Debye’s law

In the case of a perfect crystalline solid, for temperature well below the Debye temperature 0D, a c/T3 versus T graph would give a constant value c/T3 a 1 /dD. However, most crystals show deviations from the Debye s law, in particular c/T3 versus T presents a maximum. This behavior is present also in amorphous solids where the maximum is more evident and appears at temperatures higher than in crystals [40],... 

All the results confirm the fact (required by Debye s law) that the dielectric constant is a linear function of the reciprocal of the temperature. The electric moments (/x) of the molecules calculated from the slopes of the lines are in each case given under the table. 

As Stuart worked with very small densities which were determined experimentally, and in addition the values of the molecular polarization calculated from the measured values of the dielectric constants and the corresponding densities are strictly in accordance with Debye s law, the values of the electric moment obtained from the variation of the molecular polarization with temperature must be regarded as being very accurate. We should therefore expect that the results we obtained should agree with Stuart s within the range of experimental error, if the methods used are genuinely successful. 

Debye s theory on the whole in particular, the papers by Zahn Watson f, and Stuart J may be mentioned. The measurements were carried out for various temperatures the pressures and densities of the gas were chosen at random, i.e. were quite independent of each other. The electric moment [x was calculated from Debye s law... 

It is more in accordance with the spirit of the theory, however, to carry out measurements on the effect of temperature on dielectric constants not for a few arbitrary densities but with the density kept constant, i.e. with a constant number of molecules. Experiments fulfilling this condition not only exhibit the workings of Debye s law in a very beautiful way but will immediately reveal any effects of an associative nature which may be expected to occur when the density is large. 

The new Heat Theorem, according to which a0 must be equal to 0, teaches us that the curves for A and U not only meet at the absolute zero, but touch one another before they reach it according to Debye s law this contact is very close, being of the third degree. 

This paper reports the measurements of the specific heat capacity of nickel in the temperature range from 1.1 to 19.0 K. The hypothesis was advanced that the deviation from Debye s law is connected with the energy of electron conduction. 

Figure 1.13 compares the curve given by the Einsteinian relation [1.129] and that given by Debye s law [1.133]. We can see a difference between the two curves - particularly at low temperature. 

In conclusion, it can very often be admitted that, outside of metals, the specific heat capacity varies with temperature like Debye s law at low temperatures, with a law proportional to at very low temperatures (below 40 K), while Einstein s law performs better at higher temperatures. For metals, caution needs to be exercised when we come very close to absolute zero a law proportional to T is better than the T law. 

Dalton s law of partial pressure 264, 406 Davies, C. A. 449, 456, 507 Debye heat capacity equation for solids 572-80, 651-4... 

UT/6D . This limiting expression is known as Debye s third-power law for the heat capacity (problem 15). It is employed in thermodynamics to evaluate the low-temperature contribution to the absolute entropy. 

Figure 5.8 A Debye-Scherrer powder camera for X-ray diffraction. The camera (a) consists of a long strip of photographic film fitted inside a disk. The sample (usually contained within a quartz capillary tube) is mounted vertically at the center of the camera and rotated slowly around its vertical axis. X-rays enter from the left, are scattered by the sample, and the undeflected part of the beam exits at the right. After about 24 hours the film is removed (b), and, following development, shows the diffraction pattern as a series of pairs of dark lines, symmetric about the exit slit. The diffraction angle (20) is measured from the film, and used to calculate the d spacings of the crystal from Bragg s law.

COULOMB COULOMB S LAW DEBYE-HOCKEL TREATMENT COULOMETRIC TITRATION 4-COUMAROYL-CoA SYNTHETASE COUNTERION Counting efficiency,... 

Water can interact with ionic or polar substances and may destroy their crystal lattices. Since the resulting hydrated ions are more stable than the crystal lattice, solvation results. Water has a very high dielectric constant (80 Debye units [D] versus 21 D for acetone), which counteracts the electrostatic attraction of ions, thus favoring further hydration. The dielectric constant of a medium can be defined as a dimensionless ratio of forces the force acting between two charges in a vacuum and the force between the same two charges in the medium or solvent. According to Coulomb s law. 

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