Absolute zero, thermodynamic properties

The scaled elasticities of a reversible Michaelis Menten equation with respect to its substrate and product thus consist of two additive contributions The first addend depends only on the kinetic propertiesand is confined to an absolute value smaller than unity. The second addend depends on the displacement from equilibrium only and may take an arbitrary value larger than zero. Consequently, for reactions close to thermodynamic equilibrium F Keq, the scaled elasticities become almost independent of the kinetic propertiesof the enzyme [96], In this case, predictions about network behavior can be entirely based on thermodynamic properties, which are not organism specific and often available, in conjunction with measurements of metabolite concentrations (see Section IV) to determine the displacement from equilibrium. Detailed knowledge of Michaelis Menten constants is not necessary. Along these lines, a more stringent framework to utilize constraints on the scaled elasticities (and variants thereof) as a determinant of network behavior is discussed in Section VIII.E. 

In Section 2.1, we remarked that classical thermodynamics does not offer us a means of determining absolute values of thermodynamic state functions. Fortunately, first-principles (FP), or ab initio, methods based on the density-functional theory (DFT) provide a way of calculating thermodynamic properties at 0 K, where one can normally neglect zero-point vibrations. At finite temperatures, vibrational contributions must be added to the zero-kelvin DFT results. To understand how ab initio thermodynamics (not to be confused with the term computational thermochemistry used in Section 2.1) is possible, we first need to discuss the statistical mechanical interpretation of absolute internal energy, so that we can relate it to concepts from ab initio methods. 

Any system above zero absolute temperature has particles - atoms and molecules - in constant motion. Atoms and molecules in a gaseous system possess the maximum variety of motion - transport, spin, vibratory, etc. These particles constantly interact with each other and at each interaction, quantum of motion of all these types change - and in a very random manner as number of particles involved are huge (about 6 10 in a g.mole). If such interactions are all mechanical interaction i.e., free from chemical or similar changes, such as particles getting associated, or breaking up during interactions), the system remains amenable to statistical interpretation of thermodynamic properties. 

The superscript zero on a thermodynamic function (for example, AH0) indicates that the corresponding process has been carried out under standard conditions. The standard state for a substance is a precisely defined reference state. Because thermodynamic functions often depend on the concentrations (or pressures) of the substances involved, we must use a common reference state to properly compare the thermodynamic properties of two substances. This is especially important because for most thermodynamic properties, we can measure only changes in that property. For example, we have no method for determining absolute values of enthalpy. We can measure only enthalpy changes (AH values) by performing heat flow experiments. 

Even in its original form the theorem deals with chemical reactions and changes of state, that is to say, with the most important natural phenomena accompanied by evolution or absorption of heat. It is therefore natural to suspect that the heat theorem, like the two law s of thermodynamics, has its origin in the nature of heat itself. The laws of thermodynamics, as was shown in Chapters III. and V., could be traced back to the results of our everyday experience (impossibility of perpetual motion of the first and second kinds). This simple method of derivation fails in the case of the new theorem because temperatures in the neighbourhood of the absolute zero can never be the immediate objects of experience. They can only be reached by refined experimental methods. For this reason Nernst s theorem can never be susceptible of direct experimental proof, and can only be tested by its consequences. We can deduce the theorem, however, from a more general principle regarding the nature of heat and the properties of the thermodynamic functions. 

Re Entry [63], Ref. [63]) In Ref. [63], Dr. Peter Atkins doesn t seem to explicitly state that negative Kelvin temperatures are hotter than ooK, not colder than OK. He admits the possibility of attaining OK via noncyclic processes, but as we showed in Sect. 3. of this chapter purely dynamic — as opposed to thermodynamic — limitations may contravene. On pp. 103-104 of Ref. [63], he correctly states that the third law of thermodynamics is "not really in the same league" as the zeroth, first, and second laws, and that "hints of the Third Law of Thermodynamics are already present in the consequences of the second law," but that the Third Law of Thermodynamics is "the final link in the confirmation that Boltzmann s and Clausius s definitions refer to the same property." But his statement that "we need to do an ever increasing, and ultimately infinite, amount of work to remove energy from a body as heat as its temperature approaches absolute zero" neglects the rapid decrease in specific heat as absolute zero is approached as discussed in Sect. 2. of this chapter. 

Note Liquid helium has unique thermodynamic properties too complex to be adequately described here. Liquid He I has refr index 1.026,dO.l 25, and is called a quantum fluid because it exhibits atomic properties on a macroscopic scale. Its bp is near absolute zero and viscosity is 25 micropoises (water = 10,000). He II, formed on cooling He I below its transition point, has the unusual property of superfluidity, extremely high thermal conductivity, and viscosity approaching zero. 

Another remark to be made is that the absolute values of enthalpy and entropy are generally unknown. (Only a perfect crystal of one component at zero absolute temperature has zero entropy.) Quantitative results therefore mostly refer to some standard state (usually 0°C and 1 bar), where these parameters are taken to be zero. One always considers the change in thermodynamic properties, and that is quite sufficient. At constant pressure and temperature, the basic equation thus is... 

The thermodynamic quantities listed are for one mole of substance in its standard state, that is at 1 atm pressure. The enthalpies and free energies of formation of substances are the changes in those thermodynamic properties when a substance in its standard state is formed from its elements in their standard states. The standard state of an element is its normal physical state at 1 atm, and for the data given in these tables, 298.15 K. The entropies listed are absolute in the sense that they are based on the assumption that the entropy of a pure substance is zero at the absolute zero of temperature. 

The purpose of the present paper is to study the properties of an electron gas moving in a lattice of positive charges at absolute zero. This picture should correspond roughly to actual metals or metalHc solutions and in principle should furnish some new insight into the cohesive properties of pure metals and into the thermodynamic properties of mixing of allo. ... 

It is possible to effect some simplification in the equations defining the thermodynamic properties of the ions by introducing additional conventions (a convention can be defined somewhat facetiously as a convenient assumption that we know is not true). If, for example, we decide that the absolute free energies and enthalpies of all pure elements are to be set at zero, then the defining equation for free energies and enthalpies (equation 17.21) becomes the same as that for S, V, and Cp (equation 17.22). If in addition we define all properties of the hydrogen ion as zero, then the conventional ionic properties become the same as the corresponding absolute properties, and we could have stopped at equation (17.19). 

Giant clusters can serve as useful models for imderstanding the structure and chemical behavior of dispersed metals. Magnetic and thermodynamic measurements in the vicinity of absolute zero showed the Pdsei species to be the smallest particles which still have the properties of molecular clusters that distinguish them from bulk metal. 

The versatile nature of calorimeters, commercial and home-made, instruments allows direct access to the thermodynamic properties of materials being studied. Calorimetry is unintrusive in the way information is extracted during a study and highly versatile, measuring from nW to MW, from near absolute zero to several thousand kelvin. The sample studied can be in any phase or mixtures of phases and calorimetry can, in principle, be used to obtain all the thermodynamic and kinetic parameters relating to a reaction, and is limited only by the sensitivity of the instrument to detect a change. 

The thermodynamic properties for neon were calculated from the following equations, where the absolute value of entropy and internal energy are taken to be zero for the saturated liquid at the triple point. 

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