### Question

What will happen to the gas at absolute zero temperature (0 K)?

Asked by: Rohit

### Answer

First of all, the gas will no longer be a gas at absolute zero, but rather a solid.
As the gas is cooled, it will make a phase transition from gas into liquid, and
upon further cooling from liquid to solid (ie. freezing). Some gases, such as
carbon dioxide, skip the liquid phase altogether and go directly from gas to solid.

Now the question is: what are the atoms in the solid doing (if anything) at
absolute zero. Are they totally motionless? The answer is no. Atoms, being very
tiny particles, must be analyzed using quantum mechanics, and one of the
cornerstones of this theory is the Heisenberg Uncertainty Principle (HUP).

The HUP states that the uncertainty of a particle's position and momentum (mass
times velocity) are not independent of each other; the product of these
uncertainties must be greater than a certain value. In equation-ese:

(position uncertainty)*(momentum uncertainty) > h

The number 'h' is called Planck's constant, and pops up throughout quantum
mechanics. This equation requires the atoms in the solid to have a certain amount
of intrinsic jitteriness, even at absolute zero. If the atoms were totally
motionless, then both the position and momentum uncertainties would be zero,
disobeying HUP.

A pathological example of this is the element helium. Because helium is a noble
gas (that is, it cannot form covalent bonds) and it is very light, HUP requires the
uncertainty in its velocity to be quite high compared to other atoms. This makes
the helium atoms so jittery, in fact, that they refuse to solidify at all-- at
reasonable pressures, it remains a liquid even at absolute zero!

Answered by: David Dixon, Ph.D., Professor, Marquette University, Milwaukee

First off, 0K can never be achieved, since the amount of entropy in a system can
never be equal to zero, which is the statement of the second law of thermodynamics.
This can be nicely illustrated by your question:

Using the state equation for an ideal gas:

PV = nRT

T, the thermodynamic temperature will be equal to 0, so the product of the molar
gas constant R (8.31 J/mol/K) and the amount of moles n, will also be zero.

Therefore the product of PV must be zero also.
the pressure of the gas must be zero
or volume of the gas must be zero

Since neither of these can be true, the second law of thermodynamics is observed.

Answered by: David Balson, Ph.D., String Theorist, PPARC, United Kingdom