# Negative Kelvin temperature? (Recent Science paper)

Yeah I get it now.

However, for some substances, at some point S starts decreasing with increasing E.
This is when the sign of the temperature flips.

After that S starts decreasing quicker and quicker, making temperature (which is the inverse) approach zero.
I understand how in a situation where you get the usual entropy at a high energy, and the molecules sort of "peak" in their form or melt or destabilize further into a gas. Where I'm confused is on the loss of energy and S reaching equilibrium for the system... if that system is aided in cooling it to where S drops faster than E can balance, what's to stop it from becoming -K?

Also, if the motion of the intended atoms becomes negative K, from a relativity perspective, wouldn't they still have motion? And from a logic standpoint (and what I know about these things)... approaching absolute zero in an ideal system is really just continually slowing the entropy until you reach a "new" absolute zero... a new limit for how much you can slow something before the inverse energy (cold) catches up with the rest of the system and balances out like what would happen if you were adding energy and not taking it away.

P.S. - Think I sort of answered my own questions... tends to happen when I type thoughts out. Help, clarifications, corrections, a dunce hat-etc would be appreciated.

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I like Serena
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At some point you can no longer extract energy from a system.
When that happens its entropy approaches zero, which is basically what the third law of thermodynamics states.

What stops it from being possible?

Edit: I mean, I would assume it's the limit of the system being finite, and time restrictions. Would increasing the system to a (insert degree of hugeness required) change anything? Or just allowing the system to be considered limitless?

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mfb
Mentor
If you find some source of materials with negative temperatures (you won't), maybe.
That is as useful as a statement "I can use [magical box that always maintains 1000K at its outside] to extract as much energy as I want!". It is true, but that magical box does not exist.

Hold on! Let's clear something up. How does negative temperature hotter than all positive temperatures. I need clarification....
Both number lines are ordered from smallest to largest. So 1 is a colder temperature than -1.

*: In the extended sense. I don't think[Hold

Khashishi
The old posts pretty much explained every bit of it. Which part are you having trouble with?

So if a negative temperature object is in contact with a positive temperature object then heat energy will flow from the negative temperature object to the positive energy object?

If this is so then will the negative temperature object get less negative in temperature over time (colder) until it reaches absolute zero and then becomes a positive temperature object?

Khashishi
No. If you cool a negative temperature object, the temperature will become more negative until it goes to negative infinity and then "crosses over" to positive infinity and then continues to cool toward absolute zero. This looks weird because temperature is defined strangely. The reciprocal of the temperature is more fundamental than the temperature and behaves more intuitively as you cool it. The inverse temperature smoothly increases from negative to positive, crossing zero when the temperature crosses infinity.

mfb
My question is concerning what will happen to the negative temperature object if it comes in contact with the positive temperature object.

Khashishi
It doesn't change the result.

If you put two objects at different temperatures together, the reciprocal of temperature of both objects will spontaneously move toward each other. (The amount one moves versus the other depends on the thermal mass, aka the heat capacity.)

Why not give a direct answer?
What happens to the negative temperature object (not the positive one) when it comes in contact with the positive temperature object?

Which one?
The temperature would remain the same.
The temperature would become more negative.
The temperature would become less negative.

Khashishi
If you put a negative temperature object in contact with a positive temperature object, the negative temperature object will cool down and the positive temperature object will heat up. See reply #34 for what happens when the negative temperature object cools down.

Does cooling down mean the temperature becomes less negative? Or more negative?

Khashishi
Read the second sentence of #34.

mfb
Sorry, I see now. Thanks!

So this actually makes no sense (Unless there is a maximum possible temperature and lowest negative temperature). At what point does the negative temperature switches to a positive temperature without a limit?

mfb
Mentor
See the old posts. It is much easier to consider the inverse temperature, where you don't have such a jump.

0, approached from positive values, is the lowest possible temperature, and 0, approached from below, is the highest possible temperature. If you keep cooling an object with negative temperature, its temperature will go down, it will approach "infinite temperature (no meaningful sign here)" and then have a positive temperature afterwards.

And what else that doesnt make sense is if 2 negative temperature (different) objects come in contact then the greater negative temperature object would become warmer until it reaches absolute 0.

jbriggs444
Homework Helper
2019 Award
And what else that doesnt make sense is if 2 negative temperature (different) objects come in contact then the greater negative temperature object would become warmer until it reaches absolute 0.
The very negative temperature object becomes warmer only until it reaches the temperature of the less negative temperature object. They will both settle toward a medium-negative value.

The continuum of temperature values is from 0 up through +/- infinity and on up toward zero. Absolute zero is both the limit to which negative temperatures cannot reach from below and to which positive temperatures cannot sink from above. As has been suggested, consider inverse temperatures with + and - infinity as the limits on either end of the scale and "zero" in the middle and it is the exact same thing.

Ok I understand. One more question.

Can anyone touch an object of negative temperature feel and just feel a comfortable warmth they touch it? Meaning, it will not severely burn or disintegrate, them but just feel warm to the touch?

mfb
Mentor
If thermal conductivity is low enough, it could work. But then you are actually touching an object where the surface has a normal positive temperature, while the interior might still have a negative one.

That is purely hypothetical - I don't think you can have a normal solid material that you could actually touch at a negative temperature.