Expansion of a solid

The heat introduced amounts, according to the First Law, to Q = C0dT - dv + pdv. 

Combining the last two equations, we have for adiabatic compression or dilatation (Q o), 

Chemical Change.—If it be assumed that for each of the reacting substances 

Thus the absolute zero would be reached with an infinitely small transformation dv if the original temperature were dX. If, according to our Heat Theorem, we put 

In a similar manner a proof may be given, for any process whatsoever, that, on the assumption that the specific heats become negligibly small, the requirement that the curve BC shall be incapable of being realized coincides with the conclusions to be drawn from our Heat Theorem. 

---

Heat sensing, as aetual temperature or rate-of-temperature rise, and depending upon melting of a metal (fusion) expansion of a solid, liquid or gas eleetrieal sensing. 

The thermal expansivity of a solid is in general low at low temperatures and the anharmonic contribution to the heat capacity is therefore small in this temperature region and Cv m Cpm. At high temperatures the difference between the heat capacity at constant pressure and at constant volume must be taken into consideration. 

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. 

Expansion of liquids on heating. The definition of the co-efiicient of expansion of a hquid is identical with that of the coefficient of cubical expansion of a solid substance. There are two important methods of measuring the coefiicient of... 

The principle of the expansion of a solid is employed in bimetallic-strip thermometers, which are comprised of strips of two different metals bonded together, side by side. Since the metals selected for this use have... 

We shall carry out the calculation of the above described cyclic process for two special examples, viz. the expansion of a solid and a chemical process. 

Expansion of a Solid.—The application of the Second Law to this process is contained in the equation given on page 90... 

In general, the asymmetry of the energy well increases with decreasing bond strength, and consequently the thermal expansion of a solid scales inversely with its bond strength or melting point. For example, the thermal expansion coefficient of solid Ar is on the order of 10 whereas for... 

The linear expansivity of a solid, a, is defined as the increase in length per unit length at a given temperature ... 

The thermal expansion of a solid is the variation in that solid s dimensions when its temperature is changed. A few exceptions aside, dimensions generally increase when the temperature rises. This expansion is due to the anharmonicity of the molecules vibrations. 

In dealing with change in the dimensions of a sample with temperature the measurements relate to the deformation and strength of the sample. Expansion in a solid or a liquid is indicative of a decrease in surface energy. Thus, the expansion of a solid in an adsorption process may be interpreted as a decrease in surface energy. 

Many solids show marked swelling as a result of the uptake of a gas or a liquid. In certain cases involving the adsorption of a vapor by a porous solid, a linear relationship exists between the percentage of linear expansion of Ae solid and the film pressure of the adsorbed material [134, 135]. 

The expansion coefficient of a solid can be estimated with the aid of an approximate thermodynamic equation of state for solids which equates the thermal expansion coefficient with the quantity where yis the Griineisen dimensionless ratio, C, is the specific heat of the solid, p is the density of the material, and B is the bulk modulus. For fee metals the average value of the Griineisen constant is near 2.3. However, there is a tendency for this constant to increase with atomic number. 

Fluidization Vessel The most common shape is a vertical cylinder. Just as for a vessel designed for boiling a liquid, space must be provided for vertical expansion of the solids and for disengaging... 

Instruments based on the contact principle can further be divided into two classes mechanical thermometers and electrical thermometers. Mechanical thermometers are based on the thermal expansion of a gas, a liquid, or a solid material. They are simple, robust, and do not normally require power to operate. Electrical resistance thermometers utilize the connection between the electrical resistance and the sensor temperature. Thermocouples are based on the phenomenon, where a temperature-dependent voltage is created in a circuit of two different metals. Semiconductor thermometers have a diode or transistor probe, or a more advanced integrated circuit, where the voltage of the semiconductor junctions is temperature dependent. All electrical meters are easy to incorporate with modern data acquisition systems. A summary of contact thermometer properties is shown in Table 12.3. 

Liquid-in-glass thermometers measure the thermal expansion of a liquid, which is placed in a solid container, on a length scale. The mercury thermometer is one example of liquid thermometers. Alcohol is also used with this type of instrument. The temperature range is -80 to a-330 °C depending on the liquid. The quality, stability, and accuracy vary considerably. The advantages are a simple construction and low price. A disadvantage is that they are not compatible for connection to monitoring systems. 

Measurement of the expansion of a gas-liquid fluidized bed provides a measure of the holdup of solids or of the corresponding combined holdup of gas and liquid. From such measurements, the holdup of liquid may be calculated if the gas holdup has been determined independently. 

Thermometry is the science of measuring the temperature of a system or the ability of a system to transfer heat to emother system. Temperature mecisurement is important to a wide range of activities, including manufacturing, scientific research, and medical practice. Thermometry relates to the dilatrometric measurement in that the expansion of a gas, liquid or solid is used to determine temperature. 

Fig. 31 Surface pressure/area isotherms for compression and expansion of (A) enantiomeric (dashed line) and racemic (solid line) lauroylcysteine methyl esters and (B) enantiomeric (dashed line) and meso (solid line) dilauroylcystine esters at 25°C. Arrows indicate the direction of compression and expansion.

Other methods are obviously needed for liquids. In the simplest approach the thermal expansivity is derived by measurements of the density as a function of temperature. It is then necessary to correct for the thermal expansion of the solid body... 

Zuev A, Singheiser L, andHilpertK. Defect structure and isothermal expansion of A-site and B-site substituted lanthanum chromites. Solid State Ionics 2002 147 1-11. 

To model this, Duncan-Hewitt and Thompson [50] developed a four-layer model for a transverse-shear mode acoustic wave sensor with one face immersed in a liquid, comprised of a solid substrate (quartz/electrode) layer, an ordered surface-adjacent layer, a thin transition layer, and the bulk liquid layer. The ordered surface-adjacent layer was assumed to be more structured than the bulk, with a greater density and viscosity. For the transition layer, based on an expansion of the analysis of Tolstoi [3] and then Blake [12], the authors developed a model based on the nucleation of vacancies in the layer caused by shear stress in the liquid. The aim of this work was to explore the concept of graded surface and liquid properties, as well as their effect on observable boundary conditions. They calculated the hrst-order rate of deformation, as the product of the rate constant of densities and the concentration of vacancies in the liquid. 

When a shock wave propagates from one end (A) to the other end (B) of a solid body, a compression force is exerted in the wake of the shock wave that acts within the solid body. The shock wave is reflected at B and becomes an expansion wavethat propagates towards A. An expansion force is then exerted in the wake of the expansion wave that travels back from B. This process is shown schematically in Fig. 9.6. 

---