbs free energy, in those simple cases?
I am not sure if the question is correct.
 A: I am not sure what you mean by "Classical mechanics can not predict ..." The inability to predict is our limitation (we do not have the appropriate mathematical tools) and not that of classical mechanics. So you may imagine two beings one of whom has indeed solved equations for system of many bodies (or measured the path of every one of those bodies in an experiment, which is equivalent to having solutions for some set of initial and boundary conditions). Another being not able to do so, uses thermodynamics to speak of average quantities only. However the first being can also compute averages and therefore speak in thermodynamic terms. For simple systems such as freely falling body, elastic spring etc., there is nothing to average over and therefore thermodynamics does not enter the picture. However if you were to heat those bodies, then thermodynamics does come into picture because rather than look at say a freely falling body as a single entity, we must now look at it as a collection of molecules.
A: It's a very interesting question indeed. For a system, we have two kinds of energy- one is macroscopic(ordered energy) and is microscopic(disordered energy). The macroscopic energy is for the kinetic energy of the body and the potential energy due to its configuration(position of center of mass). The microscopic energy generally consists of the internal energy due to it’s molecules and its interaction. In thermodynamic terms we can say internal energy.
In the following case we will see that heat transfer is a microscopic phenomena while mechanical work done is a macroscopic phenomena.
Obviously, during inelastic collisions, there is a change in kinetic energy; question arises where this kinetic energy goes?
The reason lies in the fact that we are not including internal frictional forces
$\Delta K= W_{internal-friction}$
From our previous discussion on macroscopic and microscopic energy we can further change $\Delta K$ as $\Delta K_{macroscopic}$ and $\Delta K_{microscopic}$
Further considering the heat transfer from the surrounding environment, we proceed as:
$W_{internal}+W_{external-non-conservative}+W_{external-conservative}=\Delta K_{CM}+ \Delta_{microscopic}$
for the work done by a conservative forces, it can changed to potential difference as
$W_{external-conservative}=-\Delta E_{potential-energy}$
Also, $W_{internal}=$$\sum{i \neq j}^{} P_{ij} $
So after some reshuffling we have the final expression as
$W_{external-non-conservative}=\Delta E_{macro}+ \Delta K_{microscope}+ \sum{i \neq j}^{} \Delta P_{ij} $
Now some heat if also gets supplied you might add it to the above expression. This is explained way more beautifully using illustrations in this link:
law of conservation of energy
Hope that helped!
