Thermal agitation

Doppler broadening arises from the random thermal agitation of the active systems, each of which, in its own test frame, sees the appHed light field at a different frequency. When averaged over a Maxwellian velocity distribution, ie, assuming noninteracting species in thermal equilibrium, this yields a line width (fwhm) in cm C... 

Figure lb shows the effects of natural and introduced thermal agitation which tend to equali2e the distribution of ions. The differences in profile between dye and Cl are due only to the dye exhibiting strong close-range forces of attraction. 

Diffusion filtration is another contributor to the process of sand filtration. Diffusion in this case is that of Brownian motion obtained by thermal agitation forces. This compliments the mechanism in sand filtration. Diffusion increases the contact probability between the particles themselves as well as between the latter and the filter mass. This effect occurs both in water in motion and in stagnant water, and is quite important in the mechanisms of agglomeration of particles (e.g., flocculation). 

Warme-bestandigkeit, /. resistance to heat, -bewegung,/. heat motion, thermal agitation,. bilanz, /. heat balance, -bildner, m. heat producer, -bildung, /. production of heat, -bindtmg,/. absorption of heat. 

In a liquid that is in thermodynamic equilibrium and which contains only one chemical species, the particles are in translational motion due to thermal agitation. The term for this motion, which can be characterized as a random walk of the particles, is self-diffusion. It can be quantified by observing the molecular displacements of the single particles. The self-diffusion coefficient is introduced by the Einstein relationship... 

With rise of temperature, the polarization produced by given electrostatic charges decreases, because the thermal agitation maintains, in opposition to the field, a higher degree of disorder. At a higher temperature the loss of free energy by the dielectric is smaller that is to say,... 

In Fig. 37 two areas have been shaded. The area in the upper left corner, where protons in occupied levels are unstable, we have already discussed. In the lower right-hand corner the shaded area is one where vacant proton levels cannot remain vacant to any great extent. In aqueous solution any solute particle that has a vacant proton level lower than that of the hydroxyl ion will capture a proton from the solvent molecule, since the occupied level of the latter has the same energy as the vacant level of a hydroxyl ion. Consequently any proton level that would lie in this shaded area will be vacant only on the rare occasions when the thermal agitation has raised the proton to the vacant level of a hydroxyl ion. On the other hand, there are plenty of occupied proton levels that lie below the occupied level of the H2O molecule. For example, the occupied level of the NH3 molecule in aqueous solution lies a long way below that of H20. 

In contrast to this, consider next a solution of sodium acetate. From vSec. 09 we know that in such a solution the thermal agitation raises a certain number of protons from the solvent molecules to the vacant proton levels of the (CH GOO) ions. In the aqueous solution of such a salt, this process is known as the hydrolysis of the salt and is traditionally regarded as a result of the self-ionization of the water. In Fig. 36, however, it is clear that in the proton transfer... 

We have discussed the triply charged ion Fe+++ in aqueous solution. Let us consider now the water molecules that are in contact with such an ion, and let Fig. 50a depict one such H2O molecule. The protons in the H2O molecule will be repelled by the large positive charge of the Fe+++ ion—will be so strongly repelled that it is possible that, sooner or later, the thermal agitation will be sufficient to transfer a proton to a... 

The Sulfate Ion. In Fig. 36 we see that the vacant level of the (SO ) ion in aqueous solution lies only 0.13 electron-volt above the occupied level of HCOOH. If the interval has a comparable value when sulfate ions are present in formic acid as solvent, the thermal agitation should transfer a large number of protons from solvent HCOOH molecules to the (SO4)" ions. This was found to be the case when Na2SC>4 was dissolved in pure formic acid. Such a transfer of protons from molecules of a solvent to the anions of a salt is analogous to the hydrolysis of the salt in aqueous solution and is known as solvolysis, as mentioned in Sec. 76. In a 0.101-molal solution of Na2SC>4 in formic acid the degree of the solvolysis was found to be 35 per cent.1... 

We may now emphasize the mutual control that is exercised between adjacent water molecules. The orientation of molecule 5, for example, is controlled by the orientations of 1, 6, 7, and 8 and we may say that, in turn, molecule 5 does its share in controlling the orientations of 1, 6, 7, and 8. We may add that, throughout the liquid, near its freezing point, any local ordered arrangement arising from this kind of mutual control is not easily upset by the thermal agitation present in the liquid. 

Among the molecules, however, business is going on as usual. Iodine dissolves by the detachment of surface layer molecules from the iodine crystals. The rate at which this process occurs is fixed by the stability of the crystal (tending to hold the molecules in the surface layer) and the temperature (the thermal agitation tending to dislodge the molecules from their lattice positions). As the dissolving continues, the concentration of iodine molecules in the solution increases. 

These considerations also explain the occurrence of cases of dimorphism involving the sodium chloride and cesium chloride structures. It would be expected that increase in thermal agitation of the ions would smooth out the repulsive forces, that is, would decrease the value of the exponent n. Hence the cesium chloride structure would be expected to be stable in the low temperature region, and the sodium chloride structure in the high-temperature region. This result may be tested by comparison with the data for the ammonium halides, if we assume the ammonium ion to approximate closely to spherical symmetry. The low-temperature form of all three salts, ammonium chloride, bromide and iodide, has the cesium chloride structure, and the high-temperature form the sodium chloride structure. Cesium chloride and bromide are also dimorphous, changing into another form (presumably with the sociium chloride structure) at temperatures of about 500°. 

Classically, saturation occurs when the field is so strong and/or the thermal agitation (temperature) is so feeble that all the molecular dipoles are aligned with the field. Then, of course, increasing the applied field more is unable to cause any further alignment. 

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