General Question Regarding Internal Energy

Hi all!

I have a quick question. In my Physical Chemistry textbook, the author states,

"For a closed system in equilibrium, the internal energy (and any other state function) can be expressed as a function of temperature and volume."

Can anyone explain just how that is true? I'm quite certain I'm overlooking something fundamental here.

All the best,
JT

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Andrew Mason
Homework Helper
In my Physical Chemistry textbook, the author states,

"For a closed system in equilibrium, the internal energy (and any other state function) can be expressed as a function of temperature and volume."

Can anyone explain just how that is true? I'm quite certain I'm overlooking something fundamental here.
An interesting question. Here are my thoughts at least on the internal energy part:

If you generalize a system to consist of n particles, the internal energy of that system is the sum of the kinetic and potential energies of each particle. The potential energy of each particle is a function of the distance of that particle from other particles. The kinetic energy of each particle is the sum of each particle's translational, rotational, and vibrational energies.

If the system is in thermodynamic equilibrium, the average rotational kinetic energy and average vibrational energy are functions of the translational kinetic energy (this is the basis for the equipartition theory). And the average translational kinetic energy determines the temperature. Also, in thermodynamic equilibrium the average potential energy of the particles is determined by the average distance between particles, which is obviously a function of total volume.

AM

Woah, AM. I've never heard of the equipartition theorem before, but after reading about it, what you said about internal energy makes complete sense. Like I said, I overlooked something fundamental.

Thanks!