Temperature infinite

These are the same states as in Figure Bl.l 1.8, but attention is now drawn to the populations of the four spin states, each reduced by subtracting the 25% population that would exist at very low field, or alternatively at infinite temperature. The figures above each level are these relative differences, in convenient units. The intensity of any one transition, i.e. of the relevant peak in the doublet, is proportional to the difference of these differences, and is therefore proportionally relative to unity for any transition at Boltzmaim equilibrium, and 4 for any transition. 

It should be recognized that the smallest increment of energy will result in infinite temperatures if it is localized in a vanishingly small volume of material. Indeed, one can easily predict temperatures that vary by an order of... 

Setting p = p = Pf, at equilibrium, we find that the only real stable nonzero solution for 0 < pe < 1 is Pe 0.370. This uncorrelated approximation actually describes the infinite temperature limit (effectively, T >> 1) rather well, since as the temperature increases, local correlations of the basic Life rule steadily decrease. 

This equation describes the series of lines in Figure 5, the variable parameter being represented by The physical meaning of coefficients aj follows from comparison of eqs.(17), (18) and (19) ao equals logAo and ai=-Eo/ 2.303 RT, the subscripts 0 referring to the standard substituent, az =p ,at the infinite temperature, and as = -/3pco. Hence, 0 is obtained as -aj/a2. Direct correlations of AH and AS with a (176, 197, 198) or other parameters (199, 200) are usually bad and cannot serve to obtain the AH/AS relationship. 

The above two examples illustrate that the value of the partition function is an indicator for how many of the energy levels are occupied at a particular temperature. At T = 0, where the system is in the ground state, the partition function has the value q = 1. In the limit of infinite temperature, entropy demands that all states are equally occupied and the partition function becomes equal to the total number of energy levels. 

Fig. 7 Snapshots of the simulation systems for Cl, C2, and C3 after an isothermal crystallization following the quenching from the infinite temperature to a temperature of 2.857 Ec/kB [84]...

A to B, while a temperature drop, ATad, is observed during the adiabatic process A C. The maximum magnetic entropy for a system with a spin s, ftln(2s+ 1), reached at infinite temperatures, is indicated as a grey broken line. 

The intercept of a Clapeyron graph is not useful its value may best be thought of as the pressure exerted by water boiling at infinite temperature. This alternative of the Clausius-Clapeyron equation is sometimes referred to as the linear (or graphical) form. 

At high temperature Equation 4.95 shows the limiting behavior of (s/s ) f as it decays to its value of unity at infinite temperature... 

The importance of understanding isotope effects in the high temperature (classical) limit has been stressed before. In the limit of infinite temperature, the reduced isotopic partition function ratios all go to unity and k /k2 also goes to unity. The kinetic isotope effect becomes... 

In the noninteracting case (or infinite temperature) the model is analyzed very simply = 0, iciCfj> = 0, and thus... 

In the preceding expression, log(FJ is related to the depression of the fall-off curve at the center relative to the L-H expression in a og k/k ) vs. log(2f/(l -I- X)) plot. The values for F<. can then be related to the properties of specific species and reaction and temperature using methods discussed in Gardiner and Troe (1984). In Fig. 19, values of F for a variety of hydrocarbon decompositions are presented. As evident from this figure, in the limit of zero or infinite temperatures and pressures, all reactions exhibit Lindemann-Hinshelwood behavior and F approaches unity. From this figure, it is clear that L-H analysis generally does an adequate job in... 

It should be apparent that the magnetic susceptibility x of a paramagnetic sample (corrected for diamagnetism) should be infinite at absolute zero (with perfect alignment of the magnetic dipoles, or 100% population of the lowest Zeeman state) and zero at infinite temperature (random alignment of dipoles, equal population of Zeeman states). An obvious expression which embodies these conditions is ... 

One particular case of Eq. (A 12) has attracted considerable attention. If one sets M = E and considers the infinite temperature limit, the probabilities of the macrostates ) and Ej can be replaced by the associated values of the density-of-states function G(Ej) and G(Ej). The resulting equation has been christened the broad-histogram relation [128] it forms the core of extensive studies of transition probability methods referred to variously as flat histogram [129] and transition matrix [130]. Applications of these formulations seem to have been restricted to the situation where the energy is the macrovariable, and the energy spectmm is discrete. 

The assumption is typically made that the nuclear fuel can be treated as a heat source at an infinite temperature [12]. 

The mixed quantum classical description of EET can be achieved in using Eq. (49) together with the electronic ground-state classical path version of Eq. (50). As already indicated this approach is valid for any ratio between the excitonic coupling and the exciton vibrational interaction. If an ensemble average has been taken appropriately we may also expect the manifestation of electronic excitation energy dissipation and coherence decay, however, always in the limit of an infinite temperature approach. 

Between the activation energy AE, the correlation frequency vc and the correlation frequency v00 for infinite temperatures a dependence corresponding to the Arrhenius equation is assumed ... 

Case (ii), where the populations are equal, is known as the saturation condition, or infinite temperature case. It can be achieved in many experiments if sufficient electromagnetic radiation power is available, and in some double resonance experiments it is actually an aim. Case (iii) represents a population inversion, sometimes referred to as a negative temperature, whilst case (iv) is described as a population cooling, in the sense that it corresponds to an abnormally low temperature, even though in other respects the temperature may be considered to be normal. 

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