Molar capacity

The calculation of the molar capacity of the stationary phase is as follows ... 

When a system is heated, its temperature generally increases. This increase in temperature is dependent on the heat capacity of the system under constant volume or constant pressure. Therefore, the heat capacity is defined as the ratio of heat added to a system to its corresponding temperature change. If the system is under constant volume, the molar heat capacity is Cv, whereas the molar capacity is Cp for a system under constant pressure. Then,... 

In order to estimate the "molar capacity" of the bed that might produce an almost one hour s delay a number of simulations were carried out. The simulations were based on a dynamic model of a reactor bed, in which, together with the already mentioned effective... 

The phenomena occurring on the surface and in the liquid active phase of the vanadium catalyst have undoubtedly a major effect on the transients calculated by the dynamic models of catalytic reactors. The physicochemistry of these phenomena has not, so far, been satisfactorily elucidated. The introduction of an effective specific heat and effective molar capacity of the bed as parameters to be identified by comparing the actual transients with those predicted by the model is only a temporary measure. It cannot be expected that the phenomena occurring on the catalyst surface can be thoroughly explained without expensive and tedious studies. The results of the present investigations can be... 

About 40 - 60 minutes delay in the appearance of the maximum emission during the "cold" start-up of an SO2 oxidation reactor cannot be plausibly explained if only the absorption in the liquid melt phase is taken into account. This would require the "molar capacity" of the bed, C, of about 10 kmol / m. At such an assumption, the amount of SOg retained in the bed during the first 40 minutes of the start-up would correspond to the change in mass of the catalyst of 8 - 10%. Therefore, it seems little probable that it is solely the absorption of SOg in the bed which is responsible for such a considerable shift in the maximum emission in the unsteady state. 

A useful method for estimating the molar heat capacity of an organic liquid is based on the additivity of the heat capaeity contributions [C] of the various atomic groupings in the moleeules (Johnson and Huang, 1955). Table 2.5 lists some [C] values, and the following examples illustrate the use of the method the molar capacity values (ealmoP °C ) in parentheses denote values obtained experimentally at 20 °C ... 

Figure A2.5.2. Schematic representation of the behaviour of several thennodynamic fiinctions as a fiinction of temperature T at constant pressure for the one-component substance shown in figure A2.5.1. (The constant-pressure path is shown as a dotted line in figure A2.5.1.) (a) The molar Gibbs free energy Ci, (b) the molar enthalpy n, and (c) the molar heat capacity at constant pressure The fimctions shown are dimensionless...

Figure A2.5.4 shows for this two-component system the same thennodynamic fimctions as in figure A2.5.2, the molar Gibbs free energy (i= + V2P2> the molar enthalpy wand the molar heat capacity C. , again all at...

An exponent a governs the limiting slope of the molar heat capacity, variously y, ( or along a line tln-ongh the critical point,... 

Figure A2.5.26. Molar heat capacity C y of a van der Waals fluid as a fimction of temperature from mean-field theory (dotted line) from crossover theory (frill curve). Reproduced from [29] Kostrowicka Wyczalkowska A, Anisimov M A and Sengers J V 1999 Global crossover equation of state of a van der Waals fluid Fluid Phase Equilibria 158-160 532, figure 4, by pennission of Elsevier Science.

The heat capacity of thiazole was determined by adiabatic calorimetry from 5 to 340 K by Goursot and Westrum (295,296). A glass-type transition occurs between 145 and 175°K. Melting occurs at 239.53°K (-33-62°C) with an enthalpy increment of 2292 cal mole and an entropy increment of 9-57 cal mole °K . Table 1-44 summarizes the variations as a function of temperature of the most important thermodynamic properties of thiazole molar heat capacity Cp, standard entropy S°, and Gibbs function - G°-H" )IT. 

The explanation of the hydrogen atom spectmm and the photoelectric effect, together with other anomalous observations such as the behaviour of the molar heat capacity Q of a solid at temperatures close to 0 K and the frequency distribution of black body radiation, originated with Planck. In 1900 he proposed that the microscopic oscillators, of which a black body is made up, have an oscillation frequency v related to the energy E of the emitted radiation by... 

Fig. 12. Correlatioa of AT. The three lines represeat the best fit of a mathematical expressioa obtaiaed by multidimensional nonlinear regressioa techniques for 99, 95, and 90% recovery the poiats are for 99% recovery. = mean molar heat capacity of Hquid mixture, average over tower AY = VA2 slope of equiHbrium line for solute, to be taken at Hquid feed temperature mg = slope of equilibrium line for solvent.

In very small pores the molecules never escape from the force field of the pore wall even at the center of the pore. In this situation the concepts of monolayer and multilayer sorption become blurred and it is more useful to consider adsorption simply as pore filling. The molecular volume in the adsorbed phase is similar to that of the saturated Hquid sorbate, so a rough estimate of the saturation capacity can be obtained simply from the quotient of the specific micropore volume and the molar volume of the saturated Hquid. 

The properties of calcium chloride and its hydrates are summarized in Table 1. Accurate data are now available for the heats of fusion of the hexahydrate, the incongment fusion of the tetrahydrate, and the molar heat capacities of the hexahydrate, tetrahydrate, and dihydrate (1). These data are important when considering the calcium chloride hydrates as thermal storage media. A reevaluation and extension of the phase relationships of the calcium chloride hydrates, has led to new values for the heats of infinite dilution for the dihydrate, monohydrate, 0.33-hydrate, and pure calcium chloride (1). 

The second term in brackets in equation 36 is the separative work produced per unit time, called the separative capacity of the cascade. It is a function only of the rates and concentrations of the separation task being performed, and its value can be calculated quite easily from a value balance about the cascade. The separative capacity, sometimes called the separative power, is a defined mathematical quantity. Its usefulness arises from the fact that it is directly proportional to the total flow in the cascade and, therefore, directly proportional to the amount of equipment required for the cascade, the power requirement of the cascade, and the cost of the cascade. The separative capacity can be calculated using either molar flows and mol fractions or mass flows and weight fractions. The common unit for measuring separative work is the separative work unit (SWU) which is obtained when the flows are measured in kilograms of uranium and the concentrations in weight fractions. 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Cp = molar heat capacity at 273.15 K, J/kmol K M = molecular weight N = number of atoms in the molecule... 

The ideal-gas-state heat capacity Cf is a function of T but not of T. For a mixture, the heat capacity is simply the molar average X, Xi Cf. Empirical equations giving the temperature dependence of Cf are available for many pure gases, often taking the form... 

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