# What is the reason for absolute zero temperature?

1. Feb 17, 2013

### Jano L.

What is the empiric reason behind the assumption that there is lowest thermodynamic temperature (absolute zero)? And that all other temperatures of bodies in thermodynamic equilibrium are always higher ?

I am looking for a reason not using the entropy concept, as the entropy was derived historically with the assumption that there is lowest temperature which ideal gas can have. So the argument using entropy would be circular.

Or do you think that entropy is more fundamental than temperature and positive thermodynamic temperature is a just a consequence the properties of entropy ?

2. Feb 17, 2013

### Jorriss

This. Entropy is far more fundamental than temperature.

3. Feb 17, 2013

### Jano L.

I know such view is quite common, but if I want to avoid statistical physics, it is hard to introduce entropy first and then temperature as a derived concept. Historically, the temperature is assumed first and the entropy is derived, by the consideration of Carnot cycles - this is the way entropy was discovered. So I wonder whether there is some non-statistical, non-entropic argument for the positive temperature, which would make the historical path more sensible.

4. Feb 17, 2013

### phinds

I guess I don't even understand your question. Temperature is a measure of the motion of matter. If there is no motion, the temperature is zero. What's confusing about that?

5. Feb 17, 2013

### Jorriss

That may of been the order the phenomena were discovered but that doesn't change the fact that entropy is more fundamental to nature. Newtons laws may of been discovered before QM, but QM is still more fundamental, for example.

6. Feb 17, 2013

### Curl

7. Feb 17, 2013

### Jano L.

Well, I do not necessarily want to use the idea that temperature is direct measure of motion. It is conceivable that one has a system that has temperature and no motion - take model of two state spins for example, which can have energy and entropy but no motion. Or take ideal fluid defined by the equation of state

$$pV = nRT$$

and total energy

$$U = ncT.$$

with some constant $c$. According to the second equation, temperature is a measure of total energy $U$. But energy is an abstract concept, which can be negative in principle. (It will be other contributions to energy are negative and great enough). Then according to the second equation, the temperature will be negative too.

8. Feb 17, 2013

### Jorriss

In a sense, it still is though if one uses the more fundamental β= 1/T. Then temperature flows from low to high β and negative temperature corresponds to hotter than anything.

9. Feb 17, 2013

### Jano L.

Curl,
I know of " negative temperatures" as sometimes applied to spins and laser, but those are different thing from what I have in mind. As wikipedia says,
Such temperatures do not have the standard meaning of temperature, which is that heat flows from body with higher to body with lower temperature. When you connect such spin system with -5 K to 5 K system, the -5 K system has more energy and will give it to the system with 5 K. Such concept of temperature defines negative temperatures to conform to the laws of entropy.

But this is not without objection - such systems are not stable so it can be argued they do not have temperature at all.

I am thinking of a concept of temperature applied only to systems in equilibrium, with which, when a body has temperature -5 K, one says the body is truly colder than the system with 0 K, so heat will flow from 0 K to -5 K.

10. Feb 18, 2013

### SteamKing

Staff Emeritus
Entropy may be more fundamental than temperature, but it cannot be measured directly, unlike temperature.

11. Feb 19, 2013

### Curl

I have never seen temperature defined in terms of anything other than entropy, and in some books, using carnot engines.

I guess another way to describe it is "temperature is the thing that is the same for two objects if they are in thermal equilibrium". Then you can say that when an object cannot give any more thermal energy, it is at 0K. But obviously this is a very weak statement and in no way a definition.