Statistical Mechanics Approach To Temperature
Statistical mechanics provides a microscopic explanation of temperature, based on macroscopic systems' being composed of many particles, such as molecules and ions of various species, the particles of a species being all alike. It explains macroscopic phenomena in terms of the mechanics of the molecules and ions, and statistical assessments of their joint adventures. In the statistical thermodynamic approach, degrees of freedom are used instead of particles.
On the molecular level, temperature is the result of the motion of the particles that constitute the material. Moving particles carry kinetic energy. Temperature increases as this motion and the kinetic energy increase. The motion may be the translational motion of particles, or the energy of the particle due to molecular vibration or the excitation of an electron energy level. Although very specialized laboratory equipment is required to directly detect the translational thermal motions, thermal collisions by atoms or molecules with small particles suspended in a fluid produces Brownian motion that can be seen with an ordinary microscope. The thermal motions of atoms are very fast and temperatures close to absolute zero are required to directly observe them. For instance, when scientists at the NIST achieved a record-setting low temperature of 700 nK (1 nK = 10−9 K) in 1994, they used laser equipment to create an optical lattice to adiabatically cool caesium atoms. They then turned off the entrapment lasers and directly measured atom velocities of 7mm per second in order to calculate their temperature.
Molecules, such as oxygen (O2), have more degrees of freedom than single spherical atoms: they undergo rotational and vibrational motions as well as translations. Heating results in an increase in temperature due to an increase in the average translational energy of the molecules. Heating will also cause, through equipartitioning, the energy associated with vibrational and rotational modes to increase. Thus a diatomic gas will require a higher energy input to increase its temperature by a certain amount, i.e. it will have a higher heat capacity than a monatomic gas.
The process of cooling involves removing thermal energy from a system. When no more energy can be removed, the system is at absolute zero, which cannot be achieved experimentally. Absolute zero is the null point of the thermodynamic temperature scale, also called absolute temperature. If it were possible to cool a system to absolute zero, all motion of the particles comprising matter would cease and they would be at complete rest in this classical sense. Microscopically in the description of quantum mechanics, however, matter still has zero-point energy even at absolute zero, because of the uncertainty principle.
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