Can Absolute Zero Ever Truly Be Reached?

[ryokan]

The Third Law of thermodynamics states that absolute zero cannot be attained by any procedure in a finite number of steps.
Absolute zero can be approached arbitrarily closely, but it can never be reached.
My question is: How much (in power of ten) could it be closely approached?
Is there any limit over the thermodynamic?

 

[MiGUi]

Lets think in a process which can lead us to make a system down its temperature. We can do it by adiabatic processes connected with isothermic ones, but we have a limit given by the mechanic of the process, we cannot link two different adiabatic processes without any other process, because two adiabatics can't have common points. But when we reach lower temperatures, we have a problem.

The lowest isotherm has exactly the same points than the lowest adiabatic because zeroth entropy is at zero kelvin. So, if an isothermic can not cut another isothermic and the same occurs with adiabatics, how can we reach the zeroth one?

I don't know if my post is well explained, due to the language :)

 

[ryokan]

Lets think in a process which can lead us to make a system down its temperature. We can do it by adiabatic processes connected with isothermic ones, but we have a limit given by the mechanic of the process, we cannot link two different adiabatic processes without any other process, because two adiabatics can't have common points. But when we reach lower temperatures, we have a problem.

The lowest isotherm has exactly the same points than the lowest adiabatic because zeroth entropy is at zero kelvin. So, if an isothermic can not cut another isothermic and the same occurs with adiabatics, how can we reach the zeroth one?

I don't know if my post is well explained, due to the language :)

Thanks MiGUi, but my question is simply quantitative: How closely could be the approach to zero? Indefinitely towards zero? Is there a practical limit due to physical nature of instruments both of cooling and measure?

 

[MiGUi]

As we get closer, its more difficult keep cooling the system, because we need every time more number of processes to down the temperature. 0 K is the limit, and every approach we do to this limit depends on the technology we have at the moment.

Maybe we can reach $$10^{-50} K$$, but not nowadays.

 

[ryokan]

As we get closer, its more difficult keep cooling the system, because we need every time more number of processes to down the temperature. 0 K is the limit, and every approach we do to this limit depends on the technology we have at the moment.

Maybe we can reach $$10^{-50} K$$, but not nowadays.

Why? Why not $$10^{-55} K$$ or $$10^{-63} K$$?

 

[MiGUi]

Well, I said maybe... but you must realize that the step between 0.001 K and 0.0009 K is not as difficult to do, as the step between 0.0009 K and 0.0008 K because as we get closer to 0 K, we need more processes to down the temperature.

 

[da_willem]

Temperature is proportional to the average kinetic energy of the molecules. Due to the "Heisenberg uncertainty principle" the speed of the molecules and thus the kinetic energy cannot be zero. So there is a theoretical limit on how low a temperature can be obtained.

 

[HallsofIvy]

This website:
http://www.ph.rhbnc.ac.uk/schools/ZeroT/Absolute.html
cites experiments that have reached 30 nano-degrees above 0.

 

[ryokan]

This website:
http://www.ph.rhbnc.ac.uk/schools/ZeroT/Absolute.html
cites experiments that have reached 30 nano-degrees above 0.

Thank you, HallsofIvy. It is a very interesting website.

 

[LURCH]

If energy is quatized, as it seems to be, then there should be a theoretical limit. No system can posses less than a single quanta of energy. If this is true, what is the smallest possible unit of energy? That should be the least amount of energy any system can possess, and therefore the closest we could ever get to 0^ok.

 

[Chronos]

How about a wild guess of 7.06E-33 K? Anyone care to guess how I came up with that number? A more scientific approach, I think, be based on the zero point energy of the medium. The lowest allowed vibrational energy (zero point energy) of an atom at 0 degrees Kelvin is 1/2 hv, where h is Plancks constant and v is the vibrational frequence of the material. The value of v depends on the nature of the medium. The vibrational quantum [hv] for hydrogen is, for example, is 8.75E-20 J.

 

[da_willem]

If energy is quatized, as it seems to be, then there should be a theoretical limit. No system can posses less than a single quanta of energy. If this is true, what is the smallest possible unit of energy? That should be the least amount of energy any system can possess, and therefore the closest we could ever get to 0^ok.

Energy is not quantized in 'packets' of the same energy. The quanta of the electromagnetic field, the photon, for example has en energy proportional to it's frequency ($E=h \nu$). So there's no minimum amount of energy one quantum has to possess.

 

[ryokan]

How about a wild guess of 7.06E-33 K? Anyone care to guess how I came up with that number? A more scientific approach, I think, be based on the zero point energy of the medium. The lowest allowed vibrational energy (zero point energy) of an atom at 0 degrees Kelvin is 1/2 hv, where h is Plancks constant and v is the vibrational frequence of the material. The value of v depends on the nature of the medium. The vibrational quantum [hv] for hydrogen is, for example, is 8.75E-20 J.

Thus, over the absolute zero, it would be the zero point energy. That is a fundamental limit, that you exemplify with hydrogen.
The question then would be: over this zero point energy (medium - dependent), would it be another fundamental zero point linked to physical properties of the cooling instruments ?

 

[Chronos]

new and improved

If all the mass in the universe collapsed, the resulting black hole would have a temperature of about 4E-31. [disclaimer:I calc'd that pretty quick]. So, plug in your own favorite value for the mass of the universe into this and see what you get.
$$T = \frac{\hbar c^3}{8\pi \kappa GM}$$

 

[pervect]

The Third Law of thermodynamics states that absolute zero cannot be attained by any procedure in a finite number of steps.
Absolute zero can be approached arbitrarily closely, but it can never be reached.
My question is: How much (in power of ten) could it be closely approached?
Is there any limit over the thermodynamic?

For a gas, there will be a theoretical limit from quantum mechanics based on the minimum energy of a particle-in-a-box. This limit has been reached for the "Bose-Einstein condensates". The box size for today's BEC's is about a micron, I think (the atoms are confined by magnetic fields, not an actual box). With the atomic mass of the substance used, this gives temperatures in the 100 nanokelvin range (I'd have to look it up to be more specific, I'm probably close to the correct order of magnitude, though).

Larger boxes will lower the temperature, but they'll still be a limit based on the box size. The people making the BEC's wanted to see the BEC phenomenon, so they didn't try to make the "box" particularly big.

I'm not sure how to treat solids or liquids.

 

[Chronos]

Excellent point, pervect. For further discussion see
http://math.nist.gov/mcsd/savg/vis/bec/

 

[ryokan]

Hello pervfect and Chronos.

Thank you for your interesting answers.

 

[ryokan]

The road towards tha absolute zero seems to be a progresssive transition from thermodynamics to quantum mechanics. Yes?

 

[ryokan]

Degrees Kelvin. The book

And about Lord Kelvin, has anyone read the recent David Lindley's book entitled Degrees Kelvin: A Tale of Genius, Invention and Tragedy? I only read the John S. Rigden's comment in Science 2004;305:1406.

 

[CharlesP]

I am not certain that the zero point energy of quantum mechanics really adds a constant to the temperature scale. There must be some knowledge about that somewhere but I never saw it.

 

[ryokan]

How could we conceive time in a set of particles near 0ºK?