I understand that energy is a fairly arbitrary concept, and that it completely depends on your definition of energy. So far in my class, we have discussed:
- Entropy, $S$ (not really energy, but it seems to be closely related);
- Total internal energy, $U$, for which it is impossible to find an absolute value for;
- Enthalpy, $H=U+PV$;
- Gibbs energy, $G=H-TS$.
My questions are (and sorry if this is kind of loaded):
- Where do these formulations arise? Why is there not just one version that trumps the rest? (Total internal energy sounds like a candidate)
- In which scenarios would I be using one version over another?