Mass-Energy Calculations

The change in mass gives the change in internal energy, AL/. The enthalpy change, AH, equals AU + PAV. For the reaction given in the text, PAV is essentially zero. 

The meaning of this equation is that to any mass there is an associated energy, or to any energy there is an associated mass. If a system loses energy, it must also lose mass. Eor example, when carbon bums in oxygen, it releases heat energy. 

Calculation of the mass change for a typical chemical reaction, the burning of carbon in oxygen, will show just how small this quantity is. When the energy changes by an amount AE, the mass changes by an amount Am. You can write Einstein s equation in the form 

The change in energy when 1 mol of carbon reacts is 10 kg m /s. Hence, 

Eor comparison, a good analjdical balance can detect a mass as small as 1 X lO- kg, but this is ten thousand times greater than the mass change caused by the release of heat during the combustion of 1 mol of carbon. 

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A particular nuclide is made from the combination of Z protons and (A- Z) neutrons. Thus, a neutral atom of a specific isotope contains Z protons, Z electrons, and (A- Z) neutrons. When these particles are brought together, a small amount of mass is converted to energy. To calculate that energy, first count protons, neutrons, and electrons, and then do a mass-energy calculation using Equation. ... 

Our next step is to write the material balances and calculate the composition and quantity of flue gas. Unless there is a conversion between mass and energy, calculations such as these can be handled on a mass basis. We shall make this assumption, and also note that there is no accumulation. 

From the binding energies calculated for the different cluster compositions, we determined abundance mass spectra for heated CggLi clusters from a simple Monte Carlo simulation. Figure 11 shows the simulated mass spectra resulting from these calculations, including the Li and Cgo isotope distributions. The peaks at A = 12 and at x = 6 + n (where n is the cluster charge) observed in the experiment (Fig. 9) are well reproduced. For more details, see ref. [12]. 

If the explosion occurs in an unconfined vapor cloud, the energy in the blast wave is only a small fraction of the energy calculated as the product of the cloud mass and the heat of combustion of the cloud material. On this basis, explosion efficiencies are typically in the range of 1-10%. 

Use of the Born-Oppenheimer approximation is implicit for any many-body problem involving electrons and nuclei as it allows us to separate electronic and nuclear coordinates in many-body wave function. Because of the large difference between electronic and ionic masses, the nuclei can be treated as an adiabatic background for instantaneous motion of electrons. So with this adiabatic approximation the many-body problem is reduced to the solution of the dynamics of the electrons in some frozen-in configuration of the nuclei. However, the total energy calculations are still impossible without making further simplifications and approximations. 

The most probable speeds of methane and carbon dioxide are slower than the most probable speed of hydrogen, but CH4 and CO2 molecules have larger masses than H2. When kinetic energy calculations are repeated for these gases, they show that the most probable kinetic energy is the same for all three gases. 

X 10 J of energy or by emission of positrons with 1.04 X 10 J of energy, (a) Write the two decay reactions, (b) Calculate the molar masses of the two elemental products using mass-energy equivalence. 

Each atom of a molecule that rotates about an axis through its centre of mass, describes a circular orbit. The total rotational energy must therefore be a function of the molecular moment of inertia about the rotation axis and the angular momentum. The energy calculation for a complex molecule is of the same type as the calculation for a single particle moving at constant (zero) potential on a ring. 

When 1 mol of U-238 decays to Th-234, 5 X 10 kg of matter is converted to energy (the mass defect). Calculate the amount of energy released. 

The numerical jet model [9-11] is based on the numerical solution of the time-dependent, compressible flow conservation equations for total mass, energy, momentum, and chemical species number densities, with appropriate in-flow/outfiow open-boundary conditions and an ideal gas equation of state. In the reactive simulations, multispecies temperature-dependent diffusion and thermal conduction processes [11, 12] are calculated explicitly using central difference approximations and coupled to chemical kinetics and convection using timestep-splitting techniques [13]. Global models for hydrogen [14] and propane chemistry [15] have been used in the 3D, time-dependent reactive jet simulations. Extensive comparisons with laboratory experiments have been reported for non-reactive jets [9, 16] validation of the reactive/diffusive models is discussed in [14]. 

B. By applying the conservation equations (mass, energy) and the data from A, calculate the concentration as a function of time and position in the adsorption apparatus. 

Within the approximation of the effective mass, consideration of the field created by the condensed media is confined to substitution of the real electron mass by the effective mass. Precise calculation of the effective mass is equivalent to solution of the Schrodinger equation with the consideration of the field created by the medium, and, consequently, as noted before, is hardly possible. Thus, as far as the problem of electron tunneling is concerned, the effective mass must be considered as a phenomenological parameter. In the case of tunneling with the energy I of the order of 1-5 eV, the field created by the medium apparently increases considerably the probability of electron tunneling, and the effective mass of electron can be noticeably lower than the real mass. 

To assess the efficiency of the reactions listed in Table 7.2, Bolton et al. (1996) proposed a generally applicable standard for a given photochemical process. The proposed standard provides a direct link to the electrical efficiency. In this model, electrical energy per unit mass is calculated according to the quantum yield of the direct photolysis rate. Braun et al. (1997) calculated the quantum yield (O) according to Equation (7.13) ... 

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