# Does internal potential energy affects temperature?

1. Feb 11, 2016

### tonyjk

Hello
If I take an extreme case, where a body has only an internal potential energy with zero internal kinetic energy, does this body have a temperature? Another question related to it: if two objects A and B having different temperature: A: having only internal potential energy and B having only internal kinetic energy, can heat flow from A to B ?(temperature of A > B).
More general: Can an object at a temperature T1 (having internal kinetic energy and potential energy) have a different temperature T2 but in both case having the same internal kinetic energy and different potential energy?
Thanks

2. Feb 12, 2016

### Staff: Mentor

It can. For instance, if you have an ensemble of spin-1/2 systems in an external magnetic field, you can calculate spin temperature (beased on the ration of spin up and spin down). At the same time, it is hard for me to think of a system at thermodynamic equilibrium where you would have potential energy but no kinetic energy (because of the equipartition theorem, for instance).

If they can exchange energy, energy has to flow from A to B.

Not sure I understand your question, but if you compare a solid and a gas, at the same temperature they do not have the same kinetic energy, so they will have different temperatures for the same kinetic energy.

3. Feb 12, 2016

### tonyjk

If we compare two solids A and B ( having the same characteristics i.e same object) , if A is at temperature 1 (T1), having a K.E1 and P.E1. B is at temperature 2 (T2) having a K.E2=K.E1 and P.E2 different to P.E1. This case is possible ?
In general : Does variating internal potential energy affects the temperature if we consider the internal kinetic energy constant?

4. Feb 12, 2016

### Staff: Mentor

In general yes: if you were somehow to pump in energy only in one kind of degree of freedom, then the system will not be in internal equilibrium anymore, and after equilibrium is reached, you will find that all degrees of freedom have increased energy, and hence the temperature is higher.

5. Feb 12, 2016

### tonyjk

So you mean increasing potential energy will increase kinetic energy right?

6. Feb 12, 2016

### Staff: Mentor

The more I think about it, the less I like this distinction you are making between potential and kinetic energy, which is why a shifted in my previous post to "degrees of freedom." For instance, if you take vibrations of atoms in a crystal, they are a constant interchange of potential and kinetic energy.

For a gas, if you take "kinetic energy" to mean the kinetic energy related to the center-of-mass motion of the gas molecules, then increasing the internal potential energy of the molecules will lead, at equilibrium, to an increase in temperature. But increasing the gravitational potential energy of the gas will not change the temperature.

7. Feb 12, 2016

### tonyjk

But taking the example of a gas, increasing potential energy is due to increase in kinetic energy right?

8. Feb 12, 2016

### Vedward

Fifty years ago in high school chemistry class, we did an experiment where we dissolved a compressed spring and an uncompressed spring in acid solutions. All started at the same temperature, but the compressed spring solution had a higher temperature, attributed to the energy (potential) in the compression.

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