Temperature relations, substance-specific

Empirical equations are often used in engineering calculations. Eor example, the following type of equation can relate the specific heat capacity Cp (J kg K ) of a substance with its absolute temperature T (K). 

Closely related to specific heat is the molar heat capacity (Cm), defined as the amount of heat necessary to raise the temperature of 1 mol of a substance by 1°C. 

The concept of temperature can be defined operationally that is, in terms of a set of operations or conditions that define the concept. To define a temperature scale operationally we need (1) one particular pure or defined substance (2) a specific property of that substance that changes with a naive sense of degree of hotness (i.e., temperature) (3) an equation relating temperature to the specific property (4) a sufficient number of fixed points (defined as reproducible temperatures) to evaluate the constants in the equation in (3) and (5) the assignment of numerical values to the fixed points. Historically, many different choices have been made with respect to the five conditions listed above, and this, of course, has resulted in many temperature scales. 

The temperature dependence of specific heat shown in Fig. 51 is typical for solid f-lements where the limit value related to 1 mole of atoms (atomic heat) amounts on average to about 25 J K (6 cal K ). This atomic heat value (at a constant volume) is interpreted as three times the gas constant R. The limit values are attained by various substances at various temperatures. 

Examples of modem substance-specific density-temperature relations are found in Goodwin (6) and in Pentermann and Wagner (7). 

These forms of a generalized equation of state only require the critical temperature and the critical pressure as substance-specific parameters. Therefore, these correlations are an example for the so-called tsvo-parameter corresponding-states principle, which means that the compressibility factor and thus the related thermodynamic properties for all substances should be equal at the same values of their reduced properties. As an example, the reduced vapor pressure as a function of the reduced temperature should have the same value for all substances, provided that the regarded equation of state can reproduce the PvT behavior of the substance on the basis of the critical data. In reality, the two-parameter corresponding-states principle is only well-suited to reflect the properties of simple, almost spherical, nonpolar molecules (noble gases as Ar, Kr, Xe). For all other molecules, the correlations based on the two-parameter corresponding-states principle reveal considerable deviations. To overcome these limitations, a third parameter was introduced, which is characteristic for a particular substance. The most popular third parameter is the so-called acentric factor, which was introduced by Pitzer ... 

We can calculate the heat capacity of a substance from its mass and its specific heat capacity by using the relation C = m X Cs. If we know the mass of a substance, its specific heat capacity, and the temperature rise it undergoes during an experiment, then the heat supplied to the sample is... 

Theories of electron mobility are intimately related to the state of the electron in the fluid. The latter not only depends on molecular and liquid structure, it is also circumstantially influenced by temperature, density, pressure, and so forth. Moreover, the electron can simultaneously exist in multiple states of quite different quantum character, between which equilibrium transitions are possible. Therefore, there is no unique theory that will explain electron mobilities in different substances under different conditions. Conversely, given a set of experimental parameters, it is usually possible to construct a theoretical model that will be consistent with known experiments. Rather different physical pictures have thus emerged for high-, intermediate- and low-mobility liquids. In this section, we will first describe some general theoretical concepts. Following that, a detailed discussion will be presented in the subsequent subsections of specific theoretical models that have been found to be useful in low- and intermediate-mobility hydrocarbon liquids. 

Density is also dependent on temperature and tabulated values of density are valid only at the specified temperature. A related but more versatile is the specific gravity. This is the ratio of the density of a substance to the density of water at the same temperature. 

Reactivity1 is not necessarily an intrinsic property of a chemical substance. The hazards associated with reactivity are related to process-specific factors, such as operating temperatures, pressures, quantities handled, concentrations, the presence of other substances, and impurities with catalytic effects. 

All samples of the same substance have the same specific heat capacity. In contrast, heat capacity, C, relates the heat of a sample, object, or system to its change in temperature. Heat capacity is usually expressed in units of kJ/°C. 

It is most important to know in this connection the compressibility of the substances concerned, at various temperatures, and in both the liquid and the crystalline state, with its dependent constants such as change of. melting-point with pressure, and effect of pressure upon solubility. Other important data are the existence of new pol3miorphic forms of substances the effect of pressure upon rigidity and its related elastic moduli the effect of pressure upon diathermancy, thermal conductivity, specific heat capacity, and magnetic susceptibility and the effect of pressure in modif dng equilibrium in homogeneous as well as heterogeneous systems. 

With respect to an enzyme, the rate of substrate-to-product conversion catalyzed by an enzyme under a given set of conditions, either measured by the amount of substance (e.g., micromoles) converted per unit time or by concentration change (e.g., millimolarity) per unit time. See Specific Activity Turnover Number. 2. Referring to the measure of a property of a biomolecule, pharmaceutical, procedure, eta, with respect to the response that substance or procedure produces. 3. See Optical Activity. 4. The amount of radioactive substance (or number of atoms) that disintegrates per unit time. See Specific Activity. 5. A unitless thermodynamic parameter which is used in place of concentration to correct for nonideality of gases or of solutions. The absolute activity of a substance B, symbolized by Ab, is related to the chemical potential of B (symbolized by /jlb) by the relationship yu,B = RTln Ab where R is the universal gas constant and Tis the absolute temperature. The ratio of the absolute activity of some substance B to some absolute activity for some reference state, A , is referred to as the relative activity (usually simply called activity ). The relative activity is symbolized by a and is defined by the relationship b = Ab/A = If... 

The specific heat of a substance is the amount of heat energy, in kJ, required to increase the temperature of 1 kg of the substance by 1 K. The specific heat of skim milk increases from 3.906 to 3.993 kJ kg-1 K-1 from 1 to 50°C. Values of 4.052 and 3.931 kJ kg-1 K-1 have been reported for skim and whole milks, respectively, at 80°C (Sherbon, 1988). The specific heat of milk is inversely related to its total solids content, although discontinuities have been observed around 70-80°C. Skim-milk powder usually has a specific heat in the range 1.172-1.340kJ kg-1 K-1 at 18-30°C. 

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