# Does same temperature of two bodies = same internal energy?

1. Feb 24, 2015

### Greg777

Hello,
From what I know, internal energy of a body = sum of kinetic energies of the particles of the body + potential energy between the particles (intermolecular forces), right?
And there's this textbook question which made me question that for a while:
Two objects are at the same temperature. Explain why they must have the same internal energy.
If the objects are at the same temperature, there is no transfer of energy between them, so their
internal energy must be the same.

But is it true? I always thought the only indicator of temperature of a body is the average kinetic energy of its particles (there's nothing about potential energy). If that's true, and keeping in mind that Internal Energy=KE+PE, then the some two bodies may have the same KE (so the same temperature) but their PE may differ which results with their internal energies being different. What do you think?

http://www.hyperphysics.phy-astr.gsu.edu [Broken] seem to confirm my point of view: "Temperature is not directly proportional to internal energy since temperature measures only the kinetic energy part of the internal energy, so two objects with the same temperature do not in general have the same internal energy"

Last edited by a moderator: May 7, 2017
2. Feb 24, 2015

### Quantum Defect

"Two objects are at the same temperature. Explain why they must have the same internal energy." This seems bogus to me.

The internal energy will depend upon how much stuff you have. If you have two completely pure pieces of platinum (1 g and 10 kg) at the same temperature of 100 C, the large piece of platinum has more energy than the small piece -- i.e. you could use the large piece of platinum to make a cup of tea.

Last edited by a moderator: May 7, 2017
3. Feb 24, 2015

### Greg777

Yes, I know that internal energy also depends on the mass of a body but is my "explanation" in the first post correct if we assume that we have two different bodies with the same mass at the same temperature?

4. Feb 24, 2015

### Quantum Defect

I don't quite like the wording of the quote that you have, but the point that you are making is also true.

For example, in the case of gases, there is more energy stored in something like SF6 (lots of rotational and vibrational degrees of freedom) than there is the same number of moles of something like Xe at the same temperature (no rotational or vibrational degrees of freedom).

Last edited: Feb 24, 2015
5. Feb 24, 2015

### Greg777

Thanks for the answer. That question seemed wrong and absurd to me from the beginning - that's not cool that a supposedly reputable textbook (it's an Oxford one) makes such mistakes misguding naive highschoolers :)

6. Feb 24, 2015

### mrspeedybob

7. Feb 24, 2015

### Andrew Mason

This is a correct statement. A good example would be an ice cube at 0C sitting in liquid water at 0C. The ice has substantially less internal energy than the water per unit mass (the difference is 333 J/g). They are at the same temperature, so no heat flow occurs between the ice and water.

AM