The
temperature of anobject depends on how fast the atoms andmolecules which make up theobject can shake, or oscillate. For example, as water cools, the slowingoscillations of the molecules allow the water to freeze into ice. Thetemperature which corresponds to this point is called
absolute zero. TheCelsius scale sets the freezing point of water at 0º Celsius and the boilingpoint at 100º Celsius. This scale uses the same temperature steps as theCelsius scale, but is shifted downward. The clearest example is agas where the internal thermal energy is just the kinetic energy of the atomsand is proportional to the pressure P (see The frequency of thiselectromagnetic radiation is proportional to the absolute temperature. Some700,000 years after the start of the Universe a "sea" of freeelectrons and protons prevented the free propagation of light (think of the sunwhere the atoms are ionised - we can't see through it). The Universe has sinceexpanded dramatically and the radiation cooled. This is the
lowest naturaltemperature but is available only in deep space. As the pump removes thevapour, the
liquid evaporates, which requires energy (latent heat ofevaporation). This comes from the thermal or internal energy of the liquidwhich cools to about 1.2 K, depending on the size of the pump. The most usualhelium atoms, 4He (helium-four), have 2 protons and 2 neutrons inthe nucleus and 2 orbiting electrons. If the 3He atoms in the 6%solution are pumped away, 3He atoms from the pure 3Hewill "evaporate" into the dilute solution and produce cooling (below1 K the 4He just acts as an inert solvent in which the 3Heatoms move). The difference now is that the "vapour pressure" of 6% 3Heatoms remains constant and the cooling power continues to very lowtemperatures. Even lower temperatures canbe obtained using the magnetic properties of the nuclei of atoms such ascopper. The copper is then thermally isolated and the field is reduced to a lowvalue. The world record for thelowest temperature achieved is not a simple race. Since the nuclei themselvesare used to produce the cooling, the lowest temperatures ever obtained are inthe nuclear magnetic thermal energy. The fastest atoms can escape, as in theevaporation from a liquid. The atoms have cooled. This is the lowest kinetictemperature ever achieved. The magnetic field was thenswitched off, removing the trap. The motion of the atoms enables their originalvelocites to be measured. It is forbidden by the third law of thermodynamics.Many other fixed points are used to define the scale over a widetemperature rangesuch as the freezing point of gold at 1337.33 K and the triplepoint of hydrogen at 13.8033 K. At lower temperatures the vapour pressure ofliquid helium is used.Only the fastest atoms (shown inred) can escape from the liquid. As the vapour is pumped away it is replaced bythe evaporation of these atoms. The slower atoms (shown in blue) cannot escapefrom the attraction of the other atoms. Hence the average speed andkinetic energy of the atoms in the liquid decreases and the temperature drops.It is the only substance which remains liquid down to the very lowesttemperatures. Actually various kinds of "temperature" appear in theliterature of physics (e.g., kinetic temperature, color temperature). Therelevant one here is the one from thermodynamics, in some sense the mostfundamental. The atoms of S3 can share the
total energy in many ways. Eachstate corresponds to a particular division of the total energy in the twosubsystems S1 and S2. It's the one with the overwhelmingly largest numberof microstates for the total system S3. The atoms are not free to movefrom their positions on the wire. The total energy of the system, in amagnetic field of strength B, pointing down, is (N+ - N-)*uB, where u is themagnetic moment of each atom and N+ and N- are the number of atoms with spin upand down respectively. It is negative when the majority are down andpositive when the majority are up. The lowest possible energyste, all the spins pointing down, gives the system a total energy of -NuB,and temperature of absolute zero. There is only one configuration of thesystem at this energy, i.e., all the spins must point down. The entropyis the log of the number of microstates, so in this case is log(1) = 0. Ifwe now add a quantum of energy, size uB, to the system, one spin is allowed toflip up. The entropy is increasing quickly, and the temperature is risingas well. The entropy goes on increasing as the energy is lowered. It makessense to define the "spin-temperature" of a collection of atoms, solong as one condition is met: the coupling between the atomic spins and theother degrees of freedom is sufficiently weak, and the coupling between atomicspins sufficiently strong, that the timescale for energy to flow from the spinsinto other degrees of freedom is very large compared to the timescale forthermalization of the spins among themselves. Then it makes sense to talkabout the temperature of the spins separately from the temperature of the atomsas a whole.