Volume-heat

The mass or volume heating value represents the quantity of energy released by a unit mass or volume of fuel during the chemical reaction for complete combustion producing CO2 and H2O. The fuel is taken to be, unless mentioned otherwise, at the liquid state and at a reference temperature, generally 25°C. The air and the combustion products are considered to be at this same temperature. 

Note that in this special case, the heat absorbed directly measures a state fiinction. One still has to consider how this constant-volume heat is measured, perhaps by an electric heater , but then is this not really work Conventionally, however, if work is restricted to pressure-volume work, any remaining contribution to the energy transfers can be called heat . 

However, the discovery in 1962 by Voronel and coworkers [H] that the constant-volume heat capacity of argon showed a weak divergence at the critical point, had a major impact on uniting fluid criticality widi that of other systems. They thought the divergence was logaritlnnic, but it is not quite that weak, satisfying equation (A2.5.21) with an exponent a now known to be about 0.11. The equation applies both above and... 

Magee J W, Blanco J C and Deal R J 1998 High-temperature adiabatic calorimeter for constant-volume heat capacity of compressed gases and liquids J. Res. Natl Inst. Stand. Technol. 103 63... 

For the ideal-gas state there is an exact relation between the constant pressure heat capacity and the constant volume heat capacity, C, via the ideal-gas constant, R. 

Constant volume heat capacities for Hquid organic compounds were estimated with a four parameter fit (219). A 1.3% average absolute error for 31 selected species was reported. A group contribution method for heat capacities of pure soHds andHquids based on elemental composition has also been provided (159). 

Experimental data for Van der Waals volumes Molar volumes Heat capacities Solubility parameter and glass transition temperature... 

Figure 25 ANN model (5-8-6) training and testing results for van der Waals volume, molar volume, heat capacity, solubility parameter, and glass transition temperature of 45 different polymers.

As an example, the molar constant-volume heat capacity of argon is 12.8 J-K 1-mol 1, and so the corresponding constant-pressure value is 12.8 + 8.3... 

Use the estimates of molar constant-volume heat capacities given in the text (as multiples of R) to estimate the change in reaction enthalpy of N2(g) + 3 H,(g) —> 2 NH.(g) when the temperature is increased from 300. K to 500. K. Ignore the vibrational contributions to heat capacity. Is the reaction more or less exothermic at the higher temperature ... 

This is the infinitesimal form of Eq. 5a of Chapter 6, which also applies to reversible changes.) If the change in temperature is carried out at constant volume, we use the constant-volume heat capacity, Cv. If the change is carried out at constant pressure, we... 

V constant volume heat capacity at constant volume, Cv (J-K 1)... 

With the MBR, individual components of multiphase systems can be heated at different rates according to differences in their dielectric properties. We have termed this, differential heating. For example, the aqueous phase of a water/chloroform system (1 1 by volume), heated more rapidly than did the organic layer and a tempera-... 

The heating rate, and hence the rate of pressure increase, also depends on the volume of the reaction mixture [20], When the volume is small, the pressure increases as the volume of the reaction mixture increases. However at a certain volume this trend is reversed and a larger volume heats more slowly. For example when water was heated in a 150-mL Teflon vessel, the greatest rate of pressure increase occurs when 15 mL water are heated using a power of 560 W. The volume at which this maximum heating rate, however, varies for different solvents. For example it occurs at 20 mL for 1-propanol. 

The atomic properties satisfy the necessary physical requirement of paralleling the transferability of their charge distributions - atoms that look the same in two molecules contribute identical amounts to all properties in both molecules, including field-induced properties. Thus the atoms of theory recover the experimentally measurable contributions to the volume, heats of formation, electric polarizability, and magnetic susceptibility in those cases where the group contributions are found to be transferable, as well as additive additive [4], The additivity of the atomic properties coupled with the observation that their transferability parallels the transferability of the atom s physical form are unique to QTAIM and are essential for a theory of atoms in molecules that purports to explain the observations of experimental chemistry. 

This model, the Einstein model for heat capacity, predicts that the heat capacity is reduced on cooling and that the heat capacity becomes zero at 0 K. At high temperatures the constant-volume heat capacity approaches the classical value 3R. The Einstein model represented a substantial improvement compared with the classical models. The experimental heat capacity of copper at constant pressure is compared in Figure 8.3 to Cy m calculated using the Einstein model with 0g = 244 K. The insert to the figure shows the Einstein frequency of Cu. All 3L vibrational modes have the same frequency, v = 32 THz. However, whereas Cy m is observed experimentally to vary proportionally with T3 at low temperatures, the Einstein heat capacity decreases more rapidly it is proportional to exp(0E IT) at low temperatures. In order to reproduce the observed low temperature behaviour qualitatively, one more essential factor must be taken into account the lattice vibrations of each individual atom are not independent of each other - collective lattice vibrations must be considered. 

The experimental constant-pressure heat capacity of copper is given together with the Einstein and Debye constant volume heat capacities in Figure 8.12 (recall that the difference between the heat capacity at constant pressure and constant volume is small at low temperatures). The Einstein and Debye temperatures that give the best representation of the experimental heat capacity are e = 244 K and D = 315 K and schematic representations of the resulting density of vibrational modes in the Einstein and Debye approximations are given in the insert to Figure 8.12. The Debye model clearly represents the low-temperature behaviour better than the Einstein model. 

