Rotational temperature, equilibrium

The model [39] was developed using three assumptions the conformers are in thermodynamic equilibrium, the peak intensities of the T-shaped and linear features are proportional to the populations of the T-shaped and linear ground-state conformers, and the internal energy of the complexes is adequately represented by the monomer rotational temperature. By using these assumptions, the temperature dependence of the ratio of the intensities of the features were equated to the ratio of the quantum mechanical partition functions for the T-shaped and linear conformers (Eq. (7) of Ref. [39]). The ratio of the He l Cl T-shaped linear intensity ratios were observed to decay single exponentially. Fits of the decays yielded an approximate ground-state binding... 

The overall OD vibrational distribution from the HOD photodissociation resembles that from the D2O photodissociation. Similarly, the OH vibrational distribution from the HOD photodissociation is similar to that from the H2O photodissociation. There are, however, notable differences for the OD products from HOD and D2O, similarly for the OH products from HOD and H2O. It is also clear that rotational temperatures are all quite cold for all OH (OD) products. From the above experimental results, the branching ratio of the H and D product channels from the HOD photodissociation can be estimated, since the mixed sample of H2O and D2O with 1 1 ratio can quickly reach equilibrium with the exact ratios of H2O, HOD and D2O known to be 1 2 1. Because the absorption spectrum of H2O at 157nm is a broadband transition, we can reasonably assume that the absorption cross-sections are the same for the three water isotopomer molecules. It is also quite obvious that the quantum yield of these molecules at 157 nm excitation should be unity since the A1B surface is purely repulsive and is not coupled to any other electronic surfaces. From the above measurement of the H-atom products from the mixed sample, the ratio of the H-atom products from HOD and H2O is determined to be 1.27. If we assume the quantum yield for H2O at 157 is unity, the quantum yield for the H production should be 0.64 (i.e. 1.27 divided by 2) since the HOD concentration is twice that of H2O in the mixed sample. Similarly, from the above measurement of the D-atom product from the mixed sample, we can actually determine the ratio of the D-atom products from HOD and D2O to be 0.52. Using the same assumption that the quantum yield of the D2O photodissociation at 157 nm is unity, the quantum yield of the D-atom production from the HOD photodissociation at 157 nm is determined to be 0.26. Therefore the total quantum yield for the H and D products from HOD is 0.64 + 0.26 = 0.90. This is a little bit smaller ( 10%) than 1 since the total quantum yield of the H and D productions from the HOD photodissociation should be unity because no other dissociation channel is present for the HOD photodissociation other than the H and D atom elimination processes. There are a couple of sources of error, however, in this estimation (a) the assumption that the absorption cross-sections of all three water isotopomers at 157 nm are exactly the same, and (b) the accuracy of the volume mixture in the... 

Ratera et al. (2003) discovered valence tautomerism in the ferrocene connected through the ethylenic bond with perchlorotriphenylmethyl radical. As ascertained by Moessbauer spectroscopy, this species in the solid state exhibited a thermally induced intramolecular electron transfer resulting in the formation of ferrocenium and perchlorotriphenylmethyl anion moieties. The authors used the initial species in its trans form. If the cis form would be available, the possibility of rotation around the ethylenic bond would be interesting to disclose. According to the authors, the interconversion of the cation-radical and anion centers proceeds gradually. At ambient temperature, equilibrium composition of the tautomers is achieved. This peculiarity is important with respect to potential technical applications. 

We start at equilibrium. In the high-temperature approximation, the equilibrium density operator is proportional to the weighted sum of the operators, which we will call 4- We assume that a simple, non-selective pulse has been used at the start of the experiment. This rotates the equilibrium 2 magnetization onto the x axis. After the pulse the density matrix is therefore given by 4, and it will evolve as in equation (7) or (8). If we substitute (8) into (10), we get the NMR signal as a function of time t, as given by (11). The detector sees each spin (but not each coherence ) equally well. 

The characteristic rotational temperatures 0rot for H2, HD, and D2 are 84.8, 63.8, and 42.6°K, respectively. The symmetry of H2 and D2 require that for optical transitions, AJ = 2, while for HD, AJ = 1. At room temperature, normal hydrogen -H2 is composed of 25% para-H2 (,J even) and 75% ortho-H2 (J odd), while at lower temperatures, equilibrium hydrogen contains an increasing proportion of para-H2. These rotational species do not change form in gaseous collisions, so that it is possible to select nearly pure p-H2 (e.g., boil-off from liquid H2) and perform measurements on it and its mixtures with n-H2 over a range of temperatures, before surface catalysis... 

If, outside the thermal equilibrium, such as in supersonic flows, the two temperatures differ, then the two temperatures can be derived separately. Fig. 6.8-13 shows the appearance of the O2 Stokes Q branch at a fixed rotational temperature of 300 K and at three different vibrational temperatures. 

Equilibrium readings are taken on aliquots of the original solution that has been held for 24 hours or longer in the water bath at the desired temperature. Equilibrium specific rotations are determined on separate solutions, carefully and leisurely made up and kept for 24 hours or longer. The data for the mutarotation are converted into specific rotations by relating the observed equilibrium rotation to that of the carefully prepared solution. 

The ICP is almost in local thermal equilibrium. Indeed, the excitation temperatures (from atomic line intensity ratios) are about 6000 K [382] and the rotation temperatures (from the rotation lines in the OH bands) are 4000-6000 K (see Refs. [383, 384]). From the broadening of the Hg-line, an electron number density of 1016 cm 3 is obtained, whereas from the intensity ratio of an ion and an atom line of the same element the electron number density found is 1014 cm-3. It has also been reported that measured line intensity ratios of ion to atom lines are higher by a factor of 100 than those calculated for a temperature of 6000 K and the electron number density found is 1016 cm 3. This indicates the existence of over-ionization. This can be understood from the excitation processes taking place. They include the following. 

The temperature obtained here is for the tangential height of 21 km and agrees with that of the U.S. Standard Atmospheric Supplements, 1966, as compiled in the "Handbook of Geophysics and Space Environments". This means, that this altitude, the 02( g) molecules are in thermal equilibrium with ground state N2 molecules the collisional deactivation is faster than activation of oxygen photochemical processes (12). Thus, we were able to confirm that the present spectrometer measures the effective spectrum necessary to determine rotational temperatures with a satisfactory accuracy. The rotational temperatures of the O2 ( F ) molecule, at other altitudes were similarly obtained, the final report will be presented elsewhere (13). 

A question may be raised concerning the significance of an equilibrium Boltzmann rotational temperature for N2 and the propriety of equating it to the temperature of the gas stream, since under the condi-... 

For this reaction, a separate study of the rate constant dependence on the vibrational temperature of the N2 reactant was made. " However, in that study both the ion center of mass (CM) translational energy and the rotational temperature were 300 K. While this was an obviously important step, no true temperature dependent study was made over 900 K. True temperature here refers to the case where the translational, rotational, and vibrational degrees of freedom of the reactants are all in equilibrium and can be represented by a single temperature. 

In the same studies a determination of the vibrational temperature from the relative intensities of bands in the second positive system of N2 gave values in the range 2200-5000 K which did not change with increase in specific energy. Since the rotational temperature, probably close to the gas temperature, was almost 90% lower than the vibrational temperature, the plasma was non-isothermal under the experimental conditions which favored hydrazine formation. The non-equilibrium population of the highest vibrational levels of the nitrogen molecule has been adduced as indirect confirmation of the theory of energy catalysis (see Sect. 3). 

Typical quenching cross-sections by cold ( 1 K) helium yield a rotational quench on the order of every 10 to 100 elastic collisions whereas it can take more than 10 elastic collisions before a vibrational quench [12]. DeLucia and coworkers measured rotationally inelastic cross-sections with He of H2S, NO, and H2CO. Typical values were on the order of 1 to 10 x 10 cm at 1K [13,15,56], which is about 10 to 100 times smaller than a typical diffusive cross-section at 1 K. We therefore expect buffer-gas cooling to effectively thermalize the rotational temperature of the target molecules while leaving the vibrational temperature out of thermal equilibrium. Because the rotational and translational energy transfer cross-sections are similar, thermalization of both happens rapidly and in tandem in butfer-gas cooling. We do not detect nonequilibrium rotational populations. 

The characteristic rotational temperature, the rotational quantum Trot = h STt kl (1 is the moment of inertia) of some diatomic molecules [55] is, H2 85 K, O2 2.1 K, NO 2.4 K, CI2 0.4 K. As a consequence, the rotation of the diatomic molecules is classical at ambient conditions and each rotational degree of freedom has the energy 1/2 kT at equilibrium. That immediately yields an estimate of the rotational correlation time t,o, in the absence of an external field [58] ... 

In most of industrial applications or geophysical phenomena, the nitrogen plasma is in a state of non-equilibrium. Consequently, the gas temperature is much lower than the electron temperature. In order to estimate approximate value to the gas temperature, rotational temperature measurement is being frequently applied in practical researches and industries (Hrachova et al., 2002). Particularly, the spectrum of the second positive system (2PS), emitted as transitions from C Ou state to B Ilg state, is easy to obtain its vibrational and rotational temperatures owing to its simple transition scheme. These temperatures are determined as best theoretical fitting parameters for the spectrum observed experimentally. Observation of this band is also easy from the experimental point of view (Phillips, 1976 Koike et al., 2004 Kobori et al., 2004 Yuji et al, 2007). 

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