Volume expansion coefficients

FIGURE 12.27 Relative change in the volume expansion coefficient for air and water. 

Figure 7 Thermal volume expansivity coefficient ot25 of annealed PET fibers.

At any rate, the volume expansion coefficient, corresponding to the computed value of the ripplon-TLS term, is approximately equal to... 

The high pressures shewn here are produced by thermal expansion of the specimen at constant volume. At these pressures, the generated gas is completely dissolved in the gel-like mass. The volume expansion coefficient,... 

These equations connect the slope (dP/dT)tr of the transformation line Ttr(P) for second order transformations in the PVT-diagram to the steps in the specific volume expansion coefficient, the specific compressibility and the specific heat. 

In Fig. 3 c the schematic volume-temperature curve of a non crystallizing polymer is shown. The bend in the V(T) curve at the glass transition indicates, that the extensive thermodynamic functions, like volume V, enthalpy H and entropy S show (in an idealized representation) a break. Consequently the first derivatives of these functions, i.e. the isobaric specific volume expansion coefficient a, the isothermal specific compressibility X, and the specific heat at constant pressure c, have a jump at this point, if the curves are drawn in an idealized form. This observation of breaks for the thermodynamic functions V, H and S in past led to the conclusion that there must be an internal phase transition, which could be a true thermodynamic transformation of the second or higher order. In contrast to this statement, most authors... 

The usual free volume interpretation of Cfand Cf is questionable Cf = BD/fg and Cf = fg/Aa, where BD is the Doolittle constant, fg is the free volume fraction at Tg and Aa = oq — ag is the free volume expansion coefficient. It appears impossible to... 

For a number of dielectrics with e, > 30, TC is negative and within 15% of —aLer as illustrated by the examples given in Table 5.6. Eq. (5.34) suggests that the temperature variation of polarizability is small compared with the volume expansion coefficient in these cases. Lower-permittivity oxides have positive TC s and in their case the temperature coefficient of polarizability can be assumed to exceed the volume expansion coefficient. However, the extent to which the Clausius-Mosotti equation can be applied to ionic solids is open to debate. 

FIG. 13.36 Schematic diagram of volume expansion coefficient a during cooling, followed by heating with the same rate. 

For noncubic unit cells, the expansion or change of each cell dimension is required. The coefficients may be presented as linear for each cell dimension or as volume expansion coefficients, in which case the total volume change is divided by the initial volume. Division by the temperature... 

In heat transfer studies, the primary variable is temperature, and it is desirable to express the net buoyancy force (Eq. 9-2) in terms of temperature differences. But this requires expressing the density difference in terms of a temperature difference, which requires a knowledge of a property that represents the variation of the density of a fluid with temperature atconstant pressure. The property that provides that information is the volume expansion coefficient /3, defined as (Fig. 9-4)... 

In natural convection studies, the condition of tlie fluid sufficiently far from the hot or cold surface is indicated by the subscript infinity to serve as a reminder that this is the value at a distance where the presence of the surface is not felt. In such cases, the volume expansion coefficient can be expressed approximately by replacing differential quantities by differences as... 

We can show easily that the volume expansion coefficient /3 of an ideal as P = pRT) at a temperature T is equivalent to the inverse of the temperature ... 

In this chapter, we have considered natural convection heat transfpf where any fluid morion occurs by oatural means such as buoyancy. The volume expansion coefficient of a substance represents ihe variation of the density of that substance wilh temperanjre at constant pressure, and for an ideal gas, it is expressed as j8 = VT, where T is the absolute temperature in KorR. 

Show that the volume expansion coefficient of an ideal gas is jCl = IT, where Tis the absolute temperature. 

Temp. r. c Saturation Pressure Density P, kg/m Enthalpy of Vaporization kJ/kg specific Heal Cj, Jflrg K Therjnaf Conductivity k, W/m - K Dynamic Viscosity kg/m s P/andll Number Pr Volume Expansion Coefficient 1/K Liquid... 

In other words, the particle displacement in waves Us occurs in a direction orthogonal to that of wave propagation. As a result of field Us being solenoidal, the volume expansion coefficient of the medium during deformations involving the propagation of these waves is equal to zero. This means that Us waves are not related to volume changes. That is why such waves are described as shear waves. 

We have found out the volume expansion coefficient could be reached 3.1 that is larger than previously reported maximum values of 1.6-1.7 [6]. The high volume expansion coefficient is caused by enhancing of the sulphuric content inside porous alumina formed at high field anodising. The high volume expansion also results in low porosity of alumina, which was about 3%. This is smaller than known minimal porosity of 5% for a sulphuric electrolyte [1]. 

Thermal expansion of glass is usually expressed by the linear expansion coefficient a the volume expansion coefficient = 3a. It is usual to distinguish between the true and the mean expansion coefficient, the former being related to a certain temperature and the latter to a wider temperature range. ... 

The quantities a, c, f, F, r, and p are the thermal diffusivity, sound speed, heat capacity ratio, bulk viscosity coefficient, shear viscosity coefficient, and density of the sample, respectively and Eo, a, P and Cp are the energy fluence of the laser beam, the optical absorption coefficient, the volume expansion coefficient, and the isobaric heat capacity, respectively, of the fluid. Tlie first and second terms in Eq. 2 describe the time dependences of the thermal and acoustic modes of wave motion, respectively. Since the decays of the acoustic and thermal mode densities back to their ambient values take place on such different time scales (microsecond time scale for acoustic mode and millisecond time scale for thermal mode), they were recorded on the oscilloscope using different time bases. 

It is possible to compute a mean Gruneisen coefficient, F, for lead azide by using an effective bulk modulus, (defined by the ratio of the applied pressure to the relative volume change), and the volume expansion coefficient, a, as... 

KEY TERMS normal boiling point volume expansion coefficient... 

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