Absolute zero: Encyclopedia II - Absolute zero - Kinetic theory and motion

Absolute zero - Kinetic theory and motion

According to kinetic theory, there should be no movement of individual molecules at absolute zero, so any material at this temperature would be solid. In a monatomic gas, most of the energy is in the form of translational motion, and the temperature can be measured in terms of the distribution of this motion, with slower speeds corresponding to lower temperatures, perhaps even down to absolute zero. But this is contrary to experimental evidence, and it is predicted that helium will never solidify, no matter how much it is cooled or compressed.

Because of quantum-mechanical effects, the speed at absolute zero is larger than zero and depends, along with the energy, on the volume within which a particle is confined. At absolute zero, the molecules and atoms in a system are all in their ground state, the state of lowest possible energy, and a system has the least amount of kinetic energy allowed by the laws of physics. But the lowest possible zero-point energy for a confined particle in a box is not zero. Rather than being fixed and non-moving, the equation for the energy levels shows that no matter how low the temperature gets, even when the quantum number takes its minimum value of one, a particle still has some translational kinetic energy and motion. This is a reflection of Heisenberg's uncertainty principle, which states that the position and the momentum of a particle cannot both be known precisely at any given time.

Similarly, using the harmonic approximation for the vibrations of a diatomic molecule, the quantum harmonic oscillator yields a positive zero-point energy even when the vibrational quantum number takes its minimum value of zero. For polyatomic molecules, and for bodies such as crystals, whose normal mode motions can not be assigned to individual atoms or chemical bonds, the lowest-energy state is that of the system as a whole.

Classically, the absolute temperature T of a system of molecules at thermodynamic equilibrium assigns an average of 1/2 kT to each quadratic kinetic and/or potential energy term in each mechanical degree of freedom, where k is Boltzmann's constant. (See equipartition of energy and the role of the Boltzmann distribution in relating temperature to energy.) But quantum mechanics shows that this is obeyed only for temperatures such that kT > hν, where h is Planck's constant and ν is a characteristic frequency. As T decreases, the assumption that energy is continuously variable fails whenever hν exceeds kT. For vibrational modes in crystals, this happens at room temperature, which explains the deviation of the calculated specific heats of atomic crystals from the experimental Dulong-Petit law value of 3R /mole, a fact which puzzled late 19th century physicists and physical chemists. (Rushbrooke, p. 33)

Adapted from the Wikipedia article "Kinetic theory and motion", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki