|
Absolute zero is the lower limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reaches its minimum value, taken as 0. The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as −273.15° on the Celsius scale (International System of Units),〔 Note: The triple point of water is 0.01 °C, not 0 °C; thus 0 K is −273.15 °C, not −273.16 °C.〕 which equates to −459.67° on the Fahrenheit scale (United States customary units or Imperial units). The corresponding Kelvin and Rankine temperature scales set their zero points at absolute zero by definition. It is commonly thought of as the lowest temperature possible, but it is not the lowest ''enthalpy'' state possible, because all real substances begin to depart from the ideal gas when cooled as they approach the change of state to liquid, and then to solid; and the sum of the enthalpy of vaporization (gas to liquid) and enthalpy of fusion (liquid to solid) exceeds the ideal gas's change in enthalpy to absolute zero. In the quantum-mechanical description, matter (solid) at absolute zero is in its ground state, the point of lowest internal energy. The laws of thermodynamics dictate that absolute zero cannot be reached using only thermodynamic means, as the temperature of the substance being cooled approaches the temperature of the cooling agent asymptotically. A system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state at absolute zero. The kinetic energy of the ground state cannot be removed. Scientists have achieved temperatures extremely close to absolute zero, where matter exhibits quantum effects such as superconductivity and superfluidity. ==Thermodynamics near absolute zero== At temperatures near 0 K, nearly all molecular motion ceases and Δ''S'' = 0 for any adiabatic process, where ''S'' is the entropy. In such a circumstance, pure substances can (ideally) form perfect crystals as ''T'' → 0. Max Planck's strong form of the third law of thermodynamics states the entropy of a perfect crystal vanishes at absolute zero. The original Nernst ''heat theorem'' makes the weaker and less controversial claim that the entropy change for any isothermal process approaches zero as ''T'' → 0: : The implication is that the entropy of a perfect crystal simply approaches a constant value. The Nernst postulate identifies the isotherm T = 0 as coincident with the adiabat S = 0, although other isotherms and adiabats are distinct. As no two adiabats intersect, no other adiabat can intersect the T = 0 isotherm. Consequently no adiabatic process initiated at nonzero temperature can lead to zero temperature.'' (≈ Callen, pp. 189–190) An even stronger assertion is that ''It is impossible by any procedure to reduce the temperature of a system to zero in a finite number of operations.'' (≈ Guggenheim, p. 157) A perfect crystal is one in which the internal lattice structure extends uninterrupted in all directions. The perfect order can be represented by translational symmetry along three (not usually orthogonal) axes. Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping. For substances which have two (or more) stable crystalline forms, such as diamond and graphite for carbon, there is a kind of "chemical degeneracy". The question remains whether both can have zero entropy at ''T'' = 0 even though each is perfectly ordered. Perfect crystals never occur in practice; imperfections, and even entire amorphous materials, simply get "frozen in" at low temperatures, so transitions to more stable states do not occur. Using the Debye model, the specific heat and entropy of a pure crystal are proportional to ''T'' 3, while the enthalpy and chemical potential are proportional to ''T'' 4. (Guggenheim, p. 111) These quantities drop toward their ''T'' = 0 limiting values and approach with ''zero'' slopes. For the specific heats at least, the limiting value itself is definitely zero, as borne out by experiments to below 10 K. Even the less detailed Einstein model shows this curious drop in specific heats. In fact, all specific heats vanish at absolute zero, not just those of crystals. Likewise for the coefficient of thermal expansion. Maxwell's relations show that various other quantities also vanish. These phenomena were unanticipated. Since the relation between changes in Gibbs free energy (''G''), the enthalpy (''H'') and the entropy is : thus, as ''T'' decreases, Δ''G'' and Δ''H'' approach each other (so long as Δ''S'' is bounded). Experimentally, it is found that all spontaneous processes (including chemical reactions) result in a decrease in ''G'' as they proceed toward equilibrium. If Δ''S'' and/or ''T'' are small, the condition Δ''G'' < 0 may imply that Δ''H'' < 0, which would indicate an exothermic reaction. However, this is not required; endothermic reactions can proceed spontaneously if the ''T''Δ''S'' term is large enough. Moreover, the slopes of the derivatives of Δ''G'' and Δ''H'' converge and are equal to zero at ''T'' = 0. This ensures that Δ''G'' and Δ''H'' are nearly the same over a considerable range of temperatures and justifies the approximate empirical Principle of Thomsen and Berthelot, which states that ''the equilibrium state to which a system proceeds is the one which evolves the greatest amount of heat'', i.e. an actual process is the ''most exothermic one''. (Callen, pp. 186–187) One model that estimates the properties of an electron gas at absolute zero in metals is the Fermi gas. The electrons, being Fermions, have to be in different quantum states, which leads the electrons to get very high typical velocities, even at absolute zero. The maximum energy that electrons can have at absolute zero is called the Fermi energy. The Fermi temperature is defined as this maximum energy divided by Boltzmann's constant, and is of the order of 80,000 K for typical electron densities found in metals. For temperatures significantly below the Fermi temperature, the electrons behave in almost the same way as at absolute zero. This explains the failure of the classical equipartition theorem for metals that eluded classical physicists in the late 19th century. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Absolute zero」の詳細全文を読む スポンサード リンク
|