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?
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    $\begingroup$ If you are not going to elaborate the question by your effort to answer the question yourself, you may rather want to post it to Quora site. As it is, it does not fit the site policy and will be probably voted to be closed. $\endgroup$ – Poutnik Mar 3 at 3:09
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    $\begingroup$ Why do we use kinetic energy, potential energy, thermal energy and not just total energy ? $\endgroup$ – Poutnik Mar 3 at 3:13
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    $\begingroup$ @Poutnik Has it exactly right: the answer to all three of your questions is simply to pay close attention to what the teacher/professor says. $\endgroup$ – Ed V Mar 3 at 3:16

We use them in context with different conditions. It's often easier to evaluate/control systems with different constraints (constant pressure etc.) using particular thermodynamic potentials (the energy functions above). These functions also describe different aspects of the "total energy" the system possesses, like Poutnik says. It's somewhat like an aircraft trying to remain level by monitoring gravitational potential energy with respect to the earth, which sounds more rational than trying to keep an eye on the total mechanical energy the aircraft possesses.

thermodynamic potentials and corresponding systems

As you see, each correspondence makes it easier to monitor the system and plot responses meaningfully.

It's also easy to determine equilibrium conditions in each kind of system shown above: minimization of the respective thermodynamic potential.

Table taken from Lecture Notes of Prof. Srabani Taraphder, IIT Kharagpur.

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