# Internal Energy Dependence for a Fixed System in Fixed Phase

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1. Jul 25, 2015

### 0pt618

For a given closed system that does not experience phase transitions, does its internal energy depend only on its temperature?

2. Jul 25, 2015

### Staff: Mentor

No. This is true only for an ideal gas. For real gases beyond the ideal gas region (i.e., higher pressures) and for other materials, the internal energy also depends on pressure.

Chet

3. Jul 25, 2015

### 0pt618

Hi Chet - thanks. I have some follow up questions, and let's exclude ideal gases from the following discussion - let's consider only liquids, solids, and non-ideal gases.

From what I understand, the internal energy consists of two parts: microscopic kinetic energy and microscopic potential energy. Since the kinetic energy portion (to a good approximation at least) depends solely on temperature, then it must mean the pressure dependence comes about through potential energy - in other words, pressure affects and only affects potential energy. Am I correct?

I can envision how this is true for an non-ideal gas: As the pressure is increased, the volume decreases and the potential energy increases. (And the temperature can be kept constant during this process.)

But does the internal energy of a liquid or solid material (that does not change phase) depend on pressure? I would think that a liquid or solid does not change much as pressure is varied, as long as the pressure variation is not "too great". Am I right? Can we do something to a liquid or solid that changes only its microscopic potential energy (while maintaining the same temperature)?

Thanks,
David

4. Jul 25, 2015

### Staff: Mentor

Yes.
Yes. Exactly right.
I am not an expert on how this all plays out microscopicly. I'm a continuum guy. But, you can look in Thermo books. They give an equation for dU in terms of dT and dP. The coefficient of dP follows exclusively from equation of state P-V-T behavior of the material.

Chet

5. Jul 25, 2015

### 0pt618

Thanks, Chet.