Balance principle

Heating and cooling load calculation for HVAC system design is based on the heat balance principle. For the given building, room, or independent building zone, heat balance components should be established and analyzed. The ma or heat sources and sinks in industrial buildings are ... 

Thus this operator must satisfy the necessary demands of the particle conservation law and detailed balance principle as was the case for its simpler analogue in Eq. (4.23) and Eq. (4.24). They are... 

Being applied for the relaxation of populations (k = 0), this equality expresses the demands of the detailed balance principle. This is simply a generalization of Eq. (4.25), which establishes the well-known relation between rates of excitation and deactivation for the rotational spectrum. It is much more important that equality (5.21) holds not only for k = 0 but also for k = 1 when it deals with relaxation of angular momentum J and the elements should not be attributed any obvious physical sense. The non-triviality of this generalization is emphasized by the fact that it is impossible to extend it to the elements of the four-index... 

Here a and b are considered as fitting parameters depending on temperature. De-excitation rate constants (s < 0) are obtained from the detailed balance principle. AH fitting laws differ in the pre-exponential factor in Eq. (5.70). In the PEG model... 

Debye phenomenon and theory 59-60, 198 dense media see orientational relaxation in dense media orientational diffusion 70 Debye plateau 6, 73, 81 dephasing see adiabatic dephasing detailed balance principle, spectral collapse 137... 

In this section the application of the total mass balance principles is presented. Consider some arbitrary balance region, as shown in Fig. 1.14 by the shaded area. Mass accumulates within the system at a rate dM/dt, owing to the competing effects of a convective flow input (mass flow rate in) and an output stream (mass flow rate out). 

If the probability for the system to jump to the upper PES is small, the reaction is an adiabatic one. The advantage of the adiabatic approach consists in the fact that its application does not lead to difficulties of fundamental character, e.g., to those related to the detailed balance principle. The activation factor is determined here by the energy (or, to be more precise, by the free energy) corresponding to the top of the potential barrier, and the transmission coefficient, k, characterizing the probability of the rearrangement of the electron state is determined by the minimum separation AE of the lower and upper PES. The quantity AE is the same for the forward and reverse transitions. 

Equation (47) shows that in the Condon approximation the probabilities of forward and reverse transitions satisfy the detailed balance principle since the point q corresponds to the intersection of the potential energy surfaces (and free energy surfaces) where Haa = Hbb. Therefore, at the point q we have... 

Three different principles govern the design of bench-scale calorimetric units heat flow, heat balance, and power consumption. The RC1 [184], for example, is based on the heat-flow principle, by measuring the temperature difference between the reaction mixture and the heat transfer fluid in the reactor jacket. In order to determine the heat release rate, the heat transfer coefficient and area must be known. The Contalab [185], as originally marketed by Contraves, is based on the heat balance principle, by measuring the difference between the temperature of the heat transfer fluid at the jacket inlet and the outlet. Knowledge of the characteristics of the heat transfer fluid, such as mass flow rates and the specific heat, is required. ThermoMetric instruments, such as the CPA [188], are designed on the power compensation principle (i.e., the supply or removal of heat to or from the reactor vessel to maintain reactor contents at a prescribed temperature is measured). 

The Contalab, initially supplied by Contraves, was purchased by Mettler-Toledo, which is now placing less emphasis on this design than on the RC1. Some comments here are appropriate, however, since it is another type of bench-scale calorimeter, and units continue to be used. Its measuring system is based on the heat balance principle, in which a heat balance is applied over the cooling/heating medium. For this purpose, both the flow rate of the coolant and its inlet and outlet temperatures must be known accurately. Figure 3.12 is a schematic plan of the Contalab. 

The major advantage of this type of calorimeter is that the heat balance principle can easily be applied to the reflux condenser as well, which enables a simpler investigation of processes under reflux conditions. Another advantage is its independence of the heat transfer coefficient at the reactor wall. 

Subsequently, analytical expressions for the time dependence concentration of all components in the system were obtained based on mass balance principles and also considering the reactor type, the flow rates of the feed streams, and the concentrations of substrates. Using these models we found that the basic system considered is able to perform several informationprocessing functions, such as division, rectification, and switching. 

Fig. 14.9 Mass balance principle and stable burning point in a rocket motor.

Detailed Balancing, Principle of Chemical Reaction Chemical Kinetics... 

A typical DP cell is shown in Fig. 6.19a<23). The associated flapper/nozzle system works on a force-balance principle (see Volume 1, Section 6.2.3). The output pressure P0 is linearly related to the difference in pressure (P, - P2), thus ... 

The calorimeter that has been used to obtain the results presented in this section basically combines the power-compensation and heat-balance principles (see Sections 8.2.2.2 and 8.2.2.3). The heat-balance principle is implemented by Peltier elements [18]. This new... 

A simple approximation of the thermoforming process is based on a mass balance principle. To illustrate this concept, let us consider the thermoforming process of a conical object, as schematically depicted in Fig. 6.25. 

Abstract We formulate the balance principles for an immiscible mixture of continua with micro structure in the broadest sense for include, e.g., phenomena of diffusion, adsorption and chemical reactions. After we consider the flow of a fluid/adsorbate mixture through big pores of an elastic solid skeleton and propose suitable constitutive equations to study the coupling of adsorption and diffusion under isothermal conditions. 

We propose the balance principles for an immiscible mixture of continua with microstructure in presence of phenomena of chemical reactions, adsorption and diffusion by generalizing previous multiphase mixture [9] and use a new formulation for the balance of rotational momentum. New terms are also included in the energy equations corresponding to work done by respective terms in the micromomentum balances. 

The adsorption rate constant kaAs is calculated using kAes given by Eq. (28) and the detailed balancing principle. 

This is because the dissociation products diffusing in the liquid cage can come in contact again and again, restoring the exciplex so that the rate of their final separation is given by Eq. (3.83). The ratio of k to k as well as kf to Wb fits the detailed balance principle for the reversible reaction (3.81) ... 

The rates of the forward and backward transfers with the free-energy excess AG relate to each other according to the detailed balance principle ... 

On the other hand, in a genuine DSC instrument, sample and reference are each heated individually. A null balance principle is employed, whereby any change in the heat flow in the sample, (e.g. due to a phase change) is compensated for in the reference. The result is that the temperature of the sample is maintained at that of the reference by changing the heat flow. The signal which is recorded (dH/dt) (the heat flow as a function of time (temperature)), is actually proportional to the difference between the heat input into the two channels as a function of time (temperature). 

At thermodynamic equilibrium, Ttj must vanish for every reaction otherwise, the equilibrium could be shifted by adding catalysts or inhibitors to alter the nonzero rates TZj. Formal proofs of this "detailed balance principle are presented by de Groot and Mazur (1962). Therefore, setting 7 = 0 at equilibrium and using Eq. (2.4-3), we get... 

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