Temperature effects specific volume

Consider, for example, a PWR containing 80 te of uranium oxide enriched to 3%, with an average moderator temperature of 310 C. The effective specific volume of uranium oxide pellets will be 1.11 x 10 m /kg. The fission cross-section at a moderator temperature of 20°C/293 K, t/(293), is 582 x 10 m for U-235, while the corresponding figure for plutonium-239 is 743 x 10 m. Calculate NfOf at the start of life and at the end of life, and hence deduce the variation in the constant of proportionality, a. 

The systems of interest in chemical technology are usually comprised of fluids not appreciably influenced by surface, gravitational, electrical, or magnetic effects. For such homogeneous fluids, molar or specific volume, V, is observed to be a function of temperature, T, pressure, P, and composition. This observation leads to the basic postulate that macroscopic properties of homogeneous PPIT systems at internal equiUbrium can be expressed as functions of temperature, pressure, and composition only. Thus the internal energy and the entropy are functions of temperature, pressure, and composition. These molar or unit mass properties, represented by the symbols U, and S, are independent of system size and are intensive. Total system properties, J and S do depend on system size and are extensive. Thus, if the system contains n moles of fluid, = nAf, where Af is a molar property. Temperature... 

Abnormally low atomic heats were explained by Richarz on the assumption of a diminution of freedom of oscillation consequent on a closer approximation of the atoms, which may even give rise to the formation of complexes. This is in agreement with the small atomic volume of such elements, and with the increase of atomic heat with rise of temperature to a limiting value 6 4, and the effect of propinquity is seen in the fact that the molecular heat of a solid compound is usually slightly less than the sum of the atomic heats of the elements, and the increase of specific heat with the specific volume when an element exists in different allotropic forms. 

From the coverage made thus far, it may be of interest to record in one place the different factors which influence the rate of chemical reactions. The rate of chemical reaction depends essentially on four factors. The nature of reactants and products is one. For example, certain physical properties of the reactants and products govern the rate. As a specific example in this context mention may be of oxidation of metals. The volume ratio of metallic oxide to metal may indicate that a given oxidation reaction will be fast when the oxide is porous, or slow when the oxide is nonporous, thus presenting a diffusion barrier to the metal or to oxygen. The other two factors are concentration and temperature effects, which are detailed in Sections. The fourth factor is the presence of catalysts. 

Calculation of the pressure drop and flooding rate is particularly important for vacuum columns, in which the pressure may increase severalfold from the top to the bottom of the column. When a heat-sensitive liquid is distilled, the maximum temperature, and hence the pressure, at the bottom of the column is limited and hence the vapour rate must not exceed a certain value. In a vacuum column, the throughput is very low because of the high specific volume of the vapour, and the liquid reflux rate is generally so low that the liquid flow has little effect on the pressure drop. The pressure drop can be calculated by applying equation 4.15 over a differential height and integrating. Thus ... 

Any characteristic of a system is called a property. The essential feature of a property is that it has a unique value when a system is in a particular state. Properties are considered to be either intensive or extensive. Intensive properties are those that are independent of the size of a system, such as temperature T and pressure p. Extensive properties are those that are dependent on the size of a system, such as volume V, internal energy U, and entropy S. Extensive properties per unit mass are called specific properties such as specific volume v, specific internal energy u, and specific entropy. s. Properties can be either measurable such as temperature T, volume V, pressure p, specific heat at constant pressure process Cp, and specific heat at constant volume process c, or non-measurable such as internal energy U and entropy S. A relatively small number of independent properties suffice to fix all other properties and thus the state of the system. If the system is composed of a single phase, free from magnetic, electrical, chemical, and surface effects, the state is fixed when any two independent intensive properties are fixed. 

Before studying the properties of gases and liquids, we need to understand the relationship between the two phases. The starting point will be a study of vapor pressure and the development of the definition of the critical point. Then we will look in detail at the effects of pressure and temperature on one of the intensive properties of particular interest to petroleum engineers specific volume. 

As there exists a phase equilibrium both phases must have reached in the internal thermodynamic equilibrium with respect to the arrangement and distribution of the molecules the measuring time. Therefore, no time effects or path dependencies of the thermodynamic properties in the liquid crystalline phase should be expected. To check this point for the l.c. polymer, a cut through the measured V(P) curves at 2000 bar has been made (Fig. 6) and the volume values are inserted at different temperatures in Fig. 7, which represents the measured isobaric volume-temperature curve at 2000 bar 38). It can be seen from Fig. 7 that all specific volumes obtained by the cut through the isotherms in Fig. 6 he on the directly measured isobar. No path dependence can be detected in the l.c. phase. From these observations we can conclude that the volume as well as other properties of the polymers depend only on temperature and pressure. The liquid crystalline phase of the polymer is a homogeneous phase, which is in its internal thermodynamic equilibrium within the normal measuring time. 

Effects of structural changes on properties, such as specific heat, specific volume, and/or dynamic mechanical and electrical properties, are observed at various temperatures. A number of transitions were observed by various investigators their interpretation and the modes of identification are listed in Table 3.2. 

FIGURE 10-60 Schematic plots of specific volume versus temperature showing the effect of physical aging. 

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