Total Energy Balance

Thermodynamics. The first law of thermodynamics, which states that energy can neither be created nor destroyed, dictates that the total energy entering an industrial plant equals the total of all of the energy that exits. Eeedstock, fuel, and electricity count equally, and a plant should always be able to close its energy balance to within 10%. If the energy balance does not close, there probably is a big opportunity for saving. 

Energy balances differ from mass balances in that the total mass is known but the total energy of a component is difficult to express. Consequently, the heat energy of a material is usually expressed relative to its standard state at a given temperature. For example, the heat content, or enthalpy, of steam is expressed relative to liquid water at 273 K (0°C) at a pressure equal to its own vapor pressure. 

The quantity aAp is defined separately for each type of cooling tower. It depends on many variables jet pressure, jet division, airflow velocity, and others. The total energy balance for a cooling tower is (see Fig. 4.19)... 

Total energies (like heats of formation) may be used to calculated energies of balanced chemical reactions (reactants products) ... 

Using this model in analogy with previous studies we can calculate a magnetic moment (fi) of the system with fixed Stoner exchange parameter Id and occupation of the d states. The total energy could then be calculated as the balance between the kinetic energy and the spin-polarization energy ... 

A dynamic model should be consistent with the steady-state model. Thus, Eqs (1) and (4) should be extended to dynamic form. For the better convergence and computational efficiency, some assumption can be introduced the total amounts of mass and enthalpy at each plate are maintained constant. Then, the internal flow can be determined by total mass balance and total energy balance and the number of differential equations is reduced. Therefore, the dynamic model can be established by replacing component material balance in Eq. (1) with the following equation. 

If a batch process is being considered, or if the rate of energy generation or removal varies with time, it will be necessary to set up a differential energy balance, similar to the differential material balance considered in Chapter 2. For batch processes the total energy requirements can usually be estimated by taking as the time basis for the calculation 1 batch but the maximum rate of heat generation will also have to be estimated to size any heat-transfer equipment needed. 

After all the possibilities of conserving and transferring energy within the process have been considered, the engineer must determine what other energy must be supplied to and removed from the process. This requires a total energy balance for the whole process as well as for the individual units. 

The adiabatic flow of an ideal gas flowing through a frictionless conduit or a constriction (such as an orifice nozzle, or valve) can be analyzed as follows. The total energy balance is... 

The JAEA selects the IS-process to be the basis for commercial development mainly because it is seen more suited to large-scale nuclear hydrogen production than HTE [9] and other alternatives. However, an available HTE-based plant can be connected to the reactor in the same manner as the IS process plant is connected. The HTE similarly requires a high-temperature process heat, and about 25% of its total energy input is heat and the balance electricity, which are fully and efficiently met in-house by the reactor heat and gas turbine power plant. 

To relate the discrete particle simulations to the KTGFs, it is very useful to analyze the detailed information of the energy evolution in the system. The total energy balance of the system is obtained by calculating all relevant forms of energy as well as the work performed due to the action of external forces. 

The amount of heat actually taken up by the particles was an important quantity, as tubes operate under heat transfer limited conditions near the tube inlet. Fig. 30 shows a plot of Q against r, where Q was the total energy flow into the solid particles, for the entire segment. For inlet conditions, Q varied strongly at lower r, but was almost constant at higher values. As rcut/rp decreased from 0.95 to 0.0 and the effectiveness factor increased from nearly zero to one, the active solid volume increased by a factor of 7. If the solid temperature had remained the same, the heat sink would also have had to increase sevenfold. This could not be sustained by the heat transfer rate to the particles, so the particle temperature had to decrease. This reduced the heat sink and increased the driving force for heat transfer until a balance was found, which is represented by the curve for the inlet in Fig. 30. 

A total energy balance is useful for describing the temperature changes within the flowing gas. For this open steady flow process the total energy balance is given by... 

We start with an atom containing N electrons, with a total energy E in the initial state, denoted with the superscript i. The atom absorbs a photon of energy hv, the absorption event taking less than 10 17 s. Some 10 14 s later, the atom has emitted the photoelectron with kinetic energy Ek and is itself in the final state with one electron less and a hole in one of the core levels. The energy balance of the event is... 

The total energy balance from Section 1.2.5 is given by... 

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