# What does my textbook mean by "potential energy" while defining internal energy of a system?

Recall that thermal energy is an internal energy that consists of the kinetic and potential energies associated with the random motions of the atoms, molecules, and other microscopic bodies within an object.)

I thought internal energy $$Q-W$$ depends only on temperature (ignoring phase changes) and that the potential energy/bond dissociation energies are irrelevant in thermodynamics. They are useful in chemistry/QM. Perhaps my textbook meant gravitational potential energy. Has anyone know seen this before?

My textbook is Fundamentals of physics by Halliday

• This is a good question that has bothered me for some time. There are at least two definitions of temperature, the entropy definition and "average kinetic energy per molecule". In some cases they are the same. In some cases potential energy is accounted for if only the kinetic energy is considered, others not. Note that there is a distinction between internal energy and thermal energy. I'd love to have someone sort all that out for me. (I should post a question.) Sep 11, 2020 at 14:56
• For an ideal gas, it's neglected but do remember it does exist for a real gas. Look up joule thompson co-efficent Sep 11, 2020 at 18:49

For monatomic gases the only form of internal energy is translational i.e. the kinetic energy of the atoms. However for molecules we can also have rotational and vibrational energy as well as the translational energy.

Each active rotational mode gets $$\tfrac12 kT$$ of energy just like each translational mode. However each active vibrational mode gets $$kT$$ of energy because we get $$\tfrac12 kT$$ associated with the kinetic energy of the vibrational motion and another $$\tfrac12 kT$$ associated with the potential energy of the vibrational motion. I would guess that Halliday is referring to this.

• Ah makes sense XD potential energy may be associated with the vibrational modes for polyatomic gases. Next chapter is kinetic theory. Pretty sure he's going to clear this up there. Thank you so much! Sep 11, 2020 at 14:47

Potential energy is irrelevant only when the system includes an ideal gas since in an ideal gas the atoms don't interact with each other or there is no intermolecular forces in an ideal gas and I think you have been confused between ideal gas behaviour and real gas behaviour.

In a real gas , the molecules have intermolecular forces i.e. force because of the electrons and protons and little force due to masses. Since they interact with each other they have potential energy too .

Hope it helps 🙂.

• How did you get the emoji to appear in your answer? Sep 11, 2020 at 18:49