Dynamic specific heat

The normally used dynamic specific heat c(tu) as given by the heat capacity per unit mass is in general a complex, frequency-dependent quantity of the... 

Fig. 5.54. PE studied by TMDSC and HWS Temperature dependence of the modulus of the dynamic specific heat measured for various frequencies [61]...

Fluctuations of observables from their average values, unless the observables are constants of motion, are especially important, since they are related to the response fiinctions of the system. For example, the constant volume specific heat of a fluid is a response function related to the fluctuations in the energy of a system at constant N, V and T, where A is the number of particles in a volume V at temperature T. Similarly, fluctuations in the number density (p = N/V) of an open system at constant p, V and T, where p is the chemical potential, are related to the isothemial compressibility iCp which is another response fiinction. Temperature-dependent fluctuations characterize the dynamic equilibrium of themiodynamic systems, in contrast to the equilibrium of purely mechanical bodies in which fluctuations are absent. 

Under steady-state conditions, the temperature distribution in the wall is only spatial and not time dependent. This is the case, e.g., if the boundary conditions on both sides of the wall are kept constant over a longer time period. The time to achieve such a steady-state condition is dependent on the thickness, conductivity, and specific heat of the material. If this time is much shorter than the change in time of the boundary conditions on the wall surface, then this is termed a quasi-steady-state condition. On the contrary, if this time is longer, the temperature distribution and the heat fluxes in the wall are not constant in time, and therefore the dynamic heat transfer must be analyzed (Fig. 11.32). 

Moisture-transport simulation includes transport as well as storage phenomena, quite similar to the thermal dynamic analysis, where heat transfer and heat storage in the building elements are modeled. The moisture content in the building construction can influence the thermal behavior, because material properties like conductance or specific heat depend on moisture content. In thermal building-dynamics simulation codes, however, these... 

To overcome this problem, they proposed a working-fluid heat-addition model. This model implies that the gas dynamics are not computed on the basis of real values for heat of combustion and specific heat ratio of the combustion products, but on the basis of effective values. Effective values for the heat addition and product specific heat ratios were determined for six different stoichiometric fuel-air mixtures. Using this numerical model, Luckritz (1977) and Strehlow et al. (1979) systematically registered the properties of blast generated by spherical, constant-velocity deflagrations over a large range of flame speeds. 

Convective heat transmission occurs within a fluid, and between a fluid and a surface, by virtue of relative movement of the fluid particles (that is, by mass transfer). Heat exchange between fluid particles in mixing and between fluid particles and a surface is by conduction. The overall rate of heat transfer in convection is, however, also dependent on the capacity of the fluid for energy storage and on its resistance to flow in mixing. The fluid properties which characterize convective heat transfer are thus thermal conductivity, specific heat capacity and dynamic viscosity. 

Species concentration Capillary number Concentration of species a Computer aided design Concentration of species b Charge-coupled device Eluid specific heat Computational fluid dynamics Constrained-geometry catalyst Concentration at node i Concentration of species i Elux limiter Specific heat... 

For a thermometer to react rapidly to changes in the surrounding temperature, the magnitude of the time constant should be small. This involves a high surface area to liquid mass ratio, a high heat transfer coefficient and a low specific heat capacity for the bulb liquid. With a large time constant, the instrument will respond slowly and may result in a dynamic measurement error. 

This is another example of the application of thermogravimetry for determination of equilibrium temperatures in dissociation studies. This also enables one to calculate the heat of dissociation from the linear relation between log of dissociation pressure and 1/T. Determination of the specific heat by means of DTA was used afterwards for conversion of the heat of dissociation into the standard values of formation at 298 °K. Ba02 was chosen for these investigation56 because it has been investigated in the past by calorimetric methods and therefore gives a possibility for comparing those values obtained from static methods with those obtained from values from dynamic methods. 

Critical phenomena of gels have been studied mainly by dynamic light scattering technique, which is one of the most well-established methods to study these phenomena [18-20]. Recently, the critical phenomena of gels were also studied by friction measurement [85, 86] and by calorimetry [55, 56]. In the case of these methods, the divergence of the specific heat or dissipation of the friction coefficient could be monitored as a function of an external intensive variable, such as temperature. These phenomena might be more plausible to some readers than the divergence of the scattered intensity since they can observe the critical phenomena in terms of a macroscopic physical parameter. 

Propellants due to Heat Transfer Influencing Propellant Temperature in a Recovery Type Vehicle , Dynamic Sci Corp, South Pasadena (1962) [The following calcd properties are reported for gaseous UDMH Thermal conductivity at 323°K, cal/cm-sec-deg K, 162 x 10"7 Specific heat, cal/g-deg K, 0.165 and viscosity at 323°K, g/cm-sec, 7.86 x 10"5]... 

Eucken discovered that the molecular heat of hydrogen falls at low temperatures from 5 to 3. This and other variations in specific heats with temperature can only be interpreted in terms of quantum dynamics, and the subjection of mechanical processes taking place among gas molecules to quantum principles must be taken into consideration in theories of chemical reaction mechanisms. 

Perhaps a more decisive discrimination between Ising and mean-field behavior could be provided by the investigation of weak anomalies [6] as predicted for the specific heat. Such weak anomalies are absent in the mean-field case (cf. Table I). Except for the diameter anomalies already mentioned, no thermodynamic investigations of weak anomalies were reported so far. However, dynamical properties such as the shear viscosity and electrical conductance may show weak anomalies as well. 

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. 

Considerable evidence exits of the survival of Zintl ions in the liquid alloy. Neutron diffraction measurements [5], as well as molecular dynamics simulations [6, 7], give structure factors and radial distribution functions in agreement with the existence of a superstructure which has many features in common with a disordered network of tetrahedra. Resistivity plots against Pb concentration [8] show sharp maxima at 50% Pb in K-Pb, Rb-Pb and Cs-Pb. However, for Li-Pb and Na-Pb the maximum occurs at 20% Pb, and an additional shoulder appears at 50% Pb for Na-Pb. This means that Zintl ion formation is a well-established process in the K, Rb and Cs cases, whereas in the Li-Pb liquid alloy only Li4Pb units (octet complex) seem to be formed. The Na-Pb alloy is then a transition case, showing coexistence of Na4Pb clusters and (Pb4)4- ions and the predominance of each one of them near the appropiate stoichiometric composition. Measurements of other physical properties like density, specific heat, and thermodynamic stability show similar features (peaks) as a function of composition, and support also the change of stoichiometry from the octet complex to the Zintl clusters between Li-Pb and K-Pb [8]. 

Subsequently, we used Aspen Dynamics for time-domain simulations. A basic control system was implemented with the sole purpose of stabilizing the (open-loop unstable) column dynamics. Specifically, the liquid levels in the reboiler and condenser are controlled using, respectively, the bottoms product flow rate and the distillate flow rate and two proportional controllers, while the total pressure in the column is controlled with the condenser heat duty and a PI controller (Figure 7.4). A controller for product purity was not implemented. 

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