Hydrogen Einstein temperature

L, J, Dq and Bq are constants describing the hydrogen molecules. J is the Einstein temperature of the gas molecule, Dq its dissociation energy (e.g. the ground state energy of the gas molecule relative to the atoms at rest) and the rotational constant of the X2 molecule. Most of the translational rotational partition function is given by LT /2, The values of the constants L, J and M necessary to calculate gS are listed in Table I (see Ref. 14 for more details). ... 

It is difficult to determine the 5 parameters A, B, C, N and E in the Eqs. 5-8 in a unique i/ay because all contribute to -In K°° at high temperatures. To reduce the number of free parameters we assume N = 1 for octahedral site occupancy and select a value of C similar to those obtained by inelastic neutron scattering spectroscopy. In the case of D and T the Einstein temperature Cq and Cj were obtained by scaling C with the inverse of the square root of the hydrogen mass. The results are listed in Table II and plotted as solid lines in the Figs. 2 and 3. One sees that Eqs. 5-7 give a very good description of the -In C values. 

In Fig. 3, the orientational diffusion time constants ror of the first solvation shell of the halogenie anions CD. Br, and D are presented as a function of temperature. From the observation that ror is shorter than rc, it follows that the orientational dynamics of the HDO molecules in the first solvation shell of the Cl ion must result from motions that do not contribute to the spectral diffusion, i.e. that do not affect the length of the O-H- -Cl hydrogen bond. Hence, the observed reorientation represents the orientational diffusion of the complete solvation structure. Also shown in Fig. 3 are fits to the data using the relation between ror and the temperature T that follows from the Stokes-Einstein relation for orientational diffusion ... 

Wilkinson s catalyst. Irradiation at 366 nm of 0.001 M RhCPPh NO and 1 M cyclohexene in o-dichlorobenzene was carried out under 1 atm H2 at room temperature. The hydrogen uptake was monitored using a mercury manometer attached to the reaction flask. Hydrogen was added periodically in order to maintain 1 atm pressure in the system. The solvent and olefin were distilled twice and degassed by three freeze-pump-thaw cycles before use. A 1000 watt Hg lamp filtered with a glass filter to isolate the 366 nm Hg line was used for all photolysis experiments. The light intensity, measured by ferrioxalate actinometry, was 1.0 x 10 6 einsteins/min. 

After years of pioneering efforts atomic hydrogen has now been successfully cooled to a sufficiently low temperature for Bose-Einstein Condensation (BEC) and high precision spectroscopy. 

We recall that Bose-Einstein condensation is the macroscopic occupation of the ground state of a system at finite temperature. For a weakly interacting gas, this phase transition occurs when the inter-particle spacing becomes comparable to the thermal de Broglie wavelength A = /2nh /mkBT, where ks is the Boltzmann constant and T is the temperature. A rigorous treatment for the ideal Bose gas yields n > 2.61221 , where n is the density [35]. At a temperature of 50 yuK, for instance, the critical density for hydrogen is 1.8 x 10 cm. ... 

The adiabatic flame temperature is the flnal temperature reached by the system if one mole of the substance is burned adiabatically under the specified conditions. Using the values of C, derived from the C s in Table 4.3 and data from Table A-V, calculate the adiabatic flame temperature of hydrogen burned in (a) oxygen, (b) air. (c) Assume that for water vapor, Cp/R =4.0 -I-/ifiJT) -t- /(O2/T) + /where/(9/T) is the Einstein function, Eq. (4.88), and the values of 1.02. 3 are in Table 4.4. Calculate the adiabatic flame temperature in oxygen using this expression for Cp and compare the result with (a). 

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