The heat capacity models described so far were all based on a harmonic oscillator approximation. This implies that the volume of the simple crystals considered does not vary with temperature and Cy m is derived as a function of temperature for a crystal having a fixed volume. Anharmonic lattice vibrations give rise to a finite isobaric thermal expansivity. These vibrations contribute both directly and indirectly to the total heat capacity directly since the anharmonic vibrations themselves contribute, and indirectly since the volume of a real crystal increases with increasing temperature, changing all frequencies. The constant volume heat capacity derived from experimental heat capacity data is different from that for a fixed volume. The difference in heat capacity at constant volume for a crystal that is allowed to relax at each temperature and the heat capacity at constant volume for a crystal where the volume is fixed to correspond to that at the Debye temperature represents a considerable part of Cp m - Cv m. This is shown for Mo and W [6] in Figure 8.15. 

Constant conduction heat pipes, 13 227 Constant failure rate, 13 167 Constant-field scaling, of FETs, 22 253, 254 Constant-modulus alloys, 17 101 Constant of proportionality, 14 237 Constant pressure heat capacity, 24 656 Constant rate drying, 9 103-105 Constant rate period, 9 97 23 66-67 Constant retard ratio (CRR) mode, 24 103 Constant slope condition, 24 136-137 Constant stress test, 13 472 19 583 Constant-voltage scaling, of FETs, 22 253 Constant volume heat capacity, 24 656 Constant volume sampling system (CVS), 10 33... 

Results in Table I illustrate some of the strengths and weaknesses of the ST2, MCY and CF models. All models, except the MCY model, accurately predict the internal energy, -U. Constant volume heat capacity, Cv, is accurately predicted by each model for which data is available. The ST2 and MCY models overpredict the dipole moment, u, while the CF model prediction is identical with the value for bulk water. The ratio PV/NkT at a liquid density of unity is tremendously in error for the MCY model, while both the ST2 and CF models predictions are reasonable. This large error using the MCY model suggests that it will not, in general, simulate thermodynamic properties of water accurately (29). Values of the self-diffusion coefficient, D, for each of the water models except the CF model agree fairly well with the value for bulk water. 

Abstract Isotope effects on the PVT properties of non-ideal gases and isotope effects on condensed phase physical properties such as vapor pressure, molar volume, heats of vaporization or solution, solubility, etc., are treated in some thermodynamic detail. Both pure component and mixture properties are considered. Numerous examples of condensed phase isotope effects are employed to illustrate theoretical and practical points of interest. 

Physically, Eq. (7.63) specifies that for a spark to lead to ignition of an exoergic system, the corresponding equivalent heat input radius must be several times the characteristic width of the laminar flame zone. Under this condition, the nearby layers of the initially ignited combustible material will further ignite before the volume heated by the spark cools. 

By modifying the procedure described above to explode a wire in the water sphere while the system was under compression, they did attain explosions. Measuring the rebound of the cylinder and the loss of aluminum, they could estimate the work produced by the event. Assuming the maximum energy transfer to the water would occur by constant volume heating to the aluminum temperature, foUowed by an isothermal, reversible expansion, they estimated an efficiency of about 25%. Clearly the exploding wire led to an immediate and effective dispersal of the water. 

For the moment, we can consider the activated complex as a type of intermediate (although not isolatable) reached by the reactants as the highest energy point of the most favorable reaction path. The activated complex is in equilibrium with the reactants and is commonly regarded as an ordinary molecule, except that movement along the reaction coordinate will lead to decomposition. The activated complex can be assumed to have the associated properties of molecules, such as volume, heat content, acid-base behavior, entropy, and so forth. Indeed, formal calculations of equilibrium constants involving reactions of the activated complex to form another activated complex can be carried out (Sec. 5.6 (b)). ... 

We now distinguish solid state transformations as first-order transitions or lambda transitions. The latter class groups all high-order solid state transformations (second-, third-, and fourth-order transformations see Denbigh, 1971 for exhaustive treatment). We define first-order transitions as all solid state transformations that involve discontinuities in enthalpy, entropy, volume, heat capacity, compressibility, and thermal expansion at the transition point. These transitions require substantial modifications in atomic bonding. An example of first-order transition is the solid state transformation (see also figure 2.6)... 

The constant-volume heat capacity of the substance ( Cy) represents the variation of total energy U with T in the harmonic approximation (X is constant over T), and the integration of Cy over T gives the (harmonic) entropy of the substance ... 

During the isothermal compression process 1-2, heat is rejected to maintain a constant temperature Tl. During the isothermal expansion process 3-4, heat is added to maintain a constant temperature Th- There are also heat interactions along the constant-volume heat addition process 2-3 and the constant-volume heat removal process 4-1. The quantities of heat in these two constant-volume processes are equal but opposite in direction. 

A proposed air standard piston ylinder arrangement cycle consists of an isentropic compression process, a constant-volume heat addition process, an isentropic expansion process, and a constant-pressure heat-rejection process. The compression ratio (V1/V2) during the isentropic compression process is 8.5. At the beginning of the compression process, P=100kPa and r=300 K. The constant-volume specific heat addition is 1400kJ/kg. Assume constant specific heats at 25°C. 

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