Thermal expansion definition

Several methods of measurement of the thermal expansion have been developed as a function of the material, dimension and shape of the sample, temperature range and requested accuracy. The measurement of the linear expansion coefficient a = 1/L (AL/A7) of a sample is done by recording the length change AL (in a definite direction) due to a temperature variation AT. 

By applying the definition of the thermal expansion coefficient, given by Equation 9-39, we obtain... 

An interferometer can be used to very accurately measure the thermal expansion of solids. Although not utilized commercially to the level of dilatometry, NIST standard materials, which are in turn used to calibrate dilatometers, have had their expansion characteristics determined using interferometry. In fact, the formal definition of the meter is based on interferometric measurements. The operation of the device is based on the principle of interference of monochromatic light. The fundamental relations between wavelength and distance will first... 

The concept of free volume varies on how it is defined and used, but is generally acknowledged to be related to the degree of thermal expansion of the molecules. When liquids with different free volumes are mixed, that difference contributes to the excess functions (Prausnitz et al., 1986). The definition of free volume used by Bondi (1968) is the difference between the hard sphere or hard core volume of the molecule (Vw= van der Waals volume) and the molar volume, V ... 

The hole model for molecular liquids was elaborated by Furth [12], who supposed that the free volume of a liquid is not distributed uniformly between its molecules like in crystals, but is concentrated like some holes which can disappear in one place and appear in another place. These holes are in permanent motion, so that the situation is different from the jumps of the holes in a crystal. The appearance and disappearance of the holes in a liquid are a result of the fluctuations connected with thermal movements. These holes in liquids have no definite shape and size they can increase or decrease spontaneously. Furth [12] tried to calculate a large number of properties of the liquids viscosity, compressibility, thermal expansion, thermal conductivity, but the results were not successful. However, Furth obtained a precise result of the calculation of the volume change by melting and the entropy of melting. 

If the material has a constant thermal expansion, so that the change in volume is proportional to temperature, we should have approximately dao/dT = a, where a is constant, leading to a0(T) = ocT. This is a special case, however it is found that for real materials the coefficient of thermal expansion becomes smaller at low temperatures, approaching zero at the absolute zero for this reason we prefer to leave a0(T) as an undetermined function of the temperature, remembering only that it, reduces to zero at the absolute zero (by the definition of F0), and that it is very small compared to unity, since the temperature expansion of a solid is only a small fraction of its whole volume. 

The thermal expansion coefficients follow from the definitions for the specific thermal expansivity ... 

It has been demonstrated that molecular orientation can be achieved starting with a low molecular weight species which is oriented in an elongational flow and subsequently cured under UV-irradiation. The orientation of the monomer is frozen-in by the ultra-fast process of polymerization and crosslinking. Both extrusion and stretching can be carried out at relatively low temperatures and pressures. Polymer filaments produced in this way are definitely anisotropic as is evidenced by their birefringence and by a strong increase of the tensile modulus and a decrease of the thermal expansion coefficient in the axial direction. 

By definition, refractory metals exhibit low thermal and electrical conductivities and have equally low thermal expansion properties (Table 3.6). As a relative benchmark, common metals such as iron and copper have coefficients of linear thermal expansion on the order of 12.1 and 17.7 p,m m K , respectively. Also for comparative purposes, the electrical/thermal conductivities for Fe and Cu are 9.71 j,Qcm V78-2 Wm and 1.67p,Q cm V397W m K , respectively. 

X 10" K" and ap(1000 K) = 10.4 x 10 K". As can be seen in Table 4, these are in much better agreement with the experimental data than are the fluctuation formula results. Particularly striking is the fact that the ratios of both the calculated and the experimental values at the two temperatures are now nearly the same, 1.4 (calc.) vs 1.36 (exp.). (With the fluctuation formula, this ratio is 2.2.) It should also be mentioned that when the coefficient of thermal expansion is obtained from its definition, which involves the volume and not its fluctuation, the convergence is much more rapid than with the fluctuation method. Figure 12 shows that the final volume is reached within a few picoseconds. 

Preliminary to such a search we examine several thermodynamic properties of fluids at or close to criticality, that clearly show why and how fluctuations dominate under such conditions, (i) Consider first the isothermal compressibility, kj = —(dV/dP)T/V. At the critical point the isotherm dP/dV)r has zero slope thus, Ki grows indefinitely as T —> Tc. (ii) Using Eq. (1.3.13) and the definition for K one finds that (dV/dT)p = -(dV/dP)TidPldT)v = KiV dP/dT)y, wherein (dP/dT)v does not vanish. Therefore, the coefficient of thermal expansion, = i /V) dV/BT)p also grows without limit as the critical point is approached, (iii) According to the Clausius-Clapeyron equation in the form AH = T(Vg — Vi)(dP/dT), the heat of vaporization of the fluid near the critical point becomes very small, since Vg — Vi 0, whereas dP/dT remains finite. 

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