Adiabatic expansion coefficient

What are the main error sources in PAC experiments One of them may result from the calibration procedure. As happens with any comparative technique, the conditions of the calibration and experiment must be exactly the same or, more realistically, as similar as possible. As mentioned before, the calibration constant depends on the design of the calorimeter (its geometry and the operational parameters of its instruments) and on the thermoelastic properties of the solution, as shown by equation 13.5. The design of the calorimeter will normally remain constant between experiments. Regarding the adiabatic expansion coefficient (/), in most cases the solutions used are very dilute, so the thermoelastic properties of the solution will barely be affected by the small amount of solute present in both the calibration and experiment. The relevant thermoelastic properties will thus be those of the solvent. There are, however, a number of important applications where higher concentrations of one or more solutes have to be used. This happens, for instance, in studies of substituted phenol compounds, where one solute is a photoreactive radical precursor and the other is the phenolic substrate [297]. To meet the time constraint imposed by the transducer, the phenolic... 

Equation (26-137) is recognized as the expression for aU-gas flow by adiabattc expansion across an orifice or nozzle. The factor k is the expansion coefficient for the adiabatic flow eqnahon of state ... 

If inserted into the time-dependent Schrodinger equation (49) an multiplication with 4>q and from the left results in equations of motion for the expansion coefficients. In doing so, one also produces overlap expressions like (o), 4>m d/dt o), and /dt n) (non-adiabatic couplings), which all can be neglected in line with the neglect of the mutual chromophore wave function overlap. Therefore, we obtain the expansion coefficient s equations of motion as... 

It is clear from (A.8) and (A.9) that the gradient difference and derivative coupling in the adiabatic representation can be related to Hamiltonian derivatives in a quasidiabatic representation. In the two-level approximation used in Section 2, the crude adiabatic states are trivial diabatic states. In practice (see (A.9)), the fully frozen states at Qo are not convenient because the CSF basis set l Q) is not complete and the states may not be expanded in a CSF basis set evaluated at another value of Q (this would require an infinite number of states). However, generalized crude adiabatic states are introduced for multiconfiguration methods by freezing the expansion coefficients but letting the CSFs relax as in the adiabatic states ... 

This equation has been used for the determination of the heat capacities at constant pressure of both liquids and gases. The quantity dV/dT)p is the rate of thermal expansion and this can be measured without difficulty. The other factor, dT/dP)si is called the adiabatic temperature coefficient, since it applies to constant entropy, i.e., adiabatic, conditions. It can be determined by allowing the fluid to expand suddenly, and hence adiabatically, over a known pressure range, and observing the temperature change. ... 

The adiabatic states are also time-dependent through the classical trajectory R t). Substitution of this expansion into the time-dependent Schrodinger equation, multiplication by / from the left, and integration over r yields a set of linear differential equations of the first order for the expansion coefficients, which are equations of motion for the quanmm amplitudes ... 

Where they have a positive slope, water cools on adiabatic expansion and warms if adiabatically compressed, and the two regions are separated by the Joule-Thompson inversion curve. Much the same information is contained in the enthalpy-pressure diagram (Figure 8.6), where it can be seen that constant enthalpy changes in pressure lead to increases in temperature in one region and decreases in another. The effect of dissolved NaCl on the Joule-Thompson coefficient has been calculated by Wood and Spera (1984), and the effect will be similar for other electrolytes. Because the addition of most electrolytes to water results in a decrease in V and in a, fijT is smaller, and the net effect is to move the inversion curve to higher temperatures, as shown in Figure 8.5. 

We discuss finally the case of a thermal expansion coefficient of zero. In this case, a pressure change does not effect a temperature change of the material and also no change in volume. So no input of compression energy is achieved. In contrary to the adiabatic application of pressure in the isothermal case in fact no change in volume will occur. Therefore, the incompressible body should be more accurately addressed as the isothermal incompressible body. 

The results shown in Figs. 6.2 and 6.3 indicate that the system can be treated as a three-level one consisting of G), L), and H) and therefore, we expanded the state vector of the system in terms of the three adiabatic states. The initial nuclear WP was set to be the vibrational ground-state wave function of G), and the system is then electronically excited by a linearly polarized laser pulse e(f) of the form in Eq. 6.14. The time evolution of the expansion coefficients for k) k = G, L, and H), i/k (Q, t), where Q is the two-dimensional mass-weighted normal coordinate vector, can be obtained from the following coupled equations [32] ... 

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