Absolute Zero

An immediate consequence of temperature being related to thermal kinetic energy, is that there must be a lowest possible temperature. When the thermal kinetic energy is gone, you cannot go any lower in temperature. It thus seems reasonable to define an absolute zero of temperature as the state where the molecules have no thermal kinetic energy, and choose a temperature scale that starts at this absolute zero and goes up proportionally to the thermal kinetic energy.
However, as you approach absolute zero, as you try to remove the last vestiges of thermal kinetic energy, nature has a surprise in store. No matter what you do, there is some unremovable kinetic energy left. One of the basic predictions of quantum mechanics is that a confined particle cannot have zero kinetic energy, and the closer the confinement the more kinetic energy it has to have. A molecule in a liquid or a solid is confined to the small volume bounded by its neighbors, and therefore cannot have a kinetic energy less than that required for that volume.
The unremovable kinetic energy is called zero point energy. This energy is so small that for most substances it is not noticeable unless you carry out specially designed experiments to detect it. However, zero point energy shows up clearly in the case of liquid helium. All substances except helium freeze when cooled to a sufficiently low temperature. We can remove enough kinetic energy from the molecules so that they settle into a solid structure. But the molecular force between helium atoms is so weak that the zero point kinetic energy alone is enough to keep helium a liquid. You cannot freeze helium by cooling alone, you must also subject it to high pressures.
The existence of zero point energy suggests that we will encounter problems with the definition of temperature as we approach absolute zero. Suppose, for example, we have two substances with different zero point energies in thermal equilibrium. If the temperature is so low that any thermal kinetic energy is much less than the zero point energies, then we have a situation in which molecules with different vibrational kinetic energies are in thermal equilibrium. If we insist that two substances in thermal equilibrium are at the same temperature, then we can no longer say that temperature is proportional to the vibrational kinetic energy of the molecules.
The ideal gas thermometer does not get us out of this problem because it does not work at very low temperatures. Before the zero point energies become important, any gas we use in an ideal gas thermometer becomes liquid or solid and we no longer have an ideal gas as a working substance.
In the next chapter on entropy and the second law of thermodynamics, we will discuss the consequences of the basic idea that order does not naturally arise from disorder. In that discussion we will describe a method of defining temperature that applies to all temperature ranges. This thermodynamic definition of temperature is consistent with the ideal gas thermometer over the range that ideal gas thermometers operate, but also correctly describes temperatures near absolute zero where we have to deal with zero point energy